PhD Dissertation Computer Aided Breast Cancer Risk Breast Parenchyma in Mammography

PhD Dissertation Computer Aided Breast Cancer Risk Breast Parenchyma in Mammography
FACULTY OF SCIENCE
UNIVERSITY OF COPENHAGEN
PhD Dissertation
Gopal Karemore
Computer Aided Breast Cancer Risk
Assessment using Shape and Texture of
Breast Parenchyma in Mammography
Supervisor: Mads Nielsen,PhD
Co-Supervisor: Sami Brandt,PhD
Submitted: 02/01/2012
Preface
This constitutes Gopal Karemore’s Ph.D. dissertation. This dissertation is submitted at
University of Copenhagen in partial fulfillment of the requirements for the degree of
doctor of philosophy.
The work behind this dissertation was delivered in the period from March 2008 to
November 2011 under the supervision of professor Mads Nielsen and co-supervision
of Sami Brandt from University of Copenhagen,Denmark. The work was carried out at
Nordic Bioscience A/S between 2008-2010. At the end of 2010, the project was moved
to Synarc Research Labs followed by BiomedIQ A/S. Some of the time during PhD was
spent at Siemens Corporate research Labs, Princeton, USA and University of Pennsylvania, Philadelphia, USA under the internship program of duration three months
each.
The primary goal of this dissertation is to investigate the potential of mammographic
parenchymal texture as an imaging biomarker of (i) General risk of developing breast
cancer, (ii) Effect specific drugs involving various HRT treatments, and (iii) Estrogen
Receptor sub type specific risk. Such identification leads to better allocation of screening
resources and thereby earlier cancer detections and lower mortality rates.
Front page: Discovery of mammographic pattern that show early changes due to
development of breast cancer: A preliminary work. taken from (Karemore et al, RSNA 2011,
Chicago, USA) and discussed in Chapter 6.
The author of this dissertation can currently be contacted at:
Gopal Karemore
DIKU
Universitetsparken 1
2100 Copenhagen
Denmark
Mobile: +45 50194001
Email: [email protected]
Dedicated to my parents Aai, Baba and those whose life have been affected
directly/indirectly by Breast Cancer; in hopes of its earlier
detection,cure and prevention
Abstract
The fundamental goal of this dissertation is to investigate the potential of mammographic
parenchymal texture as an imaging biomarker of (i) General risk of developing breast cancer,
(ii) Effect specific drugs involving various HRT treatments, and (iii) Estrogen Receptor sub type
specific risk.
In first part of the work, the significance of mammographic parenchymal texture in general
risk assessment is introduced and existing approaches are surveyed. An accurate and consistent
mammographic texture resemblance (MTR) marker is developed and evaluated on various public/private datasets. Texture features based on multiscale such as Fractals, Structure Tensors,
and Gaussian Derivatives (n-jet) are studied.
Second part is focused on improving the performance of MTR by developing an anatomically
oriented breast coordinate system. Its potentials are investigated by comparing its performance on
existing mammogram registration techniques in longitudinal study. In this part we also introduce
the committee based machine learning approach that shows the improvement in classification
accuracy.
In third part, we introduce a nested cross-validation framework that automatically selects
the inner and outer scale of probability map of post processed mammogram in breast coordinate
system. This will help to understand and investigate the region on mammogram that experiences
the maximum effect of carcinogenesis in parenchymal tissue structure during the development of
breast cancer in case-control study design.
Forth part aimed at qualifying the MTR marker as an effect specific measure in clinical trials
involving various HRT treatments. Here we study the coherence properties of structure tensor
and structure enhancing diffusion that will help radiologist in visualizing the structural pattern
change in one-to-one correspondence between temporal mammograms of populations with placebo
and HRT treatment populations.
In last part, we investigate the potential of MTR as a surrogate marker of risk to develop
Estrogen Receptor subtype-specific breast cancer, compared to standard mammographic density
measures. There by to establish a non-invasive biomarker during screening process to identify
woman who would benefit most from SERM (selective Estrogen Receptor Modulators) Chemoprevention.
Conclusively, the whole intension of this dissertation is to help in identifying the woman
who has higher risk of developing general/subtype specific breast cancer, based on fully automatic
mammographic parenchymal texture marker in screening mammograms. Such identification
leads to better allocation of screening resources and thereby earlier cancer detections and lower
mortality/unnecessary biopsy rate.
Contents
1
2
Introduction, Background and Motivation
1.1 What is Breast Cancer? . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 How It Develops and What Are Their Types? . . . . . . . . . . . . . . .
1.3 What Factors Increase a Woman’s Risk of Breast Cancer? . . . . . . . .
1.4 What Protective Factors May Decrease the Risk of Breast Cancer? . . .
1.5 Why to Assess Breast Cancer Risk? . . . . . . . . . . . . . . . . . . . . .
1.6 How to Assess Breast Cancer risk? . . . . . . . . . . . . . . . . . . . . .
1.6.1 Average Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6.2 Epidemiologic Risk Factors . . . . . . . . . . . . . . . . . . . . .
1.6.3 Risk-Prediction Models . . . . . . . . . . . . . . . . . . . . . . .
1.6.4 Breast Cancer Screening: Screening Mammogram . . . . . . . .
1.7 Mammographic Parenchymal Characteristics and its Relation to Risk?
1.7.1 Mammographic Density and Risk . . . . . . . . . . . . . . . . .
1.8 Potential of Parenchymal Texture Techniques: A Motivation . . . . . .
1.9 What is the purpose of this PhD dissertation? . . . . . . . . . . . . . . .
1.9.1 Clinical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . .
1.9.2 Technical Perspective . . . . . . . . . . . . . . . . . . . . . . . . .
1.10 Background of PhD Project . . . . . . . . . . . . . . . . . . . . . . . . .
1.11 Overview of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Mammographic Parenchymal Texture Techniques in Application to Breast Cancer Risk Assessment: A Review
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Mammographic Parenchymal Texture Techniques . . . . . . . . . . . . . .
2.3 Statistical Based Texture Techniques . . . . . . . . . . . . . . . . . . . . . .
2.3.1 1st and 2nd order statistics . . . . . . . . . . . . . . . . . . . . . . .
2.4 Spatial-Statistical Texture Techniques . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Laws Texture Measure . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Fractal Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Fourier Based Texture Features . . . . . . . . . . . . . . . . . . . . .
2.4.4 Gabor and Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.5 Scale-Space Textures . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
11
11
11
12
13
13
14
14
14
14
15
17
17
18
21
21
21
22
23
28
29
31
32
32
34
34
35
36
37
38
39
2.6
2.7
3
4
5
2.5.1 Preprocessing . . . . . . . . . . . .
2.5.2 Texture Measurement within CTR
2.5.3 Feature Classification and Scoring
Results and Discussion . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Fractal Dimension and Lacunarity Analysis of Mammographic Patterns in Assessing Breast Cancer Risk : A Longitudinal and Cross-sectional Study
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Estimation of Fractal Dimension (DB ) . . . . . . . . . . . . . . . . .
3.2.2 Estimation of Lacunarity (λ) . . . . . . . . . . . . . . . . . . . . . .
3.3 Result and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Novel and Automatic Mammographic Texture Resemblance Marker (MTR)
is an Independent Risk Factor for Breast Cancer
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Study population . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Radiologist’s percentage density score (R) . . . . . . . . . . . . . . .
4.2.3 Computer-based percentage density scores (P) . . . . . . . . . . . .
4.3 Breast cancer risk mammographic texture resemblance marker (H) . . . .
4.3.1 Hormone replacement treatment mammographic texture resemblance marker (E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Aggregate mammographic marker (A) . . . . . . . . . . . . . . . .
4.4 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
An Anatomically Oriented Breast Coordinate System for Mammogram Analysis
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Construction of the Breast Coordinate System . . . . . . . . . . . . . . . . .
5.3 Numerical Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Forward Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Inverse Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Jacobians of the Transforms . . . . . . . . . . . . . . . . . . . . . . .
5.4 Gaussian Derivatives in the Breast Coordinates . . . . . . . . . . . . . . . .
5.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Mammogram Registration . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Breast Cancer Risk Assessment . . . . . . . . . . . . . . . . . . . . .
39
40
43
44
45
50
51
52
52
55
56
57
60
61
62
62
62
62
63
65
65
65
66
67
73
74
75
77
80
80
81
82
82
84
84
90
5.6
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6
A Framework to Determine Mammographic Regions that Show Early Changes
Due to Development of Breast Cancer: An Application in Risk Assessment
99
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.2.1 A Case-Control Study . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.3 Computation of Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3.1 Registering All Mammograms in an Anatomically Oriented Breast
Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3.2 Feature Sampling in a Breast Coordinate System . . . . . . . . . . . 104
6.3.3 Parenchymal Texture Features and Scoring . . . . . . . . . . . . . . 105
6.4 Learning of the Relevant Regions . . . . . . . . . . . . . . . . . . . . . . . . 106
6.4.1 Bucket Representation . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.4.2 Nested Cross-Validation (Optimizing Scale and Threshold) . . . . . 107
6.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.5.1 Nijemengen Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.5.2 mini-MIAS dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.5.3 DDSM Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.5.4 Longitudinal Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.6 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7
Quantitative Imaging and Visualization Through Structure Enhancing Diffusion Applied to Longitudinal Study Involving Hormone Replacement Therapy
(HRT)
122
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.2 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.3.1 Construction of Breast Coordinate System . . . . . . . . . . . . . . 124
7.4 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.4.1 Structure Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.4.2 Structure Tensor Construction within Breast Coordinate System . . 126
7.4.3 Structure Enhancing Diffusion . . . . . . . . . . . . . . . . . . . . . 127
7.4.4 Curvature Anisotropic Diffusion . . . . . . . . . . . . . . . . . . . . 127
7.5 Pixel Based Classification by k-NN . . . . . . . . . . . . . . . . . . . . . . . 128
7.6 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
8
Estrogen-Receptor Subtype Specific Breast Cancer Risk Estimation
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3 Method: Texture Feature Extraction . . . . . . . . . . . . . . . .
8.4 Feature Classification and Scoring . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
136
138
138
140
142
8.5
8.6
8.7
8.8
9
Estimation of PD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experiments: General Risk and ER-Subtype Specific Risk Estimation . .
8.6.1 Result: Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.6.2 Result: Processed Data . . . . . . . . . . . . . . . . . . . . . . . . .
Experiments: ER-subtype specific risk and Hormone Replacement Therapy (HRT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusions
9.1 Summary . . . . . . . . . . . .
9.2 Discussion . . . . . . . . . . .
9.3 Future Work and Implications
9.4 Conclusion . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
144
145
145
146
. 147
. 149
.
.
.
.
154
154
156
158
159
10 List of Publications
161
11 Acknowledgement
165
12 Disclosure
167
List of Figures
1.1
1.2
1.3
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
During mammography, a special low-dose X-ray machine is used to produce images of the breast. In many instances, these images can detect
breast cancers in a very early stage when they are still too small to be felt
during a physical examination. Courtesy:Wendolyn Hill . . . . . . . . . . . 16
The block diagram explaining the different factors influencing parenchymal change that results in breast carcinogenesis: A motivation behind this
dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Figure illustrating the need of more accurate image coordinate system
to capture the mammographic parenchymal tissue orientation than the
conventional Cartesian image coordinates. Courtesy: Images are taken
from Yale University School of Medicine . . . . . . . . . . . . . . . . . . . . 20
Wolfe’s classification of Parenchymal Patterns. N1 = Minimal risk. P1
= Moderate risk. P2 = Significant risk. DY = Highest risk. Courtesy:
Xeroradiographs, taken from Wolfe’s original research article published
in 1976 [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Breast density patterns. BI-RADS I = fatty breast ( <25% dense). BI-RADS
II = scattered densities (25 %-50% dense). BI-RADS III = heterogeneously
dense (51%-75% dense). BI-RADS IV = extremely dense (>75% dense).
BI-RADS = Breast Imaging Reporting Data System. (Courtesy: Journal of
National Cancer Institute,2009) . . . . . . . . . . . . . . . . . . . . . . . .
Various CAD application in mammography where texture techniques
have been used by many researchers . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Constant Thickness Region (CTR) near nipple-areolar region of mammogram with different size of window is taken into consideration for texture
feature analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Area under the ROC curve (Az) values of various texture features applied
on mini-MIAS dataset for a particular fold with respect to the various size
of ROI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Receiver Operative Curve Characteristics of various texture features applied on mini-MIAS dataset for a particular fold of cross validation . . .
5
. 29
. 30
. 31
. 40
. 41
. 42
. 45
. 46
2.9
Area under the ROC curve (Az) values of various texture features applied
on DDSM dataset for a perticular fold with respect to the various size of
ROI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.10 Receiver Operative Curve Characteristics of various texture features applied on DDSM dataset for a perticular fold of crossvalidation . . . . . . . 48
3.1
3.2
3.3
3.4
3.5
3.6
3.7
4.1
4.2
4.3
5.1
5.2
5.3
Example ROIs extracted from Cross-sectional study set: (a-d) Cancer
Cases, (e-h) Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Example of ROIs extracted from Longitudinal study (Placebo populations)
Example of ROIs extracted from longitudinal study (HRT populations) . .
(a) Selection of Constant Thickness Region (CTR) near nipple-areolar region of mammogram as a region of interest ROI, (b-d) Change in grid
caliber with decreasing box size, the area sampled by any box changed
and hence did the count. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Regression plot to calculate DB . . . . . . . . . . . . . . . . . . . . . . . . .
Regression plot to calculate λ . . . . . . . . . . . . . . . . . . . . . . . . . .
Shows longitudinal progression of different measures. Vertical bar indicate the standard deviation of the mean of the subgroups at 0 and at
2 years. Fractal Dimension (FD) decreases from baseline to follow up
in HRT population and invariant in Placebo while Lacunarity does not
change in both placebo and HRT population. . . . . . . . . . . . . . . . . .
52
53
53
54
55
56
58
Scoring of various breasts as depicted in mammograms (top) using BCPMTR scoring methodology sketched above . . . . . . . . . . . . . . . . . . 68
Normalised scores (Z statistics) of the cancer cases group, significance
of difference from the control group, and significant difference between
scores (* p <0.05, ** p <0.01, *** p <0.001) . . . . . . . . . . . . . . . . . . . 69
Scatter plot between computer-based percent density (P) and proposed
BCP-MTR method (H) stratified by cancer cases and control group . . . . 70
5.7
5.8
Illustration of the breast coordinate system . . . . . . . . . . . . . . . . .
The breast coordinate mapping can be used, for instance, in registering .
The mapping from the Cartesian system to this coordinate system is the
2D similarity transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gradient orientation histogram, on three different scales, plotted in an
arbitrary reference mammogram to which the other mammograms are
aligned by the breast coordinate transform . . . . . . . . . . . . . . . . .
Entropy of the gradient-weighted orientation histogram . . . . . . . . .
Histograms of the selected features, for the mammograms classified into
cancer and control groups, using the expert committee . . . . . . . . . .
Mean AUC scores in the function of the committee member . . . . . . .
Mean ROC curvesand their 95% confidence intervals . . . . . . . . . . .
6.1
Construction of breast coordinate system . . . . . . . . . . . . . . . . . . . 104
5.4
5.5
5.6
. 78
. 85
. 87
. 88
. 89
. 93
. 95
. 96
6.2
6.3
6.4
6.5
6.6
6.7
6.8
7.1
7.2
7.3
7.4
7.5
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
Points mapped onto the parameter space that illustrates the nonlinearity
of the coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Score map representing the cancer probabilities (likelihood) illustrated in
the mean coordinate frame . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figures showing the mask created by selected buckets of varying size
(1,2,4,8,16, and 32)on a typical mammogram . . . . . . . . . . . . . . . .
Figure showing the masks created by buckets of size 4 on a typical mammogram score map with respect to varying threshold of area under ROC
Flow diagram of steps involved in a particular iteration of a nested crossvalidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Union of all masks obtained in individual iteration of cross validation
forms estimated weight map with probabilities of important region of
maximum separation between cancer and control within breast region in
MLO view of mammograms; (b) Anatomical locations on the breast in
MLO view of mammograms . . . . . . . . . . . . . . . . . . . . . . . . . .
(a)Training and test performance over each iterations of cross validation;
(b) Performance using previously published uniform random sampling
and proposed importance sampling on 145-145 test set sampled with
various number points with error barsa . . . . . . . . . . . . . . . . . . .
. 105
. 108
. 109
. 110
. 113
. 115
. 116
Division of parametric space s, φ into 24 different sub regions considering
the uniform distributions of samples (pixel locations) in each region . . . . 125
Placebo: Baseline and Follow-up mammograms and their corresponding
structure tensor field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Placebo: Difference field of structure tensor between Follow-up and Baseline131
HRT: Baseline and Follow-up mammograms and their corresponding
structure tensor field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
HRT: Difference field of structure tensor between Follow-up and Baseline 133
Demographics of cancer cases stratified by ER positive and ER negative
receptor status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a-d) Arbitrary 3-jet features at four different scale, (e-h) Arbitrary Coherence feature map of structure tensor at four different scale . . . . . . . .
Block diagram of mammogram scoring methodology . . . . . . . . . . .
Feature sampling within various region of breast . . . . . . . . . . . . . .
A mammogram with a segmented breast quantified as dense tissue by
our fully automated software[2] . . . . . . . . . . . . . . . . . . . . . . . .
Area Under ROC Performance . . . . . . . . . . . . . . . . . . . . . . . .
Scatter plot between Texture scores and Percent Density in dataset with
raw images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cummulative distribution plot of intensities before and after Z-score normalization in processed data population . . . . . . . . . . . . . . . . . . .
Area Under ROC Performance . . . . . . . . . . . . . . . . . . . . . . . .
. 139
. 142
. 143
. 144
. 144
. 146
. 147
. 148
. 149
8.10 Scatter plot between Texture scores and Percent Density in dataset with
processed images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
9.1
The block diagram explaining the different factors influencing parenchymal change that results in breast carcinogenesis: A motivation behind this
dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
List of Tables
2.1
2.2
2.3
2.4
3.1
3.2
3.3
4.1
4.2
4.3
Performance characteristics of various Texture features on mini-MIAS
dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spearman correlation coefficients for strongest validated texture feature
in mini-MIAS dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Performance characteristics of various Texture features on on DDSM dataset
Spearman correlation coefficients for strongest validated texture feature
in DDSM dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
47
48
49
Characteristics of the Cross sectional study populations stratified by Cancer cases and Control group . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Different scorings of mammograms in placebo and HRT groups at baseline
and after 2 years of hormone treatment (Longitudinal study) . . . . . . . . 59
Spearman correlation coefficients and p values of being different from
zero in baseline study of the combined population of the placebo and
HRT treated groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Ordering of 3-jet features . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mammographic scorings according to patient stratification . . . . . . . .
Odds ratio compared to lowest quartile (Q1) age-adjusted and age,density
(C)- adjusted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Area under ROC (AUC) according to patient stratification . . . . . . . .
Correlation between the mammographic markers . . . . . . . . . . . . .
. 63
. 67
. 84
. 90
. 91
5.5
Mean intensity correlation over the longitudinal study. . . . . . . . . . .
Evaluation of Longitudinal Registration . . . . . . . . . . . . . . . . . . .
Characteristics and scores of the cross-sectional study . . . . . . . . . . .
The four coordinate systems in terms of how they define the position and
orientation correspondence. . . . . . . . . . . . . . . . . . . . . . . . . . .
Classification scores for the cross-sectional study . . . . . . . . . . . . . .
. 91
. 94
6.1
6.2
6.3
6.4
Effect of importance sampling on test set of Nijmegen study
Effect of importance sampling on mini-MIAS dataset . . . .
Effect of importance sampling on DDSM dataset . . . . . . .
Effect of importance sampling on longitudinal HRT study .
.
.
.
.
4.4
4.5
5.1
5.2
5.3
5.4
9
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. 67
. 71
. 71
114
117
117
118
7.1
Performance characteristics of various texture measures in comparison to
breast density measures in longitudinal study stratified by populations
undergoing HRT treatment (H) and placebo (P) with a duration from
0(Baseline) to 2years(Follow-up) . . . . . . . . . . . . . . . . . . . . . . . . 134
8.1
8.2
List of jet features up to third order expressed in x-y coordinates. . . . .
Pearson Correlations of density with texture measures with raw images
in the Cancer cases Vs Control discrimination experiments . . . . . . . .
Pearson Correlations of density with texture measures with raw images
in the ER + Vs ER - cases discrimination experiments . . . . . . . . . . .
Pearson Correlations of density with texture measures with processed
images after Z-score normalization in the Cancer cases Vs Control discrimination experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pearson Correlations of density with texture measures with processed images after Z-score normalization in the ER + Vs ER - cases discrimination
experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Performance of Texture measure on self ER-subtype specific data using
leave-2-out cross validation . . . . . . . . . . . . . . . . . . . . . . . . . .
Demographics of Texture measure trained for ER-subtype specific discrimination on longitudinal study evolving placebo and HRT groups at
baseline and after 2 years of hormone treatment . . . . . . . . . . . . . .
8.3
8.4
8.5
8.6
8.7
. 140
. 146
. 147
. 148
. 148
. 149
. 150
Chapter 1
Introduction, Background and
Motivation1
1.1 What is Breast Cancer?
”Breast cancer (malignant breast neoplasm) is cancer originating from breast tissue, most commonly from the inner lining of milk ducts or the lobules that supply the ducts with milk. Cancers
originating from ducts are known as ductal carcinomas; those originating from lobules are known
as lobular carcinomas. Breast cancer is a disease of humans and other mammals; while the overwhelming majority of cases in humans are women, men can also develop breast cancer. Breast
cancer is one of the largest serious diseases among women in the western world. It is the most
common and deadly cancer for women on a global scale, where breast cancer accounts for 21%
of all cancer cases and 14% of all cancer deaths” [3, 4].Approximately 230,480 new cases of
invasive breast cancer and 39,520 breast cancer deaths are expected to occur among US
women in 2011. Breast cancer incidence rates were stable among all racial/ethnic groups
from 2004 to 2008 [5].
1.2
How It Develops and What Are Their Types?
Breast cancer develops through a multistep process in which normal, healthy cells in the
breast go through stages that eventually change them to abnormal cells that multiply
out of control [4]. In most cases, cancer takes many years to develop. Breast tissue is
particularly sensitive to developing cancer for several reasons. The female hormone
estrogen stimulates breast cell division. This division can increase the risk of making
damage to DNA permanent. Furthermore, breast cells are not fully matured in girls
and young women who have not had their first full-term pregnancy. Breast cells that
1
Plagiarism Note: Section 1.1 to 1.6 of this Chapter are taken from public resources such as National
Institutes of Health (NIH) , Mayo Clinic Journal and many other public resources issued for public interest,
author of this dissertation holds no ”Rights” for any content of this kind. This was added to make the
clinical background more lucid for rest of the chapters.
11
are not fully mature bind carcinogens (cancer causing agents) more strongly and are not
as efficient at repairing DNA damage as mature breast cells [6]. The size, stage, rate of
growth, and other characteristics of the tumor determine the kinds of treatment [6].
Breast cancer is categorized into several types according to multiple different schemes,
each based on different criteria and serving a different purpose. A typical description
usually considers each of these aspects in turn: the histolopathological type, the grade
of the tumor, the stage of the tumor, and the expression of proteins and genes. As
knowledge of cancer cell biology develops these classifications are updated.
One major way of defining the type of breast cancer is whether or not it is:
Hormone receptor (estrogen or progesterone receptor) positive: About 75% of all breast
cancers are ”ER positive.” They grow in response to the hormone estrogen. About 65%
of these are also ”PR positive.” They grow in response to another hormone, progesterone.
HER2 positive: In about 20% to 25% of breast cancers, the cancer cells make too much
of a protein known as HER2/neu. These breast cancers tend to be much more aggressive
and fast-growing.
Triple negative: Their estimates range between 10% and 17%. They are called as
”triple negative” because they lack estrogen and progesterone receptors and do not over
express the HER2 protein. The majority of breast cancers associated with the breast
cancer gene known as BRCA1 are triple negative.
These classifications provide doctors with valuable information about how the tumor
acts and what kind of treatment may work best [7].
1.3 What Factors Increase a Woman’s Risk of Breast Cancer?
The strongest risk factor for breast cancer is age [8]. A woman’s risk of developing this
disease increases as she gets older. The risk of breast cancer, however, is not the same
for all women in a given age group. Research has shown that women with the following
risk factors have an increased chance of developing breast cancer:
Personal history: Women who have had breast cancer are more likely to develop a
second breast cancer [9, 10].
Family history: A woman’s chance of developing breast cancer increases if her mother,
sister, and/or daughter have been diagnosed with the disease, especially if they were
diagnosed before age 50. Having a close male blood relative with breast cancer also
increases a woman’s risk of developing the disease [9].
Genetic alterations : Inherited changes in certain genes (for example, BRCA1, BRCA2,
and others) increase the risk of breast cancer. These changes are estimated to account
for no more than 10 percent of all breast cancers. However, women who carry certain
changes in these genes have a much higher risk of breast cancer than women who do
not carry these changes [9, 11].
Breast density : Women who have a high percentage of dense breast tissue have a
higher risk of breast cancer than women of similar age who have little or no dense tissue
in their breasts. Some of this increase may reflect the ”masking” effect of fibroglandular
tissue on the ability to detect tumors on mammograms [12, 9].
Certain breast changes found on biopsy : Looking at breast tissue under a microscope
allows doctors to determine whether cancer or another type of breast change is present.
Changes associated with an increased risk of breast cancer include atypical hyperplasia
(a noncancerous condition in which cells have abnormal features and are increased in
number), lobular carcinoma in situ (LCIS) (abnormal cells are found in the lobules of the
breast), and DCIS [13, 9].
Reproductive and menstrual history : Women who had their first menstrual period
before age 12 or who went through menopause after age 55 are at increased risk of
developing breast cancer. Women who had their first full-term pregnancy after age 30
or who have never had a full-term pregnancy are also at increased risk of breast cancer.
Long-term use of menopausal hormone therapy : Women who use combined estrogen
and progestin menopausal hormone therapy for more than 5 years have an increased
chance of developing breast cancer [14, 15, 9].
Radiation therapy : Women who had radiation therapy to the chest (including the
breasts) before age 30 have an increased risk of developing breast cancer throughout
their lives [9].
Alcohol : Studies indicate that the more alcohol a woman drinks, the greater her risk
of breast cancer [16].
Body weight : Studies have found that the chance of getting breast cancer after
menopause is higher in women who are overweight or obese [17].
1.4 What Protective Factors May Decrease the Risk of Breast
Cancer?
Estrogen (decreased exposure) : Decreasing the length of time a woman’s breast tissue is
exposed to estrogen may help prevent breast cancer. Exposure to estrogen is reduced in
the following Pregnancy, Breast-feeding, Late menstruation, Early menopause [9, 15].
SERMs : Selective estrogen receptor modulators (SERMs) are drugs that act like
estrogen on some tissues in the body, but block the effect of estrogen on other tissues.
Some widely used SERMs are Tamoxifen [18],Raloxifene [19].
Aromatase inhibitors : Aromatase inhibitors lower the risk of new breast cancers in
postmenopausal women with a history of breast cancer. In postmenopausal women,
taking aromatase inhibitors decreases the amount of estrogen made by the body.
1.5 Why to Assess Breast Cancer Risk?
Recent developments in the ability to predict and alter breast-cancer risk warrant a new
look at the role of assessment of this risk in primary care. Physicians must become
adept at evaluating breast-cancer risk and counseling women about its effect on medical
decisions [20]. Several important medical decisions may be affected by a woman’s underlying risk of breast cancer. These decisions include whether to use postmenopausal
hormone-replacement therapy, at what age to begin mammographic screening, whether
to use tamoxifen to prevent breast cancer, and whether to perform prophylactic mastectomy to prevent breast cancer.
1.6 How to Assess Breast Cancer risk?
1.6.1 Average Risk
Understanding the average risk of breast cancer provides a necessary context for individual risk assessments. The average lifetime risk of breast cancer in the U.S. female
population at birth is 12 percent, or approximately one in eight. The longer a woman
lives without cancer; the lower is her risk of breast cancer over the remainder of her
lifetime. Thus, a 50-year-old woman who has not had breast cancer has an 11 percent
chance of having breast cancer in her lifetime, and a 70-year-old woman who has not
had breast cancer has a 7 percent chance of having breast cancer in her lifetime [21].
1.6.2 Epidemiologic Risk Factors
Many studies have evaluated risk factors for breast cancer. Several factors have been
consistently associated with an increased risk [20, 3]. However, because many of these
risk factors may interact, evaluating the risk conferred by combinations of risk factors
is challenging. Other risk factors have been less consistently associated with breast
cancer (such as diet, use of oral contraceptives, lactation, and abortion) or are rare in the
general population (such as radiation exposure), and are not included in currently used
prediction models.
1.6.3 Risk-Prediction Models
Four models are currently available to predict the risk of breast cancer, of which two are
used most often. The most commonly used model was developed by Gail et al. [8] from
the Breast Cancer Detection Demonstration Project, a large mammographic-screening
program conducted in the 1970s. This model incorporates the number of first-degree
relatives with breast cancer, age at menarche, age at first live birth, and the number of
breast biopsies. It predicts the cumulative risk of breast cancer according to decade up
to the age of 90 years.
1.6.4 Breast Cancer Screening: Screening Mammogram
The three most common modalities for breast cancer screening are mammogram, clinical
breast examination, and breast self-examination. The goal of these screening examinations is to detect occult breast cancer at an early stage-before it is clinically evident-and
thereby increase the probability of cure. Many researcher [10, 22, 23, 24] have shown the
increasingly strong reduction in breast cancer mortality due to screening. A screening
mammogram usually takes 2 x-ray pictures (views) of each breast. The breast tissue is
compressed, so that two views of the breast can be taken: a mediolateral (MLO) view
and a craniocaudal (CC) view. Some patients may need to have more pictures to see as
much breast tissue as possible, called magnification, or spot compression, views. Figure
1.1 shows a perticular case of MLO and CC views which are taken from a case report
[25] during screening. Widely used imaging technologies across mammogram practice
are (i) Full field digital mammography and (ii) Digitizing screen film mammography.
Full field digital mammography is a newer imaging technology in which the digital
mammogram is obtained directly in electronic (filmless) format as opposed to digitizing screen-film images for processing purposes. This digital system, which is intended
to replace traditional screen-film mammography, has the potential to facilitate various
teleradiology applications including electronic image archiving and retrieval, remote
location analysis, and computer-aided diagnosis (including serial analysis) [26].
Mammogram screening is ideally performed in conjunction with a physical examination of the breast. These two examinations are complementary to one another. Mammographic screening is able to detect some cancers that are not palpable, while some
cancers are palpable, but not detectable on mammogram. Therefore, the palpable abnormality needs to be evaluated further, even if the mammogram is normal. The first
randomized controlled trial demonstrating the benefit of the screening mammogram
and clinical breast exam in decreasing mortality was performed in 1963 by the Health
Insurance Plan breast screening project [27]. Sixty-two thousand women were randomized to either the intervention group, consisting of screening mammogram and clinical
exam, or to a control group. At ten years of follow-up, the intervention group had a 30
percent reduction in breast cancer mortality. Further randomized controlled trials confirmed the efficacy of screening mammography in decreasing breast cancer mortality.
A meta-analysis of nine randomized controlled trials and four case-control studies was
reported in 1995 [22]. Women aged 50 to 74 who received mammographic screening
had a decreased relative risk for breast cancer mortality of 0.74 in comparison to women
who did not receive mammographic screening.
However, the use of screening mammography is more controversial in women under
the age of 50, for several reasons [20]. First, because breast density is generally higher in
younger women [28], screening mammography is less likely to detect early breast cancer
at a curable stage. Thus, the reduction in mortality from breast cancer is lower. Second,
also because of their higher breast density, screening mammography in younger women
results in more false positive tests, with the associated anxiety and unnecessary biopsies
[29]. Third, because women under the age of 50 are less likely to have breast cancer,
(a) 47-year-old woman with invasive lobular carcinoma of the left breast. MLO view of the
left breast from 1996 shows no abnormality. MLO view of the left breast from 1999 shows an
apparent increase in retroglandular fat and retraction of breast parenchyma from the chest
wall
(b) 47-year-old woman with invasive lobular carcinoma of the left breast. CC view of the left
breast from 1996 shows no abnormality. CC view of the left breast from 1999 shows shrinking
volume of the outer breast.
Figure 1.1: During mammography, a special low-dose X-ray machine is used to produce
images of the breast. In many instances, these images can detect breast cancers in a
very early stage when they are still too small to be felt during a physical examination.
Courtesy:Wendolyn Hill
fewer women in this age group will benefit from screening. Fourth, the lower incidence
of breast cancer among these women increases the cost of mammography per year of life
saved to more than 100, 000 [30]. In contradiction, researchers from Cochrane institute
[31, 32] reported no reduction in mortality due to screening program which became a
topic of debate amongst the researcher.
Ultimately, the decision regarding screening mammography is up to the patient.
Therefore, it is important for a clinician to discuss the benefits and risks of mammographic screening with each individual. Early detection is critical to the chance of
successful treatment, since the cancer may be invasive and spread to the rest of the body
[13]. This detection can be very difficult, since the first signs of breast cancer are often
asymptomatic. This is why x-ray mammography is widely used to screen for breast
cancer. The mammogram can show small changes in breast tissue which may indicate
cancers which are too small to be detected either by the patient or by a doctor [22].
1.7 Mammographic Parenchymal Characteristics and its
Relation to Risk?
The relationship between parenchymal pattern and breast cancer risk has been studied
and debated for past three decades, with many subsequent reviews [33, 34, 35, 36, 37, 38,
39, 40, 12, 11, 26]. It is now clear that there is an increased breast cancer risk associated
with certain breast tissue compositions and that other known risk factors may exert
some influence on breast tissue, which causes long-and short-term changes evident on
mammogram. Wolfe [33, 34] in his consistent experiments observed a relationship between the prominence of ductal patterns and breast cancer on breast radiographs. Wolfe
believed that fat, connective tissue, and the epithelial elements are seen as dysplasia (increased radiographic density due to interlobular connective tissue) in mammography
and that periductal fibrosis is represented by prominent ductal patterns.
The work presented by Wolfe was fascinating because it suggested that (a) a measurable risk factor derived from the image, (b) the interval between screening sessions
may be adjusted according to breast composition (risk), and (c) screening practice, in
general, may be based on parenchymal pattern [26]. This hypothesis was later validated
by several researchers [41, 42, 43].
1.7.1 Mammographic Density and Risk
Some researchers have found that relative amount of radiographic density in the mammogram is related to risk (density-risk assessment)[44, 45, 46, 47]. The loose definition for
radiographic density is any image area that is not fat or not radiolucent or fibro-glandular
tissue. Roebuck et al. [48] provides a more complete definition of radiographic density.
Density measurements may be a more reliable indicator of risk as opposed to Wolfe pattern
assessment.
Several studies from past one decades indicates that density classification is an important factor to take into account when analyzing mammographic images; the proportion
of radiographic densities on the image is related to risk [26]. Hence, researchers have
started acknowledging the importance of automated density measurements. Boyd et
al. [49] showed that, by using either the radiologist’s estimation or computer assisted
manual thresholding, more proportions of radiographically dense tissue are associated
with a higher risk.
The American College of Radiology set up a guideline for accurate measurement of
tissue pattern. They developed a rating system called Breast Imaging Reporting and
Data System (BI-RADS) [50] which states that asymmetric breast tissue is judged relative
to the contralateral breast as ”a greater volume of breast tissue, greater density of breast
tissue, or more prominent ducts.” But a stable finding that fulfills the BI-RADS definition
seldom warrants a biopsy [26].
1.8 Potential of Parenchymal Texture Techniques: A Motivation
Figure 1.2: The block diagram explaining the different factors influencing parenchymal
change that results in breast carcinogenesis: A motivation behind this dissertation
In spite of being well studied and established link between breast density and cancer
risk, it has some discrepancies such as, (i) To which degree changes in density reflects
changes in risk. (ii) Whether changes in density caused by intervention or not has any
relation to changes in breast cancer risk. It is observed in many studies that, even though
two mammograms with matched age has same PD (percent density), may have different
Gail risk this is due to the fact that breast density proportion changes with time; however
it is not clear whether the breast cancer risk changes accordingly. Dense mammograms
are susceptible to masking effect hence cancers are sometimes missed in breasts classified
with the more dense patterns at the initial screening examination. These missed cancers
will then manifest in the near future, that will substantially increase the risk in short term.
Moreover, one study [51] yeilds no clear conclusions with regard to women with more
than 25 % density. Also there are various studies that showed elevated breast density due
to hormone replacement therapy but do not induces breast cancer risk [52, 53]. Hence
mammographic parenchymal pattern is still not well understood and its relation to breast
cancer risk cannot be explained by merely considering density as an imaging feature.
There is a strong need of additional measure, sensitive and consistent enough to capture
the changes in parenchymal tissue structures during the development of breast cancer.
Moreover, from the recent findings [54], It is evident that, fibroglandular and breast fat
tissue have independent effects on breast cancer risk. This suggests that, the adjustment
for non-dense tissue should also be considered while evaluating risk. The breast is a
heterogeneous composition of adipose tissue, epithelial cells (parenchymal), and fibrous
connective tissue (stromal), and most breast cancers arise from the ductal epithelial
cells [55, 26], Quantitative texture measure representing parenchymal (epithelial) tissue
structure on mammogram can be a surrogate and independent risk factor for breast
cancer. This motivates us to develop an accurate risk measure that can potentially be
used independently or in addition to breast density in both longitudinal and crosssectional study design, this is clearly illustrated in Figure 1.2, where we believe that
the three differnt ways by which the parenchymal tissue structure may change in the
course of time along with, i.e. (i) Exposure to HRT (ii) Endogeneous Hormone Exposure
(ER + risk) (iii) Change of Genetic Makeup or unknown factors. And just like density ,
mammographic parenchymal texture measure may also have an ability to detect these
changes comparable to breast density which today is state of the art.
Second motivating factor was to collect anatomical information while doing texture
analysis on mammogram, which is not taken into consideration in previous research
work [56, 57, 58, 59] based on texture measure. Figure 1.3 illustrates that, one expect
a coordinate system which represents the shape and orientation of breast tissue structure more accurately on mammogram than in conventional Cartesian coordinate system
used so far. Here, the idea is to use the shape of breast on mammogram especially in
MLO views to model as a family of two parabolas meeting at nipple location. This
will have three purposes (i) To establish one to one anatomic correspondence between
mammograms in both cross-sectional and longitudinal study (Anatomy based mammogram registration). (ii) To designed more accurate and sensitive texture measure with
respect to the anatomy of parenchymal tissue structure on mammogram, and potentially separate cancer from matched control in study where mammograms are taken
before detection. (iii) This facilitates us to study and understand the localized pattern on
mammograms that experiences maximum change due to carcinogenesis in case-control
design. And that experiences pattern change due to hormone replacement therapy in
longitudinal design.
MLO
Mammogram
Image
Coordinate
Expected
Coordinate
Figure 1.3: Figure illustrating the need of more accurate image coordinate system to capture the mammographic parenchymal tissue orientation than the conventional Cartesian
image coordinates. Courtesy: Images are taken from Yale University School of Medicine
Third motivating factor was to separate between ER + and ER - contra-later mammograms (unaffected mammograms). If we could show the potential of mammographic
parenchymal texture analysis for ER sub-specific classification, this could have significant impact in personalized ER specific risk-reduction interventions such as SERMs
and aromatase inhibitors. In present protocol, evaluation of the ER-status is performed
by means of immunohistochemistry (IHC) which has some limitation being invasive
[60].However many studies has shown the association of diffident factors including
breast density with ER status [61, 62, 63] ,till date, in our knowledge no study has
shown the association with mammogram texture and ER status on contra-later breasts.
If present study perform consistent over other study population, this may have potential
to predict the ER positive status prior to carcinogenesis and may help in better treatment such as SERMs [64]. Also it would be interesting to see the risk of developing
ER-subtype specific breast cancer in population undergoing perticular HRT treatment
than placebo.
Fourth motivating factor was to design a framework develop measures indicative
of HRT. These measures are then tested as predictors of breast cancer risk on data from
a breast cancer study. In the same way we can potentially learn patterns indicative
of breast cancer risk from the breast cancer study and test if these patterns change in
different HRT studies. In this way we hope to shed a little light on the elusive link
between the associations of mammographic parenchymal texture pattern, HRT use and
eventually with breast cancer risk. Based on this reasoning we study images from HRT
trials, building a framework to develop measures indicative of HRT. These measures
are then tested as predictors of breast cancer risk on data from a breast cancer study. In
the same way we can potentially learn patterns indicative of breast cancer risk from the
breast cancer study and test if these patterns change in different HRT studies. In this
way we hope to shed a little light on the elusive link between the associations of high
mammographic density and breast cancer risk and of increased mammographic density
and HRT use.
1.9
What is the purpose of this PhD dissertation?
1.9.1 Clinical Perspective
• To develop an accurate and consistent imaging biomarker to quantify mammographic patterns by considering anatomy and tissue orientation (parenchymal
texture) of breast on screening mammogram.
• To qualify this marker on various case-control and longitudinal studies to establish
its proof of concept.
• To qualify this marker as an effect specific measure in clinical trials involving
various HRT (Hormone Replacement Therapy) treatments.
• To investigate the potential of this marker as a surrogate marker of the risk to
develop Estrogen Receptor (ER) subtype-specific breast cancer, compared to the
standard mammographic density measures. Thereby to establish a non-invasive
biomarker during screening procedures to identify women who would benefit
most from SERM (Selective Estrogen Receptor Modulator) chemoprevention.
• To investigate and understanding the region on mammogram that experiences the
effect of carcinogenesis in parenchymal structure during the development of breast
cancer.
• Conclusively, to help identify patients who have higher risk of developing breast
cancer, based on screening by mammography. Such identification leads to better
allocation of screening resources and thereby earlier cancer detections and lower
mortality rates.
1.9.2 Technical Perspective
• To review all parenchymal texture techniques that have been widely used in mammogram image analysis community for various application, emphasis on risk
assessment.
• To develop and apply the widely used multi scale based texture features such
as fractal dimension, laccunarity, succolarity, Gabor and wavelets on available
dataset.
• To develop an anatomically oriented breast coordinate system, this coordinate
makes it possible to identify the corresponding position and orientations among
MLO mammograms, which facilitates an implicit use of registration in both crosssectional and longitudinal studies.
• To develop the texture features such as Gaussian derivatives, structure and diffusion tensors with respect to breast coordinate system.
• To improve the performance of classification in case-control settings by committeebased machine learning techniques.
• To develop a nested cross-validation framework that finds the region of interest
in anatomical breast coordinate by automatic selection of inner and outer scale of
post-processed mammogram.
• To study the dynamics of mammogram scoring methodology by various free parameters such as intensity normalization and matching across data, segmentation,
scaling, number of sampling points, classifier parameters, automatic/manual annotations, inter-radiologist scoring on mammograms.
1.10 Background of PhD Project
This project was started in March 2008 in collaboration between the University of Copenhagen and Imaging Department of NordicBioscience A/S now (BiomedIQ A/S), each
contributing with half of the funding. NordicBioscience A/S is a private research institute mainly investigating conditions and diseases that appear in the years after the
menopause and has received worldwide recognition for its clinical research especially in
the area of osteoporosis and bone disease. NordicBioscience A/S has x-ray mammograms
taken as a safety measure from HRT trials, mainly investigating osteoporosis, available
for analysis. This gives a great opportunity to investigate mammographic parenchymal
texture measure and its relation to HRT. BiomedIQ A/S is a private research organization
to research, develop and implement quantitative imaging biomarkers for use in clinical
trials and patient diagnosis, prognosis, screening, and monitoring.
We also had a collaboration with Prof. Nico Karssemeijer provider of Nijmegen
study of 495 women from a previously published case-control study on the effect of
recall rate in the Dutch biennial screening program [65]. This study was very crucial
for this project, since our aim was to develop an imaging biomarker for risk assessment
for which the necessary requirement was to have an access of mammograms from the
cases which should be taken before detection, then only we will be able to develop
a marker that can learn parenchymal texture pattern indicative of risk of developing
breast cancer in future mammograms. In this study , Screening mammograms were
collected from five of the nine Dutch regional screening organizations on the basis of
their geographic spread. Of these 495 women 245 were subsequently diagnosed with
breast cancer (123 interval and 122 screen-detected cancers). Mammograms were used
from the screening 4 years before diagnosis for screen-detected cancers and 2-4 years
before diagnosis for the interval cancers. Mammograms of 250 women without breast
cancer diagnosis in the subsequent 4 years were used as control. The design of the
original study implied that the first available mammogram was 4 years before this for
control and screen-detected cancers and 2 years before the last screening mammography
(hence 2-4 years before diagnosis) for interval cancers. This dataset was a cornerstone
for our research especially for developing a measure that can asssess general cancer risk.
I also had a chance to do some preliminary work on screening data provided by Prof.
Celine Vachone from Mayo Clinic, USA.
At the final stage of this PhD project, Prof. Despina Kontos at Computational Breast
Imaging Group, Radiology Dept., University of Pennsylvania provided me the visiting
scholarship to run some experiments on their unique dataset in order to investigate
the potential of our mammographic parenchymal texture measure in Estrogen Receptor
subtype specific breast cancer populations.
1.11 Overview of the Thesis
After an introductory chapter, the thesis is split up in three major parts depending on
the potential of mammographic parenchymal shape and texture analysis stratified by
its clinical application in risk assessment;
Part I: Focuses on the development of methods for risk estimation on general
populations (Screening mammograms).
Part II: Targets on the development of quantitative measure for the populations
involving HRT treatments.
Part III: Investigate the methods of risk estimation in ER-subtype specific populations.
The thesis contains the following chapters:
1. Introduction : This chapter gives a background, preliminaries and introduction to
justify the rationale of this PhD dissertation.
Part I
2. Mammographic Parenchymal Texture Techniques in Application to Breast Cancer Risk Assessment: A Review
This chapter summarizes and compares the mammographic parenchymal texture
techniques used in various applications such as, microcalcification detection, mass
characterization and tissue characterization. Emphasis is given on techniques that
have been used for risk assessment application on screening mammograms. Performance is evaluated and compared by Receiver Operative Characteristic curve
analysis (FROC) on one of the most commonly used database available in public
domain, such as mini-MIAS and DDSM.
3. Fractal Dimension and Lacunarity Analysis of Mammographic Patterns in Assessing Breast Cancer Risk: A Longitudinal and Cross-sectional Study
Among various texture techniques as seen in previous chapter, fractals and its
various properties have been used by many researchers in assessing breast cancer risk in mammography. It was Giger and her colleagues [66, 67, 11, 57] who
first reported the potential of fractal analysis of mammographic parenchymal patterns for the assessment of breast cancer risk through their consistent experiments.
Among other interesting observations, this group conclude that a combined group
of BRCA 1/2 gene mutation carrier exhibit a statistically different radiographic
fractal texture pattern than a carefully selected low risk group. This motivates
us to validate the fractals and its properties on our case-control where cases are
collected prior to detection and also on longitudinal study including placebo and
populations treated with HRT. In this chapter we also investigates the potential of
other fractal measures such as Lacunarity other than fractal dimension which is
not considered in [11].
4. A Novel and Automatic Mammographic Texture Resemblance (MTR) Marker is
an Independent Risk Factor for Breast Cancer
In this chapter, we investigate whether breast cancer is predicted by a mammographic texture resemblance (MTR) marker. We use previously published casecontrol study including 495 women of which 245 were diagnosed with breast cancer. In baseline mammograms, 2-4 years prior to diagnosis, the following mammographic parameters were analyzed for relation to breast cancer risk: Categorical
parenchymal pattern scores; Radiologist’s percentage density, Computer-based
percentage density; Computer-based breast cancer risk MTR marker; Computerbased hormone replacement treatment MTR marker.
5. An Anatomically Oriented Breast Coordinate System for Mammogram Analysis
In this chapter, we develop a breast coordinate system that is based on breast
anatomy to register female breasts into a common coordinate frame in 2D mediolateral oblique (MLO) view mammograms. The breasts are registered according
to the location of the pectoral muscle and the nipple and the shape of the breast
boundary. We construct a non-linear mapping between the parameter frame and
the breast region in the mammogram. This mapping makes it possible to identify
the corresponding positions and orientations among all of the ML or MLO mammograms, which facilitates an implicit use of the registration. We additionally
show how the coordinate transform can be used to extract Gaussian derivative
features so that the feature positions and orientations are registered and extracted
without non-linearly deforming the images. We use the proposed breast coordinate transform in a cross-sectional study involving screening mammogram prior to
detection and compare its performance with MTR measure developed in previous
chapter.
6. A Framework to Determine Mammographic Regions that Show Early Changes
Due to Development of Breast Cancer: An Application in Risk Assessment
In this chapter, we develop a framework that will discover the region on mammogram where changes due to breast cancer are most like to occur. We propose
a statistical framework that performs an automatic scaling and selection of region
of interest over score map which was computed with respect to anatomical breast
coordinate system discussed in previous chapter. This work suggests which regions/patterns should be more carefully considered to improve both preclinical
and follow-up screening phases of cancer advancement. Further, we validate this
pattern on various cross-sectional and longitudinal studies. We also how this
framework improves the performance of MTR in an anatomically oriented breast
coordinate system.
Part II
7. Quantitative Imaging and Visualization through Structure Enhancing Diffusion Applied to Longitudinal Study Involving Hormone Replacement Therapy
(HRT)
Short term hormone replacement therapy (HRT) use is well established for menopausal
symptom relief while the benefits and risks of long term HRT remain controversial.
Previously our mammographic parenchymal texture measure has been validated
on various studies involving HRT [52, 53, 68]. Petroudi et al. [69, 70, 71] have shown
that, the effect of isotropic diffusion and the maximum responses of the anisotropic
diffusion at various scale being significant while evaluating the effect of HRT on
mammograms. This motivates us to further extend our marker by developing a
framework to obtain a more accurate and sensitive measure that capture mammographic parenchymal pattern change related to specific effects of treatments involving Hormonal Replacement Therapy (HRT) and aging. We demonstrate how
the structure tensor and structure enhancing diffusion with its coherence properties computed in an anatomically oriented breast coordinate system followed by
statistical learning scheme that provides non subjective and reproducible measure,
as compared to the traditional BIRADS and computer aided percent density measure. We also visualize the change of breast tissue structure across mammograms
in one to one correspondence during placebo and HRT treatments.
Part III
8. Computer-Aided Parenchymal Texture Analysis in Digital Mammograms: The
Potential for Estrogen-Receptor Specific Breast Cancer Risk Estimation
Breeding evidences suggest that the etiologic and risk profile differences between
women who tend to evolve ER+ and ER- breast cancer. Therefore, in this chapter
we investigate the potential of mammographic parenchymal texture as a surrogate marker of the risk to develop Estrogen Receptor (ER) subtype-specific breast
cancer compared to the standard mammographic density measures, in a casecontrol study design. Multiple texture features including, Gaussian derivatives,
Coherence feature of structure and structure enhancing diffusion representing the
orientation and heterogeneity of the parenchymal structure were extracted using
validated algorithms discussed in our previous chapters. Both post-processed
and raw images with MLO views were analyzed for various regions of mammograms. We also learn whether population undergoing HRT exposure has tendency
towards development of ER-subtype specific breast cancer.
Part IV
10. Summary, Discussion, Conclusions This chapter contains a general summary of
the thesis, a discussion of the findings, and finally a short conclusion is derived.
Part I
Chapter 2
Mammographic Parenchymal Texture
Techniques in Application to Breast
Cancer Risk Assessment: A Review
Abstract
Texture techniques have been used extensively in mammogram image analysis research community for many years. This review chapter summarizes and compares the mammographic
parenchymal texture techniques used in various applications such as, microcalcification detection, mass characterization and tissue characterization. Emphasis is given on techniques that
have been used for risk assessment application on screening mammograms. Performance is
evaluated and compared by Receiver Operative Characteristic curve analysis on one of the most
commonly used database available in public domain, such as mini-MIAS and DDSM.
28
2.1 Introduction
It was Wolfe [1] in early eighties, who first discovered the link between mammographic
parenchymal pattern and risk of developing breast cancer. He empirically categorized
the mammographic pattern into four classes which will help in predicting with considerable accuracy which women will develop breast cancer and equally important, those
who are less likely to develop as shown in Figure 2.1. Later he shown that the density can
be a predictor of breast cancer risk in [72], which was supported and validated by many
researchers [12, 73, 74, 38, 37, 75] Some researchers have considered Wolfe’s pattern
and density simultaneously with other biological factors [55]. In late 2000, American
college of radiology introduced a quality assurance tool originally designed for use with
mammograph called Breast Imaging-Reporting and Data System (BI-RADS). These are
standardized numerical codes typically assigned by a radiologist after interpreting a
mammogram as shown in Figure 2.2. In totality, researchers believed that mammographic parenchymal pattern representing density has a potential for risk assessment.
[49] showed that, BI-RADS and computer assisted density measures are associated with
risk. Recently some researcher have acknowledge the significance of automated density
measurements [49, 76, 77, 78]. Even though mammographic density has a independent
potential of assessing a risk, however the causal relation is still unclear such as, (i) To
which degree changes in density reflects changes in risk. (ii) Whether changes in density
caused by intervention or not has any relation to changes in breast cancer risk. Even
though two mammograms with matched age has same PD (percent density) , they may
have different Gail risk [79, 80].
N1
Low Risk
P1
P2
DY
High Risk
Figure 2.1: Wolfe’s classification of Parenchymal Patterns. N1 = Minimal risk. P1 =
Moderate risk. P2 = Significant risk. DY = Highest risk. Courtesy: Xeroradiographs,
taken from Wolfe’s original research article published in 1976 [1]
Hence it is evident that there is more information to be extracted from the mammograms than mere visual perception such as density and other imaging features. This mo-
BI-RADS I
Low Risk
BI-RADS II
BI-RADS III
BI-RADS IV
High Risk
Figure 2.2: Breast density patterns. BI-RADS I = fatty breast ( <25% dense). BI-RADS
II = scattered densities (25 %-50% dense). BI-RADS III = heterogeneously dense (51%75% dense). BI-RADS IV = extremely dense (>75% dense). BI-RADS = Breast Imaging
Reporting Data System. (Courtesy: Journal of National Cancer Institute,2009)
tivates researchers across image analysis community to develop automated techniques
to classify parenchymal pattern and relate them to the risk. In the literature all CAD
techniques that have been used can be classified as the techniques used (i) In Diagnostic
mammograms, for application such as microcalcification detection, tumor characterization, breast asymmetry detection (ii) In screening mammograms for developing a
continuous measure by image analysis techniques (texture based techniques) representing a prognostic and diagnostic imaging biomarkers for assessment of breast cancer risk
as shown in Figure 2.3. Various texture techniques have been used in image processing
community and its application in mammogram image analysis is not new. An early approach to identifying abnormalities in mammograms, researchers [81, 82, 83, 84, 85, 86]
amongst many others, have focused on micro-calcifications. While various texture techniques for mass detection and its have been addressed by [87, 88, 89, 90, 91, 92, 93, 94].
In this chapter, we will review all CAD techniques that has been used in mammograms image analysis using Parenchymal Texture Techniques (PTT) by the researchers from
late nineties to present, i.e. the state of the art. Also, we will evaluate the association of
these texture features on mini-MIAS and DDSM dataset. We believe that this work will
definitely provide a concrete overview on the past, present and future aspects in this
field. Since, the texture techniques that has been used for diagnostic mammograms is
out of the scope of this article, we will focus more on techniques that has been used for
risk assessment by tissue characterization.
Figure 2.3: Various CAD application in mammography where texture techniques have
been used by many researchers
2.2 Mammographic Parenchymal Texture Techniques
Mammographic parenchymal pattern is an admixture of both stationary and nonstationary textures. Stationary because for some mammograms the local statistical
properties are same everywhere (stationary), while for some mammogram its different
(non-stationary).
There has been a lot of work done in texture analysis yet there is an ambiguity in the
common meaning of texture. However, we believe that the texture is spatial, statistical
or structural-statistical. It is spatial because texture is the relationship of group of image
elopements. Nothing can be learned about the texture from an isolated pixel, and little
from histogram (statistical) of pixel values. Hence we divide the texture techniques
based on (i) Statistical (ii) Spatial-Statistical.
Basically, the texture techniques that has been used in risk assessment can be divided
into two broad categories (i) Statistical: 1st and 2nd order statistics (ii) Spatial-Statistical:
Fractal based techniques, Laws texture feature, and Multi-resolution based techniques.
2.3 Statistical Based Texture Techniques
2.3.1 1st and 2nd order statistics
First-order statistics measure the likelihood of observing a gray value at a randomlychosen location in the image. First-order statistics can be computed from the histogram
of pixel intensities in the image. These depend only on individual pixel values and not
on the interaction or co-occurrence of neighboring pixel values. The average intensity in
an image is an example of the first-order statistic [95]. These are global measure of local
properties and shift-invariant and insensitive to the random texture variations. This
category includes measure like average gray value (AVE), variation (VAR), skewness
(SKW) and kurtosis (KRT). If I(r,c) is a image with r and c representing number of rows
and columns , then these measure are defined as,
AVE = E[I(r, c)]
(2.1)
VAR = E[(I(r, c) − AVE)2 ]
(2.2)
(I(r, c) − AVE)3
]
(2.3)
VAR3/2
(I(r, c) − AVE)4
KRT = E[
]
(2.4)
VAR2
AVE provides the most fundamental statistics of image, VAR measures the irregularity, SKW measures the extent to which outliers favor one side of the main distribution
while KRT measures the peakedness or the presence of outliers.
Second-order statistics are defined as the likelihood of observing a pair of gray values
occurring at the endpoints of a dipole (or needle) of random length placed in the image
at a random location and orientation. These are properties of pairs of pixel values. It is
achieved by co-occurrence matrices by representing non-parametric description about
the texture pattern. First order statistics destroys any spatial information, so it destroys
the spatial aspects of texture patterns and only retains their brightness information.
With Co-occurrence matrices one can capture both spatial and relative brightness information. So, instead of representing the probability of a pixel having certain value,
a joint probability of certain sets of pixels having certain values is considered. Many
techniques have been proposed for extracting texture information from co-occurrence
matrices [96, 97]. The commonly studied moments are called contrast, inverse difference moments, angular second moment, entropy and correlation. They are defined as
follows,
∑
CON =
(r − c)2 p(r, c)
(2.5)
SKW = E[
r,c
IDM =
∑ p(r, c)
(r − c)2
r,c
(2.6)
ASM =
ENT = −
∑
∑
p2 (r, c)
(2.7)
r,c
p(r, c)logp(r, c)
(2.8)
r,c
COR =
∑ (r − AVEr )(c − AVEc )p(r, c)
r,c
(SDVr )(SDVc )
∑
AVEr =
(r)p(r, c)
where,
(2.9)
(2.10)
r,c
√∑
SDVr = (
(r − AVEr )2 p(r, c))
(2.11)
r,c
It was Magnin [98] in late eighties used texture measures to classify mammograms
into four categories representing risk. He used 1st order statistics features and suggested
that the continuous labeling can be a better approach. Dhawan [81] used 1st and 2nd
order gray level histogram based statistics of the segmented microcalcification regions
and the size, number, and distance features of the segmented microcalcification cluster.
He showed the improvement in classification of ”difficult to diagnose” microcalcification
using neural network based classifier. Chan and his co-worker [99, 82, 100] investigated
the feasibility of using texture features extracted from mammograms to predict whether
the presence of microcalcifications is associated with malignant or benign pathology
using second order statistics with artificial neural networks. Later Sahiner [101] studied
the classification of regions of interest (ROI’s) on mammograms as either mass or normal
tissue using a convolution neural network (CNN).
Taylor at al [102] utilized number of local statistical texture measures, computed for
patches from digitized mammograms for sorting them according to whether the breast
tissue is fatty or dense they found that the local sleekness was a better measure in separation between fatty and dense patches. Verma [103] used a fuzzy technique in conjunction
with 1st order statistics texture features to detect a microcalcification pattern and a neural
network to classify it into benign/malignant. 2nd order statistics in the form of GLCM
(Gray Level co-occurrence matrix) and SGLD (Spatial Gray Level Dependency) has been
widely exploited for the diagnostic application such as microcalcification detection by
[104, 105, 106, 107], and tumor characterization by [108, 109, 110, 92, 111, 112].
For tissue classification and risk assessment, Tahoces and coworker [113, 114] developed a method for the quantification of breast texture, mostly 1st and 2nd order
statistics by using different algorithms to classify mammograms into the four patterns
described by Wolfe (N1, P1, P2 and Dy). Heine and Velthuizen [115] showed that a
rigorous parametric statistical analysis (variance of image) allows the continuous labeling of dense and nondense tissue. Gupta and Markey [116] used Harallick’s feature
between the MLO and CC mammographic views of breast lesions they observed that
texture features from the two views were less strongly correlated for benign lesions than
for malignant lesions. They suggested the inclusion of these texture features in a CADx
algorithm. Sheshadri [117] investigated on breast tissue classification based on statistical
feature extraction of mammograms showed the good agreement with BIRADS.
2.4 Spatial-Statistical Texture Techniques
2.4.1 Laws Texture Measure
In 1980, Laws [118, 119] discovered the new class of texture measure; he proposed the
texture energy transform which is invariant to changes in luminance, contrast and rotation without histogram equalization or other preprocessing. Texture energy is measured
by filtering with small masks, typically 5x5, averaging of the absolute image values. This
method, similar to human visual processing, is appropriate for texture with short coherence length or correlation distance. It has been widely used in mammogram image
analysis. Laws’s one dimensional convolution masks also called as Lattice Aperture
Waveform System (LAWS) of order five is shown below,
L5 = [ 1 4 6 4 1 ]
(2.12)
E5 = [ −1 − 2 0 2 1 ]
(2.13)
S5 = [ −1 0 2 0 − 1 ]
(2.14)
W5 = [ −1 2 0 − 2 1 ]
(2.15)
R5 = [ 1 − 4 6 − 4 1 ]
(2.16)
where the names of the vectors are mnemonics for Level, Edge, Spot, Wave, and Ripple.
Miller and Astley [120] found that the R5R5 (RR) mask gives the best performance for
mammograms in their different diagnostic situation. Using a sample image from each of
the abnormalities under investigation, alternative L5S5 (LS) and S5R5 (SR) masks were
evaluated by [121].
[122] used size, shape, contrast, and Laws texture features to develop the prediction module’s mass models. Derivative-based feature saliency techniques are used to
determine the best features for classification. [123] used Laws texture energy maps
for enhancement and segmentation to detect masses in digitized mammograms. [124]
demonstrated how Laws texture analysis using of the tissue surrounding MCs shows
promising results in computer-aided diagnosis of breast cancer and may contribute to
the reduction of benign biopsies.
Recently, in addition to other textural features [125] used Laws energy filters for
detection of sites of architectural distortion in prior mammograms of interval-cancer
cases.
2.4.2 Fractal Measures
A fractal is a shape that has same structural and statistical properties at all scales. Fractals
can be self similar, fractals remains the same, either statistically or literally if all their
coordinates are scaled by the same factor. If the different coordinates have to be scaled by
different factors, the fractal is self affine [126, 127]. A fractal is characterized by various
measures such as Fractal Dimension, Lacunarity or succolarity.
There has been several methods proposed in computing fractal dimension of an
image, they all are described in [128] out of them, the most popular and widely used
method is mammogram image analysis is Box-counting method suggested by [129]. In
boxcounting method, image is covered with boxes of size 1/2n , where n takes values
0,1,2,...∞ and count each time the number of boxes N(n) of this size which are needed
to cover the image. The fractal dimension is then defined as
logN(n)
n→∞ log2n
D = lim
(2.17)
Multifractals is becoming popular over fractals dimensions and its properties. Recent
studies have improved our understanding of both scaling and statistical properties of
natural images and it is now broadly accepted that the fractal dimension, used as a sole
texture descriptor, does not provide complete textural information [130, 131]. We believe
mammograms are are characterized by a set of fractal dimensions (i.e. multifractal
indices) rather than by a single fractal dimension. Multifractal indices can provide
better textural description especially in natural image classification [132, 133], however
mammograms are not directly considered as a natural image but the physical process
by which x-ray images are scan can be considered as a natural dynamic process and
mammogram may be characterized by different spatial and time scaling. Multifractals
have been used by many researchers for various medical imaging applications described
in [134]. However, its application in mammography is very limited. In previous section
we have seen the computation of fractal dimension using box counting method, where
estimation of the number of boxes that cover the image does not take into account
the distribution of the points inside the set and this irregularity of the distribution is
completely transparent to the fractal dimension algorithms. Multifractal measures can
disclose those properties because they look into the distribution of points and not only
into their spatial relation [131, 133].
In the literature, we have found no use of multifractals in mammography for the
application of risk assessment and tissue classification. As per our knowledge fractals
and its properties are most widely used texture measure after nth order statistics. Since,
fractals were used extensively, we believe to mention the significance of multifractals in
this review.
In nineties, Caldwell and co-workers [135] applied a fractal measure for image pattern
classification and risk assessment, which resulted in good agreement with the radiologist. Yaffe, Byng et al. [136] used fractals and skewness indices for the quantitative measurements of parenchymal pattern. For both measure, high degree of correlations was
observed for radiologist measurements on the RCC, LCC and RMLO views. Velanovich
et al. [137] showed the potential of fractal analysis to evaluate mammographically discovered breast masses by quantifying the difference between their shapes and texture.
Chan et al. [138] discovered the algorithm that combines several artificial intelligent
techniques with the fractals measures for detection of masses in mammograms. Maidment et al. [139] showed that mammogram texture can be qutified by fractal measures
later synthesized by projections of simulated adipose tissue compartments. They hypothesized that the synthetic and clinical texture has similar properties, assuming that
the mammogram texture reflects the 3D tissue distribution. Jouny et al. [140] showed
the potential of fractal measure in addition to SOM and NN classifier for the diagnosis
of cancerous region in mammogram. Fractal analysis is used by [138, 141] to derive
shape features to perform pattern classification of breast masses and tumors. Giger and
her group [66, 67, 57, 11] consistently shown the potential of fractal dimension in differentiating between the low-risk women and the BRCA1/BRCA2 gene-mutation carriers.
Fractals and its various properties such as lacunarity and succolarity for quantifying the
change in breast tissue during HRT treatments has been used by [142, 143]. Recently
[144, 145] shown the fractals and its application in detecting microcalcification and architectural distortion in prior mammograms, while implications of various texture feature
including fractals in tomothynthesis dataset shown by [146, 147].
2.4.3 Fourier Based Texture Features
Normalized Fourier Descriptor [148] is a frequency-domain characterization of the
smoothness of the boundary. The human visual system analyzes the textured images by
decomposing the image into its frequency and orientation components. The number of
frequency selective filters depends on the image size. For an image of size six filters with
center frequencies at 1, 2, 4, 8, 16, 32, and 64 cycles/image while the orientation filters
can be centered at 0, 45, 90, and 135.Fourier descriptors give a complete and flexible
description of an object’s shape with the additional advantage that they are translation,
rotation, and scale invariant [149, 95].
Vidal et al. [113] developed a method for the quantification of breast texture represented by Fourier features to classify mammograms into the four patterns described
by Wolfe (N1, P1, P2 and Dy). Theodoridis et al. [150] use radial distance signal using
the discrete Fourier transform (DFT) and the discrete wavelet transform (DWT) as additional carrier signals to characterize the mammographic masses. Recently, Rangayyan
and his group [151, 152] has used phase portrait analysis in frequency domain to detect architectural distortion in mammograms of interval cancer cases taken prior to the
detection of breast cancer.
2.4.4 Gabor and Wavelets
The Fourier transform is an analysis of the global frequency content in the signal. Many
applications require the analysis to be localized in the spatial domain. This is usually
handled by introducing spatial dependency into the Fourier analysis. The classical way
of doing this is through what is called the window Fourier transform [153, 95]. The
window Fourier transform (or short-time Fourier Transform) of a 2D image I(x,y) is
defined as follows,
"∞
f (x, y)e−i2π(ux+vy) dxdy
(2.18)
Fw (u, v) =
−∞
where u and v are the spatial frequency contents of the signal f(x,y). When the window
function w(x,y) is Gaussian, the transform becomes a Gabor transform.
In the spatial domain, a 2D Gabor filter is a Gaussian kernel function modulated by
a sinusoidal plane wave. The Gabor filters are self-similar: all filters can be generated
from one mother wavelet by dilation and rotation. Gabor function f is defined as follows,
2
y2
σx
σ2y
−0.5( x2 +
f (x, y) = e
)
cos(2πµ0 x + ϕ)
(2.19)
where, µ0 and ϕ are the frequency and phase of the sinusoidal wave. The values σx and
σ y are the sizes of Gaussian envelope in the x and y directions, respectively.
The texture feature for each pixel is computed as the absolute average deviation of
the transformed values of the filtered images through Gabor filter within a window
[153].
Initially, [154] had shown the use of Gabor function as a model of the receptive fields
of neurons in the visual cortex and its application in digital mammograms for mass
characterization.
In [155, 145, 125] a bank of Gabor filters is used to obtain the orientation field of the
given mammogram for the analysis of left-right (bilateral) asymmetry in mammograms
and architectural distortion. Zheng et al. [156] proposed a breast cancer detection algorithm, named the ”Gabor Cancer Detection” where, Gabor filter bank is formed with five
bands by four orientations (horizontal, vertical, 45 and 135 degree) in Fourier frequency
domain. For each mammographic image, twenty Gabor-filtered images are produced.
Fuzzy C-means clustering technique and k-nearest neighbor (KNN) classifiers are used
to reduce the number of false alarms.
Recently, lesion diagnosis in mammogram images were developed by [157] based in
the technique of principal component analysis which has been used in efficient coding
of signals and 2D Gabor wavelets used for computer vision applications and modeling
biological vision. Casti et al. [158] implemented the bilateral asymmetries detection
algorithms based on Gabor filters analysis.
The idea of Wavelet is explained in details by Daubechies (1992) who stated that
wavelets are functions that are used as the basis to represent other functions. This one
is called mother wavelet. Wavelets decomposition is based on applying 2D wavelets
transform to the image and a set of four different coefficients are produced in each level of
decomposition. The produced coefficients are Low frequency coefficients (A), Vertical
high frequency coefficients (V), and Horizontal high frequency coefficients (H), High
frequency coefficients in both directions (D). Most populous wavelets are Daubechies-4,
Daubechies-8, and Daubechies-16, different level of decomposition are used to represent
the number of low frequency coefficient as a texture features.
In late nineties consistent effort was made by researchers [159, 160, 161] in combining
wavelet features and neural network, mostly for the micro-calcification detection. In
[123, 162], authors classified tumors stratified by various properties such as radial,
circumscribed, microcalcifications, and normal samples; and also benign, malignant,
and normal ones. Zadeh et al. [163] applied multi-wavelet transformations to the regions
containing microcalcification clusters in addition to conventional shape quantifiers and
co-occurrence-based method of Harallick. They reported the experiment where multiwavelet method outperformed over other texture features. Recently, [164] has shown
the potential of various wavelet features on prior mammograms.
2.4.5 Scale-Space Textures
Scale-space aspects of an image is formed by looking at it at many different scales simultaneously it also called as deep structure of an images. It describes the abundant details
and multiple levels of abstraction, yet favoring omission of information that is unlikely
to be useful. It has wide application in image analysis such as the extraction of features,
the measurement of optic flow and stereo disparity, orientation analysis, segmentation,
image enhancement, they all are explained in detail here [165] and practical framework
to handle images in scale space is described by [166, 167]. Texture features based on scale
space makes an explicit relationship between two scales of interest, the characteristic
grain size of image elements, and the size of a frame of view [168, 169]. Among the
large set of texture features in scale space one is the set of invariant, differential features
proposed by Romeney [165]. These features describe all local intrinsic properties of
scalar image at fixed level of resolution. Other one is the set of local, partial derivatives
up to order n, commonly referred to as the n − jet. The jets are useful descriptors of local
image structure, shown to be related to the processing of visual system [170, 165].
These features are the main focus of this thesis and its application are explained in
detail in following chapters of this dissertation. However, the use of various scale space
texture features used by various other researchers is as follows
In late nineties, Karssemeijer et al. [171, 172] detected the satellite distortions in
mammograms by determining the orientations of the intensity map at each pixel using
a multiscale approach. At a given scale, accurate line-based orientation estimates are
obtained from the output of three-directional, second-order, Gaussian derivative operators. Netsch et al. [173] used Laplacian response denoted as the scale-space signatures
for the detection of clustered microcalcifications in digital mammograms. Petroudi
and collegues [69, 70, 71] showed the effect of responses of the isotropic diffusion and
the maximum responses of the anisotropic diffusion at various scales while evaluating
the effect of HRT on mammograms. Raundahl et al. [174, 175, 176, 177] proposed
texture features based on Hessian at multiple scales in application of quantifying the
effects caused by various hormone replacement therapy (HRT) at least as good as standard methods. Karemore, Nielsen, and Brandt et al. in their consistent experiments
[178, 179, 52, 53, 180, 181, 182, 183, 184, 185, 186, 187], showed the potential of mammographic parenchymal texture techniques on various dataset involving risk assessment
application, they specifically used n-jet features with committee based machine learning
techniques. Rest of the chapters in this dissertation explains these methods in detail.
2.5
Experiments
To investigate the potential of individual texture features discussed in previous section
we use two databases which are widely used by various research groups in mammogram
image analysis research community.
mini-MIAS database [188] is composed by the Medio-Lateral Oblique views of both
breasts of women. This dataset is freely available and has been widely used for mammography classification in many studies [189]. The MIAS database provides annotations
for each mammogram, and one of them is micro-calcification. 23 mammograms with
pixel resolution 200 micron each from normal and micro calcified subjects are taken. The
reason for including only micro-calcification subjects is that, we are interested in patterns
that may have discrepancies in early stage of metastasis in breast and micro-calcification
is one of them. Similar hypothesis is performed by [124] for risk assessment application.
Secondly, we use DDSM database designed by [190]. The primary intension to use
DDSM dataset is to facilitate sound research in the development of computer algorithms
to aid in screening [190]. We use a set which consists of 366 (183 each from normal
and cancer subjects) Medio- Lateral Oblique mammograms from HOWTEKTM scanner
with 12-bit pixel depth and 43.5 microns pixel resolution. Normal cases are formed
for patients with normal exam results that have had previous normal exams in the last
four years. A normal screening exam is one in which no further ”work-up” is required.
Cancer cases are formed from screening exams in which at least one pathology proven
cancer is found [191]. DDSM dataset was decompressed and provided with a agreement
by [192].
2.5.1 Preprocessing
As both MIAS and DDSM dataset were pre-processed by vendor specific algorithms,
hence it is important to correct non-uniform illumination or shading artifacts present if
any using local normalization algorithm that uniformizes the local mean and variance
of an image. We choose Z-score normalization [193] for this purpose. Intensities from
breast region are normalized, and effect of Z-score normalization stratified by cancer
cases and control population can be seen in Figure 2.5.1 for mini-MIAS dataset and in
Figure 2.5.1 for DDSM dataset. Region of Interest is considered for all our experiments
from the central region of the breast where compression during the mammography
procedure is constant and so the thickness of the breast. Many researcher has proven the
importance of this region [57, 164], they referred this region as CTR (Constant Thickness
Region). In our experiment CTR is approximated by a square window of a particular
size with particular breadth and height specified by number of pixels. We choose
window of size 50*50,100*100...500*500. CTR is located with a automatic method where
the centroid of breast region is considered as a origin of a circle that circumscribed the
CTR. By choosing different radius CTR with different size can be generated. This can be
illustrated in Figure 2.5
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0
0
0.2
Control
Cancer Cases
50
100
150
200
250
0
−6
(a) Before Normalization
Control
Cancer Cases
−4
−2
0
2
4
6
(b) After Normalization
Figure 2.4: Effect of Z-score normalization represented by cumulative distributive function of intensities within the breast region between control and cancer case populations
in mini-MIAS dataset
2.5.2 Texture Measurement within CTR
Once CTR is located on mammogram, various texture features are extracted as explained
below
1st order statisics texture features as explained in Section 2.3.1 such as mean, variance,
skewness and kurtosis is computed using image histograms specified by CTR. 2nd order
statistics texture features as explained in Section 2.3.1 are used by building GLCM within
CTR with various angle 0°,45°,90°and 135° between pixel-of-interest and its neighbor
with ordering of values in the pixel pairs as symmetric. Various properties of GLCM
mainly Contrast, Correlation, Energy, and Homogeneity is computed. Fractal features
mainly fractal dimension and lacunarity using box counting method as explained in our
previous work [142] is computed. In addition to Fractal dimension and lacunarity , a
multifractal features are also computed using box counting method as mentioned in [133,
Region
of Interest
Figure 2.5: Constant Thickness Region (CTR) near nipple-areolar region of mammogram
with different size of window is taken into consideration for texture feature analysis
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0
0
Control
Cancer Cases
1
2
3
4
5
0.2
6
7
x 10
(a) Before Normalization
4
0
−6
Control
Cancer Cases
−4
−2
0
2
4
6
8
(b) After Normalization
Figure 2.6: Effect of Z-score normalization represented by cumulative distributive function of intensities within the breast region between control and cancer case populations
in DDSM dataset
194, 131]. fourier features are computed within CTR region for forty different frequency
bands spanned over entire frequency content. Average amplitude of frequencies within
each band is considered as a texture signature. Gabor texture features are computed
within CTR with Gaussian kernel with a width of 5,10...40 pixels following octaves
along x and y direction with sinusoid of 5 different center frequencies equally spanned
over 0 to π4 . Texture signature is computed by the entropy of resultant image after
convolving CTR with respective Gabor kernels in addition to its mean and variance of
intensities. Wavelet features as described in Section 2.4.4 is computed by as described
in [195, 196] with Daubechies wavelet up to level of 64 (db64) is computed. Three
characteristics properties such as coarseness, contrast and directionality as proposed by
[96] is computed from all db levels and represented as a wavelet texture signatures.Run
length texture features are computed by building run-length matrices within CTR as
described in [197, 107] with same parameter as used for building GLCM matrices,
discussed above.
1
2.5.3 Feature Classification and Scoring
From classification trees to neural networks, there are many possible choices for what
classifier to use. The Support Vector Machine (SVM) approach is considered a good candidate because of its high generalization performance without the need to add a-priori
knowledge, even when the dimension of the input space is very high [198]. Intuitively,
given a set of points which belongs to either one of two classes, a linear SVM finds the
hyper plane leaving the largest possible fraction of points of the same class on the same
side, while maximizing the distance of either class from the hyper plane. According to
[199], this hyper-plane minimizes the risk of misclassifying examples of the test set. We
use linear SVM classifier with 10 fold cross validation. For each cross-validation performance is averaged over all possible size of CTR on test data. Performance is evaluated
by computing the area under receiver operative characteristics curve (AUC)[200, 201].
SVM classifier is used for individual texture features and finally used for combined
features. Correlation coefficient of strongest texture feature within each texture group
is computed by non parametric Spearman’s rank correlation coefficient [202] method,
where strongest texture feature is found by rank based feature selection method [203].
Texture analysis and classification is done using High-Performance Computing (HPC)
with 100 nodes, each with average execution time ≈ 3.4 second per image. Matlab [204]
programming is used for all experiments.
1
Texture analysis based on Scale-Space is not included in this chapter since its application on various
datasets will be covered in detail in rest of the chapters of this dissertation
2.6 Results and Discussion
In the present study, we have analyzed the parenchymal pattern of mini-MIAS and
DDSM datasets. Figure 2.7 shows how the performance is varied with respect to the
change of size of ROI over CTR region in task of discriminating mammograms between
micro-calcifications and control populations. Interestingly no feature is seen to have
a stable performance over variable ROI size. This also explains why it is necessary
to average the performance over all ROI size and all folds of cross validation. For a
perticular fold of the cross validation the performances are in Figure 2.8. The Figure 2.1
shows the performance of various texture features are averaged over all sizes of ROI
and all folds of cross validation. The best performance was obtained by Gabor based
texture features with AUC = 0.63 (p <0.05), followed by combined texture features with
AUC = 0.62 (p <0.05) and lowest was Fourier, wavelet and multifractals AUC=0.58.
[205] used a subset of the MIAS database (about 100 images per class) and obtained
a 50 % of correct classified mammograms. While [206] reported the 73 % and used a
subset of 60 images per class. Current finding is in between these two previous findings.
However, it is important to note that, we have taken considered cases only from microcalcification category as depicted as preliminary indication of cancer; obviously it is
difficult to find good classification on these data as compare to other category of cases
within mini-MIAS dataset. Similar experiment is done by [124], where analysis of the
tissue surrounding the MC cluster as depicted on screening mammograms is done by
various texture features for the prediction of malignancy.
While in case of DDSM dataset, the corresponding result as that of mini-MIAS
discussed above dataset is shown in Figure 2.9, 2.10 and Table 2.3. Laws texture features
outperform over other texture features with AUC = 0.66 (p <0.05) followed by wavelet
AUC = 0.64 (p <0.05) and lowest was with second order statistics. While the combine
performance is deteriorated to AUC = 0.53 (N.S.) however, the current performance on
DDSM dataset is in between the results obtained by [206] i.e. 50 % and [69] i.e. 71 % of
correct classification rate.
We believe that the reason of better performance in DDSM as compare to that of
mini-MIAS is due to the fact that the cancer cases within DDSM are taken from the
cancer group where most of them are malignant and due to the fact that the tissue
structure change is more prominent during the development of breast cancer, therefore it parenchymal texture pattern in DDSM dataset is more discriminative than the
subpopulation of mini-MIAS dataset considered in this study.
Tabel 2.2 and 2.4 presents the correlation information of various texture featurs with
each other in mini-MIAS and DDSM dataset respectively. It is worth noting that almost
every texture features are independent with significance, this justifies that different
texture features carries different texture information of mammographic parenchymal
pattern.
0.85
1st order statistics
Second order statistics
Laws
Fractals
Multifractals
Fourier
Gabor
Wavelet
Run length
Combined
0.8
AUC
0.75
0.7
0.65
0.6
0.55
0.5
50*50
100*100 150*150 200*200 250*250 300*300 350*350 400*400 450*450 500*500
ROI Window Size in (pixels * pixels)
Figure 2.7: Area under the ROC curve (Az) values of various texture features applied
on mini-MIAS dataset for a particular fold with respect to the various size of ROI
2.7 Conclusion
In this chapter, we have briefly examined a number of recent and past texture techniques that has been used for mammographic parenchymal pattern analysis for various
applications. We have also examined the potentials of these methods on widely used
databases across mammogram image analysis community. Even with this relatively
restricted emphasis on risk assessment application, there are a vast number of literatures on texture analysis to be considered especially from computer vision and machine
learning research community. There are many different techniques in existence, and
each year many new and improved methods are reported. In addition to breast density,
a mammographic parenchymal texture can provide additional information and should
be considered in future studies. We hope this consideration may improve the quality and accuracy of risk assessment in screening mammogram where mammographic
parenchymal patterns are the area of research.
1
Sensitivity
0.8
0.6
1st order statistics
Second order statistics
Laws
Fractals
Multifractals
Fourier
Gabor
Wavelet
Run length
Combined
0.4
0.2
0
0
0.2
0.4
0.6
1−Specificity
0.8
1
Figure 2.8: Receiver Operative Curve Characteristics of various texture features applied
on mini-MIAS dataset for a particular fold of cross validation
Table 2.1: Performance characteristics of various Texture features on mini-MIAS dataset
Feature
First order statistics
Second order statistics
Laws
Fractals
Multifractals
Fourier
Gabor
Wavelet
Runlength
Combined
a
AUC
0.62
0.59
0.60
0.59
0.58
0.58
0.63
0.58
0.61
0.62
a
(SEM)b
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
Area under the ROC curve (AUC) averaged over all sizes of ROI and all folds of cross validation are
given to indicate the performance of classification between mammograms from micro-calcifications and
control populations b Standard Error of Mean
Table 2.2: Spearman correlation coefficients for strongest validated texture feature in
mini-MIAS dataset
Feature
1st
2nd
Laws
Fractals Multifractals Fourier
Gabor
1st
– 0.62 †† 0.94 †† -0.42 †
0.04 NS
-0.15 NS 0.98 NS
2nd
–
0.56 †† -0.37 †
0.02 NS
-0.21 NS 0.66 ††
Laws
–
-0.34 †
0.03 NS
-0.04 NS 0.96 ††
Fractals
–
0.07 NS
0.07 NS -0.41 †
Multifractals
–
-0.01 NS 0.01 NS
Fourier
–
-0.16 NS
Gabor
–
Wavelet
Run length
Where, † is (p < 0.05) and †† is (p < 0.001) indicates p-value, the probability of
large as the observed value by random chance
Wavelet Run length
0.94 ††
0.56 ††
0.86 ††
-0.41 †
0.10 NS
-0.35 †
0.92 ††
-0.28 †
–
getting a correlation as
-0.23 NS
0.01 NS
-0.20 NS
0.16 NS
0.12 NS
0.32 †
-0.24 NS
–
0.9
1st order statistics
Second order statistics
Laws
Fractals
Multifractals
Fourier
Gabor
Wavelet
Run length
Combined
0.85
0.8
AUC
0.75
0.7
0.65
0.6
0.55
0.5
50*50
100*100
150*150
200*200
250*250
300*300
350*350
ROI Window Size in (pixels * pixels)
Figure 2.9: Area under the ROC curve (Az) values of various texture features applied
on DDSM dataset for a perticular fold with respect to the various size of ROI
1
Sensitivity
0.8
0.6
1st order statistics
Second order statistics
Laws
Fractals
Multifractals
Fourier
Gabor
Wavelet
Run length
Combined
0.4
0.2
0
0
0.2
0.4
0.6
1−Specificity
0.8
1
Figure 2.10: Receiver Operative Curve Characteristics of various texture features applied
on DDSM dataset for a perticular fold of crossvalidation
Table 2.3: Performance characteristics of various Texture features on on DDSM dataset
Feature
AUC
a
(SEM)b
First order statistics
0.55
0.01
Second order statistics
0.53
0.00
Laws
0.66
0.02
Fractals
0.61
0.02
Multifractals
0.54
0.04
Fourier
0.61
0.01
Gabor
0.59
0.01
Wavelet
0.64
0.02
Runlength
0.65
0.01
Combined
0.53
0.04
a
Area under the ROC curve (Az) averaged over all sizes of ROI and all folds of cross validation are
given to indicate the performance of classification between mammograms from cancer cases and control
populations b Standard Error of Mean
Table 2.4: Spearman correlation coefficients for strongest validated texture feature in
DDSM dataset
Feature
1st
2nd
Laws
Fractals Multifractals Fourier Gabor Wavelet Run length
1st
– 0.53 †† -0.12 NS 0.08 NS
-0.12 NS
2nd
–
-0.07 NS -0.01
0.05 NS
Laws
–
-0.39 ††
-0.21 †
Fractals
–
0.26 ††
Multifractals
–
Fourier
Gabor
Wavelet
Run length
Where, † is (p < 0.05) and †† is (p < 0.001) indicates p-value,
large as the observed value by random chance
0.35 ††
-0.56 ††
-0.12 NS
0.30 ††
-0.03 NS
-0.01 NS
-0.14 †
0.68 ††
–
the probability of getting a correlation as
0.18 NS
0.13 NS
-0.28 ††
0.41 ††
0.08 NS
–
0.04 NS 0.42 ††
0.35 †† -0.26 ††
0.04 NS -0.53 ††
0.21 † 0.58 ††
0.06 NS 0.10 NS
0.52 †† 0.54 ††
–
0.18 †
–
Chapter 3
Fractal Dimension and Lacunarity
Analysis of Mammographic Patterns in
Assessing Breast Cancer Risk : A
Longitudinal and Cross-sectional Study
Abstract
Structural texture measures are used to address the aspect of breast cancer risk assessment in
screening mammograms. In this chapter, we investigate whether texture properties characterized
by local Fractal Dimension (FD) and Lacunarity contribute to assess breast cancer risk. FD
represents the complexity while the Lacunarity characterize the gappiness of a fractal. Our crosssectional case-control study includes mammograms of 50 patients diagnosed with breast cancer
in the subsequent 2-4 years and 50 matched controls. The longitudinal double blind placebo
controlled HRT study includes 39 placebo and 36 HRT treated volunteers for two years. ROIs
(CTR region) with a dimension of (250*150 pixels) were created behind the nipple region on these
radiographs. Box counting method was used to calculate the fractal dimension (FD) and the
Lacunarity. Paired t-test and Pearson correlation coefficient were calculated. It was found that
there were no differences between cancer and control group for FD (p = 0.8) and Lacunarity (p =
0.8) in cross-sectional study. In the longitudinal study, FD decreased significantly (p <0.05) in
the HRT treated population while Lacunarity remained insignificant (p = 0.2). FD is negatively
correlated with Lacunarity (-0.74, P <0.001), BIRADS (-0.34, p <0.001) and Percentage Density
(-0.41, p <0.001). FD is invariant to the mammographic texture change from control to cancer
population but marginally varying in HRT treated population. This study yields no evidence
that lacunarity or FD are suitable surrogate markers of mammographic heterogeneity as they
neither pick up breast cancer risk, nor show good sensitivity to HRT.
50
3.1 Introduction
The breast is composed of a mixture of epithelial and fibrogladular tissue together
with fatty tissue [74]. Distribution of this mixture on mammogram is referred to as
the mammographic parenchymal pattern. Fat is radiographically lucent and appears
dark on the image, whereas fibroglandular tissue is radiographically dense and appears
brighter [207]. Mammographic perenchymal patterns are being increasingly used as
intermediate markers in studies investigating the etiology of breast cancer [208, 45].
It is well established that women with radiologically dense breast are at higher risk of
developing breast cancer than women whose breast are radiologically lucent [75, 12]. The
use of Hormone Replacement Therapy (HRT) is currently a subject of debate because of
the possibility of an increase in the incidence of breast cancer and difficulties associated
with breast cancer detection. Although HRT for post-menopausal women improves
quality of life by relieving menopausal symptoms and is thought to have beneficial effects
on osteoporosis, coronary heart disease, and brain function in long-term, the relationship
between HRT and breast cancer is the major reason for women not considering or
discontinuing HRT [208, 209, 14]. Mammographic density is a strong risk factor for
breast cancer. However, whether changes in mammographic density are associated
with risk remains unclear [210, 52, 211] Initial methods for assessing mammographic
density were entirely subjective and qualitative; however, in the past few years methods
have been developed to provide more objective and quantitative computer assisted
density measurements [212, 213]. In past few years researchers are trying to develop
a quantitative measure that can sense the tissue pattern change or density change in
mammograms this mainly includes image texture analysis techniques (see Chapter 2) on
mammograms such as 1st and 2nd order statistics of gray level distribution Laws Energy
[214], Wavelet [215], Gabor[216] and Fractal measure. Although, Fractal measures are
most frequently used in mammogram image analysis in application to mass detection
[217], tissue classification [218] , micro calcification [219], very few researchers [212, 45]
have used fractal for risk assessment particularly in screening mammogram. Among
them the most consistent research outcome is reported by Giger et al. in [66, 67, 11, 57]
where they conclude that a combined group of BRCA 1/2 gene mutation carrier exhibit
a statistically different radiographic fractal texture pattern than a carefully selected low
risk group. This motivates us to validate the fractals and its properties on our casecontrol study where cases are collected prior to detection and also on longitudinal
study including placebo and populations treated with HRT. In this chapter we also
investigates the potential of other fractal measures such as Lacunarity other than fractal
dimension which is not considered in previous fractal related research in mammography
[11, 135, 138, 139].
(a)
(b)
(e)
(f)
(c)
(g)
(d)
(h)
Figure 3.1: Example ROIs extracted from Cross-sectional study set: (a-d) Cancer Cases,
(e-h) Control
3.2 Materials and Methods
Our cross-sectional case-control study [220] includes mammograms (MLO view) of 50
patients diagnosed with breast cancer in the subsequent 2-4 years and 50 matched
controls. The longitudinal double blind placebo controlled HRT study [52] includes 39
placebo and 36 HRT treated volunteers for two years. All mammograms were digitized
and processed for intensity normalization using Z-score normalization [193]. ROIs with
same dimension (250*150 pixels) were selected manually behind a nipple region near
nipple-areola of mammogram. This is done to focus the attention on the most important
region where the change in parenchymal pattern is prominent as reported by Giger et
al. [57]. It also serves a purpose to suppress pectoral muscle which is not a subject of
interest for this analysis. ROI size was kept constant for all images in dataset as shown
in Figure 3.1, 3.2 and 3.3. Fractal dimension and lacunarity of each mammographic
ROI was estimated as described below. All images were registered by thin-plate spline
algorithm with a consistency term [221].
3.2.1 Estimation of Fractal Dimension (DB )
As seen from previous chapter, fractal properties are use to establish a preliminary
estimation of the complexity and intrinsic dimensionality [222, 127]. Although there
(a) (Baseline 1)
(b) (Follow-up 1)
(c) (Baseline 2) (d) (Follow-up 2)
Figure 3.2: Example of ROIs extracted from Longitudinal study (Placebo populations)
(a) (Baseline 1)
(b) (Follow-up 1)
(c) (Baseline 2) (d) (Follow-up 2)
Figure 3.3: Example of ROIs extracted from longitudinal study (HRT populations)
(a)
(b)
(c)
(d)
Figure 3.4: (a) Selection of Constant Thickness Region (CTR) near nipple-areolar region
of mammogram as a region of interest ROI, (b-d) Change in grid caliber with decreasing
box size, the area sampled by any box changed and hence did the count.
Ln count
17
16
15
-5
-3
-4
-2
Ln ε
Figure 3.5: Regression plot to calculate DB
are many fractal measures that has been studied from past few decades [128, 129, 223],
Fractal Dimension (FD) is the most important and frequently used fractal measure in
medical image analysis [224, 128]. There is a wide variety of techniques to estimates the
FD of an image such as power spectrum method [225], covering blanket method [226],
and box counting method [129]. The FD estimation techniques typically differ in their
definition of the scale parameter and measured image characteristics. Consequently,
they produce widely different FD estimates, often capturing different textural image
properties [224]. We adopted box counting method as described in [227, 129]. The basic
procedure to find Fractal Dimension using this method is to systematically lay a series of
grids of decreasing caliber (the boxes) over an image and record data (the counting) for
each successive caliber. The caliber is the size of the boxes in pixels, ϵ, and the number,
N, is the count of boxes that had foreground pixels in them as shown in Figure 3.4.
Determining FD by examining how (N) changes with scale (ϵ) by finding the slope of
the logarithmic regression line between N and ϵ. This is shown as follows,
DB = slope(
log N
)
log ϵ
(3.1)
Figure 3.5 shows a particular regression line for N and ϵ at particular grid position
on ROI.
3.2.2 Estimation of Lacunarity (λ)
Lacunarity [228, 222, 207] is a counterpart to the fractal dimension that describes the
texture of a fractal. It has to do with the size distribution of the holes. Roughly speaking,
2.0
Ln λ
1.5
1.0
0.5
0.0
-5
-3
-4
-2
Ln ε
Figure 3.6: Regression plot to calculate λ
if a fractal has large gaps or holes, it has high lacunarity; on the other hand, if a fractal is
almost translation invariant, it has low lacunarity. Different fractals can be constructed
that have the same dimension but that look widely different because they have different
lacunarity. Lacunarity (λ) is generally based on the pixel distribution for an image, which
we get from scans at different box sizes at different grid orientations. Basic number for
Lacunarity, λ, is
σ
2
λϵ,g = CVϵ,g
= ( )2ϵ,g
µ
(3.2)
Where σ represent standard deviation and µ represents average (mean) of pixels per
box at given size (ϵ) in a box count at a given position (g). Figure 3.6 shows the slope of
the Ln-Ln regression line of λ over all ϵ at particular grid position. To put heterogeneity
from one perspective and one series of grid sizes into an average, the mean (λ or Λ)
from all ϵ sized boxes at a grid orientation, g, is calculated. We have used 1 to 48 pixel
size boxes for each of four grid position on ROI. Both fractal dimension and lacunarity
was calculated using ImageJ[229] with Java plugin FracLac[227].
3.3 Result and Discussion
Table 3.1 shows the characteristics of the cross sectional study populations stratified by
Cancer and Control group. Paired, two tailed t-tests and Pearson correlation coefficient
for various measure were calculated for HRT group as shown in Table 3.2. It was found
that there is no difference between cancer and control group in cross-sectional study
using both FD (p=0.8) and Lacunarity (p=0.8). Whereas our earlier published work,
which will be discussed in next chapter of this dissertation on heterogeneity examination
of radiographs (BC-HER) [230, 231, 232] breast cancer risk score separated these groups
significantly (p=0.002). In the longitudinal study, FD decreased significantly (p <0.05)
in the HRT treated population while Lacunarity remained insignificant (p=0.2). From
Table 3.3 , It is also observed that, FD is negatively correlated with Lacunarity (-0.74, p
<0.001), BIRADS (-0.34, p <0.001) and Percentage Density (-0.41, p <0.001). It is worth
noting that, FD is invariant to the mammographic texture change across control and
cancer population but marginally varying in HRT treated population. This study yields
no evidence that Lacunarity or FD are suitable surrogate markers of mammographic
heterogeneity as they neither pick up breast cancer risk, nor show good sensitivity to
HRT.
3.4 Conclusion
FD does not exhibit difference between cancer cases and control group. Lacunarity
shows no significant change in either of the studies. The conclusion is that ”BIRADS,
Percentage density, and to some degree Fractal dimension may broader relate to changes
in parenchymal tissue structure”.
Table 3.1: Characteristics of the Cross sectional study populations stratified by Cancer
cases and Control group
Cancer Cases (n = 50)
66.68 ± 0.51
66.30 ± 0.48
25.03 ± 0.35
24.86 ± 0.33
2.03 ± 0.01
2.04 ± 0.01
1.07 ± 0.01
1.07 ± 0.01
2.30 ± 0.12
2.07 ± 0.14 ††
0.2 ± 0.02
0.19 ± 0.02†
Data shown Mean± Standard Error of Mean (SEM)
BIRADS [50] (Breast Imaging Reporting and Data System) indicates the radiologist’s opinion of the
absence or likelihood of breast cancer
Age (years)
BMI (kg/m2 )
Fractal Dimension (DB )
Lacunarity (λ)
BIRADSa
Percentage Density
a
Control (n = 50)
Placebo
HRT
.
N.S
.
N.S
100 %
N.S.
p<0.0
N.S.
100 %
N.S.
5
HRT
0
Years
Placebo
0
2
(a) Fractal Dimension
Years
2
(b) Lacunarity
HRT
0.0
p<
100 %
0
HRT
01
.0
<0
Years
(c) BIRADS
p
p<0.001
N.S.
Placebo 100 %
2
01
0
p<0.001
N.S.
Placebo
Years
2
(d) Percent Density
Figure 3.7: Shows longitudinal progression of different measures. Vertical bar indicate
the standard deviation of the mean of the subgroups at 0 and at 2 years. Fractal
Dimension (FD) decreases from baseline to follow up in HRT population and invariant
in Placebo while Lacunarity does not change in both placebo and HRT population.
Table 3.2: Different scorings of mammograms in placebo and HRT groups at baseline
and after 2 years of hormone treatment (Longitudinal study)
Placebo (n = 39)
HRT (n = 36)
Fractal Dimension (DB )
Baseline
Follow up
1.95 ± 0.006
1.95 ± 0.006
1.95 ± 0.007
1.94 ±0.005⋆
Lacunarity (λ)
Baseline
Follow up
1.1 ± 0.01
1.09 ± 0.005
1.1 ± 0.01
1.1 ± 0.008
BIRADS
Baseline
Follow up
2.3 ± 0.12
2.28 ± 0.13
2.08 ± 0.15
2.62 ± 0.15⋆ ⋆ †
Baseline
0.2 ± 0.02
0.19 ± 0.02
Follow up
0.2 ± 0.02
0.29 ± 0.027⋆ ⋆ †
Data shown Mean ± Standard Error of Mean (SEM), ⋆ (p < 0.05) and ⋆⋆ (p < 0.001) indicates significant
difference compared to baseline,† (p < 0.05) indicate significantly larger absolute effect compared with
Placebo or HRT group. All tests are two-sided Wilcoxon rank sum test[233] of different median
Percent Density
Table 3.3: Spearman correlation coefficients and p values of being different from zero in
baseline study of the combined population of the placebo and HRT treated groups
BIRADS
Percent Density
Lacunarity
Fractal Dimension
BIRADS
–
0.93 ††
0.28 †
-0.34 †
Percent Density
–
0.4 ††
-0.41 ††
Lacunarity
–
-0.74 ††
Where, † = (p < 0.05) and †† = (p < 0.001) indicates p-value, the probability of getting a correlation as
large as the observed value by random chance
Chapter 4
A Novel and Automatic Mammographic
Texture Resemblance Marker (MTR) is
an Independent Risk Factor for Breast
Cancer
Abstract
We investigated whether breast cancer is predicted by a breast cancer risk mammographic texture
resemblance (MTR) marker. A previously published case-control study included 495 women
of which 245 were diagnosed with breast cancer. In baseline mammograms, 2-4 years prior to
diagnosis, the following mammographic parameters were analyzed for relation to breast cancer risk: (C) categorical parenchymal pattern scores; (R) radiologist’s percentage density, (P)
computer-based percentage density; (H) computer-based breast cancer risk MTR marker; (E)
computer-based hormone replacement treatment MTR marker; and (A) an aggregate of P and H.
Density scores, C, R, and P correlated (τ = 0.3-0.6); no other pair of scores showed large (τ >0.2)
correlation. For the parameters, the odds ratios of future incidence of breast cancer comparing
highest to lowest categories (146 and 106 subject respectively) were C: 2.4(1.4-4.2), R: 2.4(1.44.1), P: 2.5(1.5-4.2), E: non-significant, H: 4.2(2.4-7.2), and A: 5.6(3.2-9.8). The AUC analysis
showed a similarly increasing pattern(C: 0.58 ± 0.02, R: 0.57 ± 0.03, P: 0.60 ± 0.03, H: 0.63
± 0.02, A: 0.66 ± 0.02). The AUC of the aggregate marker (A) surpasses others significantly
except H. HRT-MTR (E) did not significantly identify future cancers or correlate with any other
marker.Breast cancer risk MTR marker was independent of density scores and more predictive of
risk. The hormone replacement treatment MTR marker did not identify patients at risk.
60
4.1 Introduction
The second most common form of cancer in Europe is breast cancer with an estimated
429,900 cases in 2006 [234], and therefore screening and risk profiling are essential tools
for early detection in order to improve survival [235]. The Gail model [236] is an
established tool to establish the risk of breast cancer in clinical practice. Recent reports
indicate that the addition of breast density and other risk factors to the Gail model may
increase the ability to predict cases of breast cancer [75].
Among the numerous methodologies for density scoring, the categorical density
scoring of the Breast Imaging Report and Data System (BI-RADS) was originally proposed by the American College of Radiology for quantifying masking effects [50]. Before
this, Wolfe patterns [237] were introduced to assess the risk of breast cancer. Both methods rely on an expert’s categorization of the mammographic appearance. Advantages
in terms of a continuous score, but still requiring the interaction of a radiologist, are
provided by an interactive threshold measurement method that expresses the area of
dense tissue as a percentage of the total breast area [40]. Although it is well established
that density measurements are associated with breast cancer risk, still several aspects
are questioned. Hormone therapy is known to increase breast density, certain regimes
are known to relate to breast cancer risk [238], but the degree to which density and risk
are causally related during hormone therapy is not known [239, 240]. Recent studies
have indicated that not just density but also heterogeneity in mammograms is associated with risk [207, 164, 11]. Lastly, the causal relation between risk of breast cancer and
density is at best hypothesized, and the optimal approach to derive information from
mammograms relating to risk of breast cancer is still argued [164, 241].
This motivated us to revisit the derivation of cancer risk from mammograms with
new measures taking not just the density, but also its texture, into account. By applying
computerized pattern recognition techniques [230], the local texture may be assigned
a score that we examine for association to predisposition to develop breast cancer.
Likewise recognition of textures induced by oestrogen treatment may be given a score.
This methodology, unlike measures based on predefined aspects of the texture [207,
164, 11], may recognize any appearing pattern. We investigated the degree to which
texture recognition of local patterns could identify patients at high risk and whether
the information related to and/or increased the power of categorical and/or planimetric
density scoring for prediction of future breast cancer. Furthermore, we analyzed the
relation between recognition of textures relating to hormone replacement treatment and
risk of breast cancer.
0
Please see the disclosure for this Chapter
4.2 Materials and methods
4.2.1 Study population
The study population of 495 women derives from a previously published case-control
study on the effect of recall rate in the Dutch biennial screening program [220]: ”Screening mammograms were collected from five of the nine Dutch regional screening organizations on the basis of their geographic spread. They provided the screening mammograms of 30 consecutive women recently diagnosed with screen-detected cancer, of
30 consecutive women recently diagnosed with interval cancer, and of 60 consecutive
control women without evidence of breast cancer. The women were included in this
study only if screen-negative mammograms from at least two screening examinations
preceding diagnosis were available”. Women participating in this program were asked
to give written informed consent for their data to be used for evaluative purposes. Participants were aged between 49 and 81 years. Of these women 245 were subsequently
diagnosed with breast cancer (123 interval and 122 screen-detected cancers). Mammograms were used from the screening 4 years before diagnosis for screen-detected cancers
and 2-4 years before diagnosis for the interval cancers. Mammograms of 250 women
without breast cancer diagnosis in the subsequent 4 years were used as control. It was
subsequently checked that cases and controls had similar age distributions at the last
screening mammogram before detection (controls 61.3 0.4 years, interval cancers 61.8
±m 0.6 years, screen-detected cancers 61.7 ± 0.5 years). The design of the original study
implied that the first available mammogram was 4 years before this for control and
screen-detected cancers and 2 years before the last screening mammography (hence 2-4
years before diagnosis) for interval cancers was re-used in the present study. A fourcategory scale resembling the BIRADS scale was used: 1: denoting fatty (<5% dense);
2: scattered (5-25% dense); 3: moderately dense (25-75% dense); and 4: extremely dense
(>75% dense) breast tissue.
4.2.2 Radiologist’s percentage density score (R)
Mammograms were scored by a trained radiologist (Paola Petersen) by isolating dense
tissue with a radiologist-selected threshold and the area percentage of dense tissue to
overall breast size was recorded [40].
4.2.3 Computer-based percentage density scores (P)
Breast density and textures were quantified by a computer, as follows: first, the breast
tissue was segmented automatically by finding the breast boundary and the pectoral
muscle [242]. An intensity threshold separating the dense from the non-dense tissue
was automatically determined in a computerised implementation [243], simulating the
approach proposed by Byng et al. [40], but in an operator-independent fashion. The
density score was defined as the area percentage of segmented dense tissue of the
Table 4.1: Ordering of 3-jet features
Nr.
∂x
∂y
1
2
3
4
5
6
7
8
9
10
0
0
1
0
1
2
0
1
2
3
0
1
0
2
1
0
3
2
1
0
total area of the segmented breast (Figure 4.1). Implementation was done with Matlab
software (Mathworks, MA, USA).
4.3 Breast cancer risk mammographic texture resemblance
marker (H)
The textural information in every pixel in the segmented breast is used for scoring
heterogeneity [230]. In earlier studies [52, 53, 244] , the identical methodology was used
for scoring. However, there it was adapted to recognizing texture relating to HRT versus
placebo treatment status instead of future breast cancer status of the subject. Centered
in every pixel location, a collection of Gaussian multi-scale features also called as 3-jet
[170] consisting of all partial derivatives up to third order was recorded at scales 1 mm,
2 mm, 4 mm, and 8 mm. We define the partial derivative of the image, I, at scale, σ, as
∂I
(4.1)
∂x
Where Gσ denotes the Gaussian with standard deviation σ. This is implemented by
analytical derivation of the Gaussian prior to convolution using the fact that G∗∂I = I∗∂G
[170]. The numerical implementation takes advantage of the Fast Fourier Transform and
the convolution is carried out through the Fourier domain [245].
3-jet gives 10 features per scale s with multiple combination of partial derivatives as
shown in Table 8.1.
In addition, pixel location relative to the centre (the point of greatest distance to the
boundary) of the breast was recorded. If the changes we are investigating are localized
this knowledge would help reduce noise from changes in unimportant regions. If
there are important changes in one region simultaneous with important, but manifested
inversely in the conventional features, in another region, this knowledge might improve
Ixσ = Gs ∗
classification dramatically. This array of 6 numbers (texture at four different scales and
two positions parameters) recorded in the individual pixel locations were considered
as a feature vector. In evaluating the performance of the classification of a certain
feature set (set of feature vectors), the data is split up in a training and a test set,
each consisting of 100 cancer and 100 control patients. Standard Sequential Forward
Selection [246] is used as feature selection algorithm with recognition rate quantified as
area under ROC curve (AUC). To gather information on which features are selected, 100
SFS runs are calculated. Each run uses a new random train and test set. Final set of
features are selected by plotting histograms of AUC of 100 runs, features belonging to
maximum AUC are selected as a final features. Different point set consisting of different
number of feature vectors are sampled uniformly throughout the breast region within
mammogram. Typical selection was 1000, 2000,...10000 number of points within each
mammograms. Machine memory only allow maximum up to 10000 points. A pixel
based approximate nearest neighbor classifier (ANN) [247] is used for the scoring in
such a way that, it was counted, how many of the k , most alike arrays originated from
cases versus controls. These counts acted as votes or, respectively, high risk and low risk
(Figure 4.1).where k was chosen from 100,200....500 depending on the number of points.
The reason for using ANN instead of traditional k-NN classifier is that, computing exact
nearest neighbors in dimensions much higher than 8 seems to be a very difficult task. Few
methods seem to be significantly better than a brute-force computation of all distances.
However, it has been shown that by computing nearest neighbors approximately, it is
possible to achieve significantly faster running times (on the order of 10’s to 100’s) often
with a relatively small actual errors [247]. In this approach, the contribution of each of
the k neighbors is weighted according to its distance from the test sample, giving greater
weight to closer neighbors. Hence, the vote of a particular feature vector of point set is
given as
Vote(Feature) =
1∑
1
k
k i=1 ϵ + distancei
(4.2)
Where i = 1,2,...k (number of maximum nearest neighbors selected) and distancei is
the Euclidean distance of the ith neighbor from the test sample. ϵ is used for numeric
stability.
1 ∑
Vote(Feature j )
M j=1
M
Vote(Mammogram) =
(4.3)
where, j = 1,2,....M (number of features sampled within mammogram)
With a number of experiments, it is observed that averaging the votes over all point
set reduces the bias that may occur due to a particular point set of uniform sampling
within mammogram. Hence average vote Vote(Mammogram) is considered as a final
score for a mammogram as shown below
Vote(Mammogram) =
Z
1 ∑
Vote(Mammogramp )
Z p=1000
(4.4)
Where, p = 1000,2000,....Z (number of point set considered for feature sampling within
mammogram)
The test was performed in leave-two-out fashion where data from one control and one
case to be scored were left out simultaneously. In this way subsequent case/control status
was not used when assessing the individual and any bias towards this is eliminated
[248, 230]. Image analysis and calculations were performed with Matlab Software [204].
4.3.1 Hormone replacement treatment mammographic texture resemblance marker (E)
A scoring process identical to the H scoring explained above was used. The only
difference was that the voting was now based on comparison to mammograms from
an HRT trial of women receiving HRT or placebo treatment respectively. This permits
measurement of HRT-texture recognition [230]. This scoring method was shown to
be effective in separating oral HRT and placebo groups, and was significantly better
than the radiologist’s categorical or percentage density scorings [230], but no relation to
cancer was demonstrated. Improvement of marker E is explained in detail in Chapter 7.
4.3.2 Aggregate mammographic marker (A)
An aggregate measure was computed based on all scores using logistic regression. To
avoid multi-colinearity issues scores not contributing significantly to the model were
removed. This was done as a backwards stripping model removing most insignificant
score until all remain significant.
4.4 Statistical Analysis
Data presented are expressed as mean ±SEM unless otherwise indicated. Group characteristics were compared with the non-parametric two-sided Wilcoxon signed rank
test. Different markers were compared with a similar test on the z statistics normalizing
control group scores to zero mean and unit variance. High risk and low risk thresholds
of the individual continuous markers were determined by wo methodologies, either to
reveal stratifications quantitatively identical to those by the categorical scoring (C) or
based on quartiles. Odds ratios for quartiles and for high risk versus low risk and their
confidence intervals were computed with the Mantel-Haenszel 95% confidence interval.
Logistic regression models were used for adjustment for density and for odds ratio per
standard deviation analysis. Differences in odds ratio were tested with likelihood ratio
tests. The area under the ROC curve (AUC), its standard deviation, and significant
differences of AUCs were computed with the method of DeLong et al.[249]. Correlations were computed using Kendall’s τ stratified into diagnosis groups to remove the
influence of diagnosis. The uncertainty in the model of the aggregate mammographic
marker (A) was analyzed for the influence of the individual data points in a leave-one
out fashion. All tests were two-sided and considered significant when p <0.05.
4.5
Results
The radiologist’s categories of dense tissue (C) included 106, 243, 144, and 2 women
respectively. An inherited property from our new use of the original study data [220] is
the 2-year age- elevation in the interval cancer group. Table 4.2 shows patients measurement stratified into controls, interval cancers, screen-detected cancers, and all cancers.
All scores showed higher values in cases than controls, and higher in interval cancers
than screen-detected cancers. The categorical score (C) significantly separated cancer
and control (p = 0.001) and also interval and screen cancers (p = 0.04). Similar results
were obtained for the area percentage (P) (cancer versus control p <0.0001, screen versus
interval cancer p = 0.04). The HRT-MTR score (E) did not separate cancer from control
significantly (p = 0.06), whereas the breast cancer risk MTR score (H) significantly separated cancer and controls (p<10− 6). Neither texture resemblance measure significantly
separated screen and interval cancers ((E) p = 0.23, (H) p = 0.12). The modeling of aggregate score (A) only included P and H after stripping was A = 0.048P + 88.0H − 44.6, by
construction of zero mean and unit variance. The aggregate score (A) separated cancers
and controls at a significance level p<10− 9 . The model parameters had a coefficient of
variation smaller than 1% from leave-one-out testing. Category stratification of patients
(106 women with <5% dense tissue versus 146 with >25%) exhibited an age-adjusted
odds ratio 2.4(1.4-4.1) of future breast cancer incidence. A quantitatively identical stratification (106 lowest (21.4% fractile) versus 146 highest (29.5% fractile) scoring) gave
for R: 2.4(1.4-4.1) P: 2.5(1.5-4.2), E: non-significant, H: 4.2(2.4-7.2), and A: 5.6(3.2-9.8).
The latter is significantly higher than the radiologist’s categorical scores (p = 0.03) or
radiologist’s percentage density (p = 0.01). The stratification into high risk versus low
risk according to the quartiles of the continuous measures (E, R, P, H, and A), resulted
in a significant prediction by all measures in Q4, but only H remained significant after
adjustment for categorical density (C) (see Table 4.3). The z statistics (see Figure 4.2) and
c statistics (area under the ROC curve, Table 4.4) indicated that the power of separating
out cases from control of percentage area scoring (P) was greater, although insignificant,
than the radiologist’s categorical scoring (C). The power of BCR-MTR score (H) was
significantly larger than radiologist’s categorical scoring (C) (z statistics p = 0.0001, c
statistics p = 0.001). The HRT-MTR score was insignificantly different from random
according to the z statistics (p = 0.06), but significantly so according to the c statistics (p
= 0.001). The aggregate scoring had significantly larger power than any other scoring
(z statistics: (E) p<10− 7 , (C) p<10− 4 , (R) p = 0.001, (P) p = 0.004, c statistics: (E) p<10− 6
, (C) p<10− 5 , (R) p<10− 6 , (P) p<10− 6 , except when compared to BCR-MTR score (H)
Table 4.2: Mammographic scorings according to patient stratification
Control
(n=250)
Interval cancers Screen cancers Cancers,all p value of control
(n=123)
(n=122)
(n=245)
Vs cancer cases
E:HRT-MTR
1.61 ± 0.02
C:Categorical
1.97 ± 0.05
R:Radiologist’s (%)
19.7 ± 0.8
P:Area percentage (%) 13.20 ± 0.70
H:BCP-MTR
0.80 ± 0.06
A:Aggregate of P and H -0.31 ± 0.06
All numbers are shown as mean ± SEM
1.67 ± 0.02
2.23 ± 0.06
23.30 ± 1.0
18.10 ± 1.0
1.21 ± 0.08
0.37 ± 0.09
1.64 ± 0.02
2.11 ± 0.06
21.30 ± 0.90
15.7 ± 1.0
1.07 ± 0.08
0.27 ± 0.09
1.66 ± 0.01
2.18 ± 0.04
22.30 ± 0.70
16.90 ± 0.70
1.15 ± 0.06
0.32 ± 0.06
N.S.
<10− 2
<10− 2
<10− 3
<10− 6
<10− 9
Table 4.3: Odds ratio compared to lowest quartile (Q1) age-adjusted and age,density
(C)- adjusted
Q2
Q3
Q4
OR per std
2.3 (1.4-3.8)
N.S.
2.1 (1.3-3.5)
1.2 (1.0-1.5)
N.S.
N.S.
N.S.
N.S.
R: Radiologist’s percentage
N.S.
2.4 (1.5-4.1)
1.7 (1.1-2.9)
1.2 (1.0-1.5)
N.S.
N.S.
N.S.
N.S.
P: Area percentage
N.S.
1.8 (1.1-2.9)
2.3 (1.4-3.8)
1.4 (1.2-1.7)
N.S.
N.S.
N.S.
N.S.
H: BCP-MTR
1.6 (1.0-2.1)
3.1 (1.9-5.2)
3.4 (2.1-5.8)
1.6 (1.3-1.9)
N.S.
2.0 (1.2-3.3)
1.7 (1.1-2.9)
1.3 (1.1-1.6)
A: Aggregate of P and H
1.8 (1.1-2.9)
3.5 (2.1-5.9)
3.8 (2.3-6.5)
1.8 (1.4-2.1)
–
–
–
–
Odds ratio is defined from respectively the highest/lowest F % quantile of the population, according to
the various scores
E: HRT-MTR
(Figure 4.3). HRT-MTR score (E) did not correlate with any other measure in any group.
The various density scores (C, R and P) all correlated in all groups. The texture scores
(E and H) did not correlate with each other and only the computerized density score (P)
had large correlation (τ>0.2) in any category or overall (Table 4.5). The BCR-MTR score
(H) did not significantly correlate with age in either group or full population. Also, we
for the curiosity used size of projected breast as a weak surrogate for weight/BMI and
found no relation either.
4.6 Discussion
Breast density is a strong risk factor for breast cancer [250, 251]. Both radiologist’s
categorical density scores and the computer-automated percentage density scores were
associated with breast cancer with odds ratios of 2.4 and 2.5, respectively (for a <5%
dense versus >25% and similar stratification). These were comparable to earlier findings for similar age distributions where odds ratios of 3.5, 1.8 [252], and 2.0 [253] were
reported. The computer-automated methods deviated from the radiologist’s scoring,
Hetrogeneity
Density
Area %
Low
Low
High
High
BCP-MTR
Score
Low
High
Low
High
Cancer-Like
Control-Like
Figure 4.1: Scoring of various breasts as depicted in mammograms (top) using BCP-MTR
scoring methodology sketched above
1
0.9
**
Normalised Score
0.8
***
0.7
0.5
***
0.4
0.3
***
*
0.6
**
N.S.
0.2
0.1
0.0
HRT-MTR
Cat.
Area %
BCP-MTR
Agg.
Figure 4.2: Normalised scores (Z statistics) of the cancer cases group, significance of
difference from the control group, and significant difference between scores (* p <0.05,
** p <0.01, *** p <0.001)
Proposed BCP−MTR method (H)
0.54
Cancer
Control
0.53
0.52
0.51
0.5
0.49
0.48
0.47
0.46
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Computer−based percentage density (P)
Figure 4.3: Scatter plot between computer-based percent density (P) and proposed BCPMTR method (H) stratified by cancer cases and control group
Table 4.4: Area under ROC (AUC) according to patient stratification
Interval Cases
Vs Control
(n=373)
Scree Cases
Vs Control
(n=372)
All Cases
Vs Control
(n=495)
E: HRT-MTR
0.57 ± 0.03
0.53 ± 0.03
0.56 ± 0.02
(Ý)
C: Categorical
0.60 ± 0.03
N.S.
0.58 ± 0.02
(0)
R: Radiologist’s density
0.60 ± 0.03
N.S.
0.57 ± 0.03
(ì)
P: Percent density
0.63 ± 0.03
0.57 ± 0.03
0.60 ± 0.03
(B)
H: BCP-MTR
0.66 ± 0.03
0.61 ± 0.03
0.63 ± 0.02
(è)
Ý
Ý0ìB
Ý
A: Aggregate of P and H
0.69 ± 0.03
0.63 ± 0.03
0.66 ± 0.02
Ý0ìB
Ý0ìB
Ý0ìB
Ý, 0, ì, B, and è, indicates significantly larger than E, C, R, P, and H respectively with (p <0.05)
Table 4.5: Correlation between the mammographic markers
Control
n=250
Interval cancer
cases (n=123)
C Vs R
0.61
0.52
C Vs P
0.37
0.34
C Vs H
0.18
N.S.
R Vs P
0.30
0.30
R Vs H
0.11
N.S.
P Vs H
0.28
0.30
Kendall’s tau for the cases where p <0.05
Screen cancer
cases (n=122)
Cancer Cases
all (n=245)
All
(n=495)
0.61
0.28
N.S.
0.20
N.S.
0.33
0.57
0.31
0.12
0.25
N.S.
0.33
0.60
0.36
0.17
0.29
0.09
0.31
but correlated with it. This deviation must be further examined to establish their relationship.
The breast cancer risk MTR score showed strong association with breast cancer
relative to the density-based markers, for the overall population in comparing average
scores, in its ability to discriminate cancer status based on the area under the ROC curve,
and comparing tails of the distribution of high versus low risk, showing odds ratios of
[238, 253] depending on stratification. The BCR ˘ MTR score may thereby improve
screening effectiveness, leading to earlier referral and subsequently a better long-term
survival [235].
Breast density is not currently used to assess risk in standard clinical procedures, nor
is it considered a tool for general assessment of breast cancer risk. One reason, on top
of general inertia, may be our inadequate understanding of the possible causal relation
between density and risk and their induced changes. Several studies have shown that
breast density increases with hormone replacement therapy, but to date, there are no
studies that have directly assessed whether the changes relate to the risk of breast cancer
[239, 240]. A low-fat, high carbohydrate diet has also induced changes in density with, as
yet, unknown relation to breast cancer risk [12]. It has been reported [254] that changes
in density as assessed by BIRADS do relate to changes in risk, but not in all studies
[255, 256].
The breast cancer risk MTR score is based on local small scale texture of size less
than 8mm, whereas area percentage measurements include global and large scale structures. A major component in the MTR score is the third order intensity derivative in
the anterior-posterior direction. Since fibroglandular tissue is predominantly oriented
in this direction, the measure captures deviations from the typical tissue orientation
and does not change with the amount of dense tissue, but may reflect the local disorganization or heterogeneity. Area percentage and MTR scores are thus sensitive to
different mammographic appearances that may originate from different biological processes. With regard to density, it has been suggested that this is related to epithelial
and stromal proliferation [257], resulting in a local high turnover with deposition of
collagen and proteoglycan [258] leading to a fibrotic phenotype [259]. This local deregulation may lead to an altered local matrix environment, altered matrix quality, which
has been shown to involve insulin-like growth factor I and matrix metalloproteinasis
[260] and tissue inhibitors of matrix metallo-proteinasis (TIMP) [259]. Such matrix alterations are commonly observed in phenotypical and morphological transformations
of high turnover and cancer [261]. This may well be understood in the context that
the components in the extra cellular matrix (ECM) may not only anchor cells in proper
spatial patterns, but also play important parts in regulating cell morphology, function,
and apoptosis [260]. Mammographic density may therefore include effects of an altered
matrix composition which in turn is associated with carcinogenesis.
The MTR score is associated with local disorganization. The biological understanding
of this being independent from matrix composition (density), may find support in other
connective tissues and pathologies. For example, in bone metastasis a distinct structure
of high turnover bone, woven bone, is found in the periphery of the bone metastasis
in proximity to normal structured laminar bone [262]. Although the protein of these
bone types may largely overlap the functional characteristics are highly and significantly
different [262]. Taken together, proper structures are essential for preservation of cell
function and fate, and therefore early disorganized structure, visualized as increased
mammo-graphic heterogeneity, may reflect the prevalence for tumor genesis of the
local environments. Hence, we may hypothesize that altered matrix composition may
be captured as an increase in density, whereas increased turnover leading to altered
matrix organization may be captured as an increase in the BCR-MTR score. This is
supported by the fact that the measurements seem independently to identify patients
at risk. The aggregate score shows a significantly higher AUC than do the individual
scores and higher odds ratios than does the area percentage density score for almost
all stratifications. Further-more, the significance level of separating out patient groups
by scores was found to be a simple multiplication of the significance levels indicated
by the individual scores. Lastly, virtually no significant correlation was found between
density measurements and the breast cancer risk MTR score. This made us conclude
that density and the risk score provide complementary and independent information
on the individual patient’s breast cancer risk, and may originate in different processes.
The categorical scores and percentage density measures were more indicative of interval
cancers than of screen-detected cancers, although they still were predictive of both. This
agrees with earlier findings that the incidence of interval cancers is to a larger degree
attributable to breast density [253], so that on average they exhibit higher density. The
breast cancer risk MTR scoring showed no difference in value between interval and
screen-detected cancers. Hence, heterogeneity seems unrelated to masking effects of
density (at most 4% of the variation in heterogeneity is explained be density), and may
as such provide additional information, especially for those at high risk.
The present study involves a time horizon of 2-4 years. Yet to be examined is the
state at which heterogeneities appear, to monitor their longitudinal changes, and to
identify the causal relations between the breast cancer risk MTR score and breast cancer.
The hormone replacement treatment MTR score quantifies local texture patterns that
were found to separate out the treatment group from placebo controls in a double-blind,
controlled study [230]. These patterns relate to the local stripiness of the tissue and may
as such relate to the amount of organized and oriented fibrous tissue. In the present
study, HRT-MTR scoring is neither related to density nor to incidence of breast cancer.
This may be seen as indirect evidence supporting the debated hypothesis that density
changes found during hormone replacement treatment need not necessarily relate to
breast cancer risk [239, 240].
Interesting questions lie in the relation to mammographic and breast density, the longitudinal development of scores as well as their relation to treatment effects and subsequent position of localized findings. The breast cancer risk MTR score is fully automated
and has the clinical advantages in terms of reproducibility, objectivity, and scalability,
potentially leading to cost effective and efficient screening of women.Replication of our
findings in other populations will be important prior to its clinical use. Especially the
impact of potential confounders such as ethnicity, body mass index, age, earlier hormone treatment, menopause status, mammographic and digitalization technology and
calibration must be examined and potentially compensated for when quantifying resemblance. Interesting questions lie in the relation to mammographic and breast density,
the longitudinal development of scores as well as their relation to treatment effects.
4.7
Conclusion
Measurement of mammographic texture, possibly arising locally from increased turnover
and subsequent disorganization, provided strong evidence of breast cancer risk. It was
independent and stronger related to risk than density scorings, and as such provided
additional information. Hence, an aggregate measure combining their separate information provided significantly higher risk segregation.
Chapter 5
An Anatomically Oriented Breast
Coordinate System for Mammogram
Analysis
Abstract
We have developed a breast coordinate system that is based on breast anatomy to register female
breasts into a common coordinate frame in 2D mediolateral (ML) or mediolateral oblique (MLO)
view mammograms. The breasts are registered according to the location of the pectoral muscle
and the nipple and the shape of the breast boundary because these are the most robust features
independent of the breast size and shape. On the basis of these landmarks, we have constructed
a non-linear mapping between the parameter frame and the breast region in the mammogram.
This mapping makes it possible to identify the corresponding positions and orientations among
all of the ML or MLO mammograms, which facilitates an implicit use of the registration, i.e.,
no explicit image warping is needed. We additionally show how the coordinate transform can
be used to extract Gaussian derivative features so that the feature positions and orientations are
registered and extracted without non-linearly deforming the images. We use the proposed breast
coordinate transform in a cross-sectional breast cancer risk assessment study of 490 women, in
which we attempt to learn breast cancer risk factors from mammograms that were taken prior
to when the breast cancer became visible to a radiologist. The coordinate system provides both
the relative position and orientation information on the breast region from which the features
are derived. In addition, the coordinate system can be used in temporal studies to pin-point
anatomically equivalent locations between the mammograms of each woman and among the
mammograms of all of the women in the study. The results of the cross-sectional study show that
the classification into cancer and control groups can be improved by using the new coordinate
system, compared to other systems evaluated. Comparisons were performed using the areaunder-the-receiver-operating-characteristic-curve (AUC) score. In general, the new coordinate
system makes an accurate anatomical registration of breasts possible, which suggests its wide
applicability wherever 2D mammogram registration is required.
74
5.1 Introduction
Assessing the breast cancer risk on the basis of a 2D mammogram is a difficult but important problem in medical imaging. Breast cancer risk assessment refers to quantifying
the breast cancer risk for a patient on the basis of a mammogram in which cancer is not
distinguishable to the radiologist. Numerous studies have investigated the relationship
between mammographic density and breast cancer risk, and women with high breast
density appear to have a four- to six-fold increase in breast cancer risk [263, 264, 257].
More recently, it has been suggested that the heterogeneity of the mammogram texture
is also related to the the mammographic risk [231, 142]. However, the link between the
heterogeneity of the mammogram and the breast density with respect to breast cancer
risk is not well understood.
Previous chapter [179, 177] suggests a framework for obtaining accurate and sensitive
measurements of breast density change due to various hormonal replacement therapies
by calculating changes in texture, i.e., examining the heterogeneity of mammograms.
These methods include the calculation of N-jet features [265] or Gaussian derivatives1
up to the order of three in four different scales. The Gaussian derivatives are typically
computed with respect to the image basis vectors, which are aligned with the rows and
columns of the image. However, there are clear disadvantages to expressing coordinates
in the natural image coordinate frame, compared to expressing coordinates relative to
the anatomy of the breast or tissue structures.
Most of the previous approaches for the automated analysis of 2D mammograms
first segment the breast region and then conduct the analysis inside the breast region in
the x,y coordinate system. This is the case even when the mammograms are registered
because the analysis is performed with respect to the x,y coordinate system of the
registered image. However, the x and y-axis directions do not have a direct anatomical
meaning, and due to the variability between the shapes of the breasts, a fixed direction
in one mammogram may anatomically correspond to a completely different direction
in another. In addition, the explicit warping of the images can produce image artefacts
due to image resampling, a result that would not be desirable.
To circumvent the problems above, we have developed an anatomical breast coordinate system that identifies corresponding positions and locations among arbitrary
mediolateral (ML) or mediolateral oblique (MLO) view mammograms. Our starting
hypothesis was that feature registration according to anatomical orientations and positions gives additional discrimination power to feature classification between cancer and
control patient groups in breast cancer risk assessment. Moreover, we believe that it will
help us to characterise and quantify where changes related to the increased cancer risk
occur in the breast, allowing us to further weight the corresponding regions to improve
risk assessment. In addition, our method has wider applicability because the coordinate
0
Please see the disclosure for this Chapter
Gaussian derivatives refer to the image derivatives approximated with the image convoluted with a
selected derivative of the Gaussian kernel.
1
system could be used in any of the traditional mammogram analysis tasks that require
mammogram registration. This method additionally has the potential for novel clinical use, such as helping a radiologist compare temporal mammograms from the same
patient, because the algorithm points out the corresponding regions in the breast (see
Fig. 5.2).
The breast coordinate transform can be seen as a 2D mammogram registration
method2 ; however, due to its construction, there is no need to explicitly warp the
images. Registration artefacts are avoided due to the lack of explicit warping. The
breast coordinate transform can be used both for bilateral registration and for longitudinal registration (see, e.g., [266]). In contrast to the traditional pairwise registration, our
idea is to identify the anatomical coordinate system for the images and to extract the
features from the original images in the orientations and positions defined by the breast
coordinate frame while maintaining the local scales of the images. In other words, we
will define the mapping that defines the local correspondence between breasts as soon
as the their anatomical landmarks, or breast parameters, have been identified. Thus, the
registration here refers to the computation of the breast parameters, which are computed independently for each mammogram; the registration is global in the sense that
the breast coordinate system defines the matching locations and orientations between
all mammograms for which the breast parameters have been identified.
There are several works in the literature addressing the automatic extraction of the
anatomical landmarks. The localisation of the pectoral muscle has been considered, e.g.,
in [267, 268, 269]. The nipple location has been considered in [270, 271, 272, 273, 274, 269]
and the breast boundary in [270, 275, 271, 276, 274]. The automatic finding of these
features is, however, beyond the scope of this work, and the starting point for our work
is that the line approximating the pectoral muscle, the nipple location, and the breast
boundary approximation are known or given manually.
The closest existing work to ours, to our knowledge, is [277], where Georgsson
considered bilateral registration for bilateral comparisons; in addition, there are several
works that address the registration of breasts in three dimensions [278, 279, 280]. Georgsson defined the two-dimensional coordinate system by the distance from the skin-line
and the distance to the nipple-line along an equidistant curve. We instead construct a
nonlinear parametric coordinate system based on a subset of second order curves. Our
coordinate system is minimally identified from the location of the nipple, two points on
the breast boundary, the boundary normal direction at the nipple, and the pectoral line.
Our breast cancer risk assessment system utilising the coordinate system is essentially
constructed as follows. In the training phase, the computer is fed cross-sectional risk
assessment data, i.e., a database of mammograms, one for each patient, where the
image label identifies which patients developed cancer at a later time point and which
patients did not. The computer extracts features of the mammograms with respect to the
2
One can recover the 3D information by taking at least two mammogram images from two directions,
such as the MLO and CC views, and viewing them in stereo. The quantitative problem of finding the
relative pose between the MLO and CC views in 3D, using the disparity between the image pair, is known
as the pose estimation problem and, as our registration is in 2D only, is beyond the scope of this paper.
anatomical coordinate system, selects the features that maximise the separation between
the cancer and control groups, and estimates the risk classifier. In the testing phase, a
novel mammogram is fed into the system, and the features, selected on the training
phase, are extracted with respect to the anatomical coordinate frame. On the basis of
the features, the trained classifier calculates the risk score.
The organisation of this paper is as follows. The construction of the breast coordinate
frame is first discussed in Section 5.2, and then, its numerical implementation is reported
in Section 5.3. Section 5.4 reports how Gaussian derivatives can be computed using
the proposed coordinate frame. The experiments are reported in Section 5.5, and the
discussion follows in Section 5.6.
5.2 Construction of the Breast Coordinate System
In the design of the breast coordinate systam, we require the following properties from
the transform: (1) it should be based on anatomical features available in the mammograms; (2) it should establish point-wise correspondences between different breasts; (3)
the number of parameters should be as small as possible to achieve robustness; (4) the
transform should depend continuously and smoothly on the variations of the shape of
the breast; and (5) the mapping, its inverse, and their Jacobians, should be numerically
computable.
The breast is a mass of glandular, fatty, and fibrous tissues. The breast is composed of
several sections or lobes housing smaller sections or lobules (milk producing glands) that
are linked by ducts (milk passages) extending towards the nipple. The lobules and ducts
are surrounded by fat and fibrous connective tissue that separate the breast tissue from
the skin and the pectoral muscles. The underlying structure of the breast motivates us to
derive a coordinate system for mammograms by considering the anatomical orientation
of the tissues.
We start with the fact that there are three anatomical features in the breast, the nipple,
the breast boundary, and the pectoral muscle, that can be robustly found in each 2D ML
or MLO mammogram. We therefore use these features as geometric reference features
(see Fig. 5.1): we identify the nipple as the 2D point A, we approximate the border of
the pectoral line and the breast tissue as the pectoral line BC, and we identify the breast
boundary as a curve containing the point A. Because only the nipple is identified as a
single 2D point in a mammogram and it has a clear anatomical and geometric meaning,
it is selected as the origin of our coordinate system.
So far in our construction, we have a point-wise correspondence at the nipple, while
the pectoral line forms a line correspondence. To establish point-wise correspondences
between the remaining points, we first note that we need two parameters to continuously parametrise 2D mammograms. Moreover, coordinate lines arising from such
a parametrisation would be non-linear and would furnish a suitable replacement for
(linear) lines, which do not have any direct anatomical meaning. As a line is fully determined by two distinct points on the line, a natural question to keep our coordinate
B
A
C
(a)
B
j
p |BC|
D
(x,y)
j
s|AD|
j0
A
C
(b)
(c)
Figure 5.1: Illustration of the breast coordinate system. (a) The breast parameters are
the landmarks A, B, and C, and the breast boundary normal at A. The points B and C are
the intersections of the pectoral line and the parabolic breast boundary approximations.
(b) The breast coordinates (s, ϕ) of the point (x, y) in the Cartesian coordinate frame
are defined as the relative distance from the nipple along the parabolic line and the
direction of the parabola at the nipple, respectively. The parabola is computed from
the nipple point A, the direction angle ϕ at A, and the point D on the pectoral line,
ϕ
where |BD| = π |BC|. (c) The parabolic breast boundary approximations are in this case
computed from manually selected points defining the nipple, one point on each side of
the breast boundary, and a point defining the breast boundary normal at the nipple; the
pectoral line is fitted to manually selected points on the pectoral line.
system simple and robust is whether there would be a suitable family of curves that we
could solve from three points.
Instead of a family of lines, we selected a family of second order curves as the
candidates for coordinate lines of the breast coordinate transform. A general second
order curve has five parameters (six distinct elements in the symmetric 3 × 3 coefficient
matrix minus the homogeneous scaling), which can be solved uniquely from five points
in a general position on the curve. We pick up the subset of general second order
curves by considering the parabolae (where the discriminant vanishes), which have the
additional constraint that their vertex points are at the nipple. Such parabolae have three
degrees of freedom, i.e., three points, in a general position, are sufficient to uniquely
identify such parabolae.
The remaining anatomical landmark, the breast boundary, is approximated by the
left and right branch of the two parabolae that both have the vertex at the nipple. In
addition, to make the boundary approximation continuous up to the first order at the
nipple, we require that the first principal axes of the two parabolae coincide. To identify
these boundary parabolae, the normal direction at the nipple and additionally one point
on each side of the boundary curve is needed. The intersection points of the parabolic
boundary approximation and the pectoral line are defined as points B and C in Figure 5.1.
The nipple has, both anatomically as well as in our construction, a central role.
Because there is a branch of milk ducts originating from the nipple, to take the breast
anatomy into consideration, we require that a branch of parametric curves coinciding at
the nipple A forms the coordinate lines of the coordinate system. Moreover, because we
have selected the parabolic approximation for the breast boundary curves, it is natural
to define the coordinate lines as the family of parabolae the vertices of which are at the
nipple.
The family of parabolae is parametrised by the angle ϕ ∈ [0, π] between the direction
vector of the parabola at the vertex A and the tangent, parametrised by the angle ϕ0 ,
of the breast boundary at A (see Fig. 5.1b). To make the parametrisation unique, we
need one more constraint equation for the parabolae. We thus require that the uniform
direction span at the nipple A corresponds to a uniform span of the intersection points
on the pectoral line. In other words, we constrain the intersection point D on the line
ϕ
BC and the parabola to lie with the distance π |BC| from B.
To complete the breast coordinate transform, we need another parameter that parametrises
the points on the parabolae. To keep the relative scale of the breast intact and acknowledging the role of the nipple as the centre of our coordinate system, we define the
parameter s as the relative geodesic distance from the nipple to the pectoral line in the
image. That is, s will vanish at A and have a value of unity on the pectoral line, and the
relationship 0 < s < 1 holds between the nipple and the pectoral line.
To summarise, the breast parameters or the distinct points A, B, C and the tangent
direction angle ϕ0 encode the shape of the breast. Given the breast parameters, there is a
one-to-one mapping between the breast coordinate pair (s, ϕ) and the image coordinates
(x, y) within the area defined by the parabolic boundary approximation and the pectoral
line. The details of the numerical computation of this mapping and its inverse will be
considered in the following section.
5.3 Numerical Implementation
5.3.1 Forward Transform
Let us first consider the computation of the forward transform T : X → Ω, where X ⊂ R2
denotes the image area enclosed by the parabolic breast boundary approximation and
the pectoral line excluding the nipple and Ω = (0, 1] × [0, π] such that
( )
( )
s
x
=T
.
(5.1)
ϕ
y
The computation is divided into two parts: finding the parabola C, parametrised by ϕ,
which coincides with the given point (x, y) = (x0 , y0 ), and then solving for the relative
distance s.
To simplify the representation of the parabola, we transform the parabola into the
coordinate frame where the vertex is in the origin and the symmetry axis is the y-axis.
The parabola transforms onto this normalised frame by applying the transform
(
)
(
)
R t
x − xA
′
x =
x ≡ Dx=R
ˆ
0 1
y − yA
(
)(
)
(5.2)
cos(ϕ + ϕ0 ) sin(ϕ + ϕ0 ) x − xA
≡
,
− sin(ϕ + ϕ0 ) cos(ϕ + ϕ0 ) y − yA
to its points, represented in the homogeneous form on the left, where R is the 2 × 2
rotation matrix and t is the 2 × 1 2D translation vector. The parabola in the transformed
coordinate frame then has the form
 y′0

 x′ 2 0

0
′
y0 ′
 0

′
′T 

(5.3)
y = ′ 2 x ⇔ x  0 0 − 1  x′ ≡ x′ T C′ x′ = 0.

2
x0

1
0 −2 0
Hence,
0 = x′ T C′ x′ = xT DT C′ Dx ≡ xT Cx , f1 (x, y, ϕ).
(5.4)
To find ϕ, corresponding to (x, y), we need to find the zero crossing of the function
f1 (x, y, ϕ) with respect to ϕ. The zero crossing is, however, not unique for a given
(x, y); therefore, we perform the search as follows. Let (xD , yD ) be the point intersection
between the line BC and the conic defined by ϕ, and let l be the line that goes through the
point (x, y) and is parallel to the tangent of the boundary parabolae at (xA , yA ). Let (x̃, ỹ)
be the intersection point of the parabola ϕ and the line l, which is on the same branch
of the parabola as (xD , yD ). The search for ϕ is performed by finding the zero-crossing
of the signed distance between the points (x̃, ỹ) and (x, y), in the function of ϕ; this is a
simple one-dimensional search.
As soon as ϕ is identified, we compute the relative geodesic distance s from the
nipple A, normalised so that the point D on the pectoral line has the unity distance along
the same geodesic. In practise, we write the normalised parametric form of the parabola
in the function of the parameter ζ as
 (
( ) 
)
1 0 
ζ
x
−
x
A
=  x′0 2  R
ζ2
y − yA
0 y′
0


( )
( ) ( )
1 0′  ζ
x
x
T


y0 
+ A .
⇔
= R 
2

0 x′ 2 ζ
yA
y
(5.5)
0
Hence,
s=
where
√
(
)2
∂y(ζ)
+
dζ
sabs (ζ) =
∂ζ
0
(
)
√
1 √
= ζ a2 + ζ2 + a log ζ + a2 + ζ2 − a log |a|,
2a
∫
ζ
∂x(ζ)
∂ζ
)2
sabs (ζ)
,
sabs (ζD )
(5.6)
(
(5.7)
and a = y′0 /x′0 2 .
5.3.2 Inverse Transform
Let us then consider the numerical implementation of the inverse transform T−1 : Ω → X,
where
( )
( )
x
−1 s
=T
.
(5.8)
y
ϕ
First, the conic coefficient matrix C corresponding to ϕ is solved by using (5.2), (5.3) and
(5.4), using the point D as (x0 , y0 ).
Next we search for the zero crossing of the implicit function
h(ζ) = s(ζ) − s
(5.9)
with a one-dimensional search. There is a two-fold ambiguity for the zero-crossings,
where the solutions ζ1 and ζ2 are related by ζ1 = −ζ2 . The correct solution is selected
by picking the solution that is on the same branch of the parabola as the point D. The
coordinates (x, y) are then finally obtained from (5.5).
5.3.3 Jacobians of the Transforms
The implicit form of the breast coordinate transform for the corresponding coordinates
(x, y) and (s, ϕ) can be written as
f(x, y, s, ϕ) = 0
) (
)
f1 (x, y, ϕ)
xT Cx
⇔
≡
=0
f2 (x, y, s, ϕ)
s(x, y, ϕ) − s,
(
(5.10)
where we have used the fact that ζ depends on (x, y, ϕ) according to (5.5).
Let us first consider the Jacobian of the forward transform. Locally, we are interested
in the behaviour of the implicit function g : X → Ω, which defines the transform T
locally as the mapping (x, y) 7→ (s, ϕ). Using the implicit function theorem, we find the
Jacobian of the forward transform by setting z = (x, y) and implicitly differentiating
f(z, g(z)) = 0
(5.11)
∂g
∂f
= 0, ⇔ D1 f + D2 f
= 0,
∂z
∂z
(5.12)
on both sides, which yields
where
(
D1 f =
2xT CT2×3
∂s
∂x
∂s
∂y
)
,
 T ∂C

x ∂ϕ x 0 
 ,
D2 f =  ∂s

−1
∂ϕ
(5.13)
and c = vec(C). Thus, the Jacobian of the forward transform is
JT ≡
∂g
= − (D2 f)−1 D1 f.
∂z
(5.14)
The Jacobian of the inverse transform is, similarly,
JT−1 = (JT )−1 = − (D1 f)−1 D2 f.
5.4
(5.15)
Gaussian Derivatives in the Breast Coordinates
When the breast coordinate system is used in image analysis, one may need to extract
Gaussian derivative features from the images with respect to the coordinate frame. We
thus investigate how to compute arbitrary mixed Gaussian derivatives from mammograms so that the derivative directions are attached to a common reference coordinate
frame. In extracting the features, the local scale of the breasts is kept constant as we assume that the local discriminating factors have a fixed physical size, even though breasts
globally have large variability in size. To make aligned feature extraction between different mammograms of different people, we thus match the positions and orientations
using the breast coordinates but do not alter the local scale.
In practice, the positions are matched by computing the features in fixed locations
defined by (sn , ϕn ), n = 1, 2, . . . , N in the parameter space, while the corresponding
image locations (x(sn , ϕn ), y(sn , ϕn )) are computed using the inverse transform T−1 . The
orientations, corresponding to the unit vectors us and uϕ oriented in the directions of the
s and ϕ axes in the parameter space at (sn , ϕn ), are obtained as the column vectors (j1 and
j2 ) of the Jacobian of the inverse transform, evaluated at (sn , ϕn ). To preserve the scale
of the image to be processed, we normalise the orientation vectors to the unit vectors
v1 = j1 /|j1 | and v2 = j2 /|j2 |.
The goal is to estimate the higher order derivatives of the original image in the
directions v1 and v2 by using Gaussian derivatives and a fixed scale on the image plane.
We first consider the case of a single derivative in the direction v1 , corresponding to
the direction u1 in the parameter space. Let θ1 be the polar angle of the vector v1 . The
Gaussian derivative in the direction v1 for the image f is
( )
D
Dθ1 (g ∗ f ) = (cos θ1 sin θ1 ) x (g ∗ f )
Dy
(
)
(
)
(5.16)
T Dx (g ∗ f )
T gx ∗ f
= vθ1
= vθ1
D y (g ∗ f )
gy ∗ f
(
)
≡ vTθ1 ∇g f .
In general, we are interested in an arbitrary mixed derivative
Dθ1 · · · Dθ1 Dθ2 · · · Dθ2 (g ∗ f ) ≡ Dkθ11 Dkθ22 (g ∗ f )
| {z }| {z }
k1 times
(5.17)
k2 times
where the derivative is computed k1 times corresponding to the direction u1 and k2 times
in the direction u2 , where θ1 and θ2 are the polar angles of the direction vectors v1 and
v2 , respectively. Generalising the equations above, we may write
(
)
Dkθ11 Dkθ22 (g ∗ f ) = Dkθ11−1 Dkθ22 (vTθ1 ∇g f )
( ( ( (
))))
= Dkθ11−2 Dkθ22 vTθ1 ∇ vTθ1 ∇g f
) )
( (
(5.18)
= Dkθ11−2 Dkθ22 vTθ1 ∇∇Tg f vθ1
)
(
= Dkθ11−2 Dkθ22 vTθ1 Hg vθ1 ,
where Hg is the second order Gaussian derivative tensor (Hessian). The quadratic form
ij
j
ij
vTθ1 Hg vθ1 ≡ Dg viθ1 vθ1 where Dg denotes the second order Gaussian derivative of the
image with respect to the variables i and j while using tensor notation and the Einstein
summation convention. The tensor notation thus allows us to write
i1 ···ik1 j1 ··· jk2 i1
vθ1
Dkθ11 Dkθ22 (g ∗ f ) = Dg
ik
j
jk
· · · vθ11 vθ12 · · · vθ22 ,
(5.19)
Table 5.1: Mean intensity correlation over the longitudinal study.
Method
Correlation coefficient
Unregistered
0.79
Intensity registration
0.92
Breast coordinate registration 0.918
± 0.04
± 0.02
± 0.007
i1 ···ik j1 ··· jk
2
where Dg 1
is the Gaussian derivative tensor of the order k1 + k2 , containing all
of the mixed Gaussian derivatives of that order. In other words, the mixed Gaussian
derivatives of an arbitrary order in the directions v1 and v2 can be computed as a
contraction of the Gaussian derivative tensor and the unit vectors oriented in the same
directions.
5.5 Experiments
5.5.1 Mammogram Registration
The parameters of the breast coordinate transform, i.e., the three landmark points A, B,
and C and the direction ϕ, were determined as follows. First, the boundary parabolae
were computed by four manually selected points: the nipple A, a point on the upper
and lower part of the breast boundary, respectively, and one more point in the breast
in the normal direction from the nipple. The pectoral line was computed from three
additional manually selected points lying on the boundary of the pectoral muscle in
the mammogram, by least squares fitting. The intersection of the boundary parabolae
and the pectoral line were then computed; from the two pairs of solutions, the pair of
solutions that lay on the respective sides of the boundary normal at the nipple were
selected as the estimates for B and C. The breast coordinates are illustrated in Fig 5.2.
To quantitatively evaluate the breast coordinate transform, we first estimated the
correlation coefficient of intensity values between the baseline and the follow-up mammograms of 37 patients from a placebo group of a longitudinal study [281, 142], assuming
that no significant change in intensity occurred within an interval of 2 years in the placebo
group. We computed the correlation coefficient by using no registration, intensity-based
registration [282, 221], and our proposed breast-coordinate-system-based registration,
using one thousand randomly picked positions inside the breast region visible in the
mammogram. The results are shown in Table 5.1, where the mean correlation coefficient
over the test population is used as the result and the standard error of the mean (SEM) as
the bounds. The results suggest that the anatomical landmarks provide equally prominent but more stable intensity correlation scores compared to the direct intensity-based
registration.
(a)
(b)
Figure 5.2: The breast coordinate mapping can be used, for instance, in registering (a)
the baseline and (b) the follow-up mammograms. The curves plotted on the images
illustrate the breast coordinate lines s = 0.1, 0.2, . . . , 1 and ϕ = 0, π/9, 2π/9, . . . , π.
We further compared the breast coordinate registration, which is what we call the
non-linear system, to two different coordinate systems: (1) the translation-registered
system and (2) the similarity-registered system, which were constructed as follows. The
translation-registered coordinate system is the original image coordinate system where
the origin has been moved to the nipple [283]. In the similarity-registered system, the
nipple is likewise set to the origin. In addition, the mammogram is rotated so that
the pectoral line becomes a vertical line (see Fig. 5.3); the position correspondence is
determined by defining the distance of the pectoral line to be unity from the pectoral
muscle, but the local scales are kept intact in the feature extraction similar to how they
are kept intact in the proposed non-linear coordinate system.
Using the non-linear breast coordinate transform, we then computed gradient orientation histograms, weighted by the gradient magnitude, from a database of 490 mammograms from the Nijmegen case-control study [283]. The gradient orientation, neglecting
the sign of the gradient, was computed in the uniform 58 × 98 grid in a reference mammogram with an increment of ten pixels. The locations of the grid points and sixteen
local orientations in the other mammograms were identified by the breast coordinate
transform and its inverse transform, and the gradient direction was computed by using
the Gaussian derivative filters on three different scales. The gradient weighted orientation histograms are illustrated in Fig. 5.4, where the most frequent gradient direction
at each location is displayed. The gradient orientation histograms reflect the fact that
the breast tissue, outside of the glandular tissue, is in most cases horizontal with respect to the reference mammogram. In addition, the pectoral muscle has its distinctive
tissue orientation as does the glandular tissue region, which has distinctive statistical
behaviour.
We additionally analysed the weighted gradient orientation histograms by estimating
the entropy
16
∑
H(x, y) = −
Pi (x, y) log Pi (x, y),
(5.20)
i=1
h (x,y)+ϵ
where we use the biased estimates3 P̂i (x, y) = 16ϵ+i ∑ hi (x,y) for the orientation probabilities,
i
and 0 < ϵ << 1. The entropy of the orientation histograms is displayed in Fig. 5.5 for
the translation-registered, similarity-registered and non-linear coordinate systems. It
can be seen that the registration of the breasts using the non-linear breast coordinate
system substantially reduces the entropy of the orientation histograms, indicating that
the histograms are less random compared to the unregistered mammograms. Moreover,
the entropy image follows the anatomical structure of the breast.
Finally, we compared different coordinate systems for longitudinal registration by
registering ten pairs of baseline and follow-up mammograms using different, both
landmark-based and global, registration methods (the three landmark-based methods
above, thin plate spline registration with landmarks as in [283], similarity by intensity
By this choice, limn→∞ P̂i (x, y) = Pi (x, y). In addition, for the ideal orientation histogram hi (x, y) =
nδ(i − i′ ), peaked at i = i′ , limn→∞ Ĥ(x, y) = 0.
3
y'
(x'0,y'0 )
1
x'
O'
Figure 5.3: Simplified breast coordinate system for comparison that registers the mammograms into the nipple-centred coordinate system, where the pectoral muscle forms
the vertical line with unity distance from the nipple. The mapping from the Cartesian
system to this coordinate system is the 2D similarity transform x′ = sRx + t, of which the
Jacobian is simply sR, where s, R, and t denote the scaling, the 2D rotation matrix, and
the translation vector, respectively.
(a) σ = 1
(b) σ = 2
(c) σ = 4
Figure 5.4: Gradient orientation histogram, on three different scales, plotted in an arbitrary reference mammogram to which the other mammograms are aligned by the breast
coordinate transform. The black lines illustrate the most frequent gradient orientation
(sign neglected) at each position with respect to the coordinate system of the reference
mammogram. With respect to the reference mammogram, the lower and upper parts
of the breast systematically have the largest gradient in the vertical direction, which
supports the fact that the mammograms have been anatomically registered.
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
(a) Unregistered
(b) Translation
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
(c) Similarity
(d) Non-linear
Figure 5.5: Entropy of the gradient-weighted orientation histogram on the scale σ = 1.
The histogram is scaled so that a uniformly distributed orientation, i.e., a completely
random orientation, has a value of unity (red). An ideal histogram, peaked at only one
direction, has the entropy zero (blue) because in a perfect coordinate system, the image
gradient would have the same orientation (least random) in every mammogram with
respect to the coordinate system. The gradient orientation is least random for the nonlinear registration, especially at the breast boundary approximation close to the nipple,
whereas the orientation is the most random close to the pectoral line.
Table 5.2: Evaluation of Longitudinal Registration
Registration Method
std(d) [pix]
median(d) [pix]
51
36
37
24
93
41
48
51
41
21
20
17
76
31
36
42
Unregistered
Translation
Similarity
Non-linear
Thin Plate Spline [283]
Intensity Least Squares
Normalised Correlation [284]
Mutual Information [285]
least squares, and similarity by normalised correlation [284], were compared through
translation by optimising Mattes’ mutual information [285]). As the ground truth, we
used ten matching feature points (x, y) ↔ (x′ , y′ ) in each image pair inside the breast
region, where the points were manually picked by an expert independently from the
registration, or the points were only used in the evaluation. The points in the followup mammogram (x′ , y′ ) were then mapped into the baseline image coordinates (x̂, ŷ),
and we evaluated the standard deviation and the median of the Euclidean distance
d(x, y; x̂, ŷ) over all of the selected points, which consisted of 100 points. The results are
collected in Table 5.2. It can be seen that the breast coordinate system provides the best
registration, but it also shows that the geometric correspondence is not exact; however,
registration inaccuracy is 17 pixels in the median at best because the 3D features are
non-rigidly projected onto the 2D image planes.
5.5.2
Breast Cancer Risk Assessment
Next, we further evaluated the breast coordinate transform by analysing the separation
of the cancer (n = 245) and control (n = 245) groups in the age-matched cross-sectional
study of 490 images taken from the Nijmegen study, a Dutch screening program (see
Table 5.3). This study is a risk-assessment study, where the case radiographs were taken
two years prior to cancer detection. In addition to the manually picked points that
defined the breast parameters, as described in the previous section, the breast regions
were manually segmented by a radiologist for feature-extraction purposes. The image
set was randomly divided into independent 100–100 training and 145–145 blind test
sets, where the blind test set was only used in evaluating the results.
In the risk-assessment experiment, we compared the proposed non-linear coordinate system to the translation-registered and similarity-registered coordinate systems,
introduced in the previous section, as well as to a hybrid coordinate system. The hybrid system is a combination of the similarity-registered and the non-linear coordinate
Table 5.3: Characteristics and scores of the cross-sectional study
Age (years)
BMI (kg/m2 )
Percentage Density
BIRADS score
Cancer (n = 245)
Control (n = 245)
66.7 ± 0.5
25.0 ± 0.3
0.20 ± 0.02
2.3 ± 0.1
66.3 ± 0.5
24.9 ± 0.3
0.19 ± 0.02
2.1 ± 0.1
Scores refer to the mean ± SEM.
Table 5.4: The four coordinate systems in terms of how they define the position and
orientation correspondence.
Position
Translation
x′ =x + t
Similarity
x′ =sRx + t
Non-linear (s, ϕ)=T(x)
Hybrid
(s, ϕ)=T(x)
Orientation (j1 j2 )
I
1 T
R
s
−1
JT (x)
1 T
R
s
systems, in such a way that the position correspondence is defined by the non-linear
coordinate system; however, the local orientations are defined by the similarity registration. The definitions of the position and orientation correspondence for the four
coordinate systems are summarised in Tab. 5.4, where the orientation vectors are to be
normalised so that v1 = j1 /|j1 |, v2 = j2 /|j2 |.
We extracted Gaussian derivative features at four different scales up to the order
of three (the 3-jet features) [286] in all of the three coordinate systems. The Gaussian
derivatives were computed in the orientations defined in Table 5.4, as described in
Section 5.4. In this way, we obtained 40 features per location in the image, i.e., 10
features of the 3-jet with scales 1, 2, 4, and 8 mm. Resolution of each image while
scanning was 5 pixels/mm, following the guidelines provided in [287]. In addition to
the 3-jet features, we augmented the feature vector with the two element position vector
to encode the spatial location of the Gaussian derivative features with respect to the
coordinate system.
For the features, we used the approximate kNN classifier [288], with k = 100, and
the sequential forward selection (SFS) method [289]. Our feature selection algorithm is
based on greedy sequential selection of the features, extracted at 1000 random positions
inside the radiologist segmented breast region. The SFS selection is repeated on different
50 image subsets of the training data. The entire procedure is then repeated 20 times for
different sets of points, after which the overall best 20 feature sets or committee members,
Algorithm 1 Our Feature Selection Procedure
Require: 100–100 set S as the input
Ensure: The expert committee as the output
for i = 1 to 20 do
Extract the 42 features at 1000 random positions inside the mask in each image
for j = 1 to 50 do
Divide the set S randomly into 50–50 training and 50–50 validation sets St and Sv
Run SFS to find the feature subset L that maximally separates St
Store the feature indices in L into the array F
Compute the AUC-score of L on Sv . A(i, j) ← AUC
end for
end for
Find the 20 highest AUC scores from A and return the corresponding feature sets from
F as the expert committee
on the basis of the area-under-the-receiver-operating-characteristic-curve (AUC) [290]
score on the validation set, are selected to be the expert committee. Our feature selection
procedure is sketched in Algorithm 1.
The feature selection results are summarised in Fig. 5.6, which shows the histograms
of the features selected by the feature selection procedure for all of the four methods.
It can be seen that the similarity-registered, non-linear, and hybrid coordinate systems
have similar histograms, and in all of the methods, the most frequently occurring feature
was the y′ or ϕ derivative on the scale σ2 = 2mm in the 3-jet space. In addition, no
committee member indicated position features in the non-linear coordinate system, but
they appear in the similarity-registered and the hybrid coordinate systems. In addition,
in the translation-based coordinate system, the most often selected features were on the
coarsest scale σ4 = 8mm.
The classification scores were then computed on the blind test data set of the 145–
145 images, each from the cancer and the control group. For random sets of 1000
points inside the manually segmented breast regions and the selected feature subset,
the kNN scores are fused together by computing the mean kNN score over the points
in each image [232] and then using all of the images for computing the AUC score. This
procedure is repeated for 100 different sets of points and all of the feature subsets in
the expert committee; the resulting AUC scores are used as the result. The evaluation
procedure is summarised in Algorithm 2.
The classification evaluation results are shown in Figure 5.7, where we plot the mean
AUC scores over the sets of points, in the function of the committee member. The error
bars indicate the mean ± standard deviation. It can be seen that the variation between
the scores provided by the committee members is relatively high, whereas the variation
over the sets of points is smaller. Figure 5.8 additionally shows the mean ROC curves,
computed over the committee members, as well as their 95% confidence intervals. The
results are finally summarised by computing the mean AUC and the SEM over the
(c) Non-linear
s
L
σ
4
ssφ
Lφφφ
4
σ
Lsφ4
σ
L 4
Lσs 4
σ
Lσssφ
3
Lσφφφ
3
Lσsφ3
s
L 3
Lσ3
Lσssφ
2
σ
Lσφφφ
2
sφ
Lσ2
L 2
Lσs 2
σ
Lσssφ
1
Lσφφφ
1
Lσsφ1
σ
L 1
σ
Ls 1
11
11
10
10
9
9
8
8
7
7
6
6
5
Counts
y’
x
L
L
σ
4
xy
σ
4
yyy
Lσxxy
4
L 4
Lσx 4
σ
Lσxxy
3
Lσyyy
3
Lσxy3
Lσ3
Lσx 3
Lxxy
2
yyy
σ
Lσ2
xy
Lσ2
L 2
Lσx 2
σ
Lσxxy
1
yyy
Lσ1
xy
Lσ1
σ
L 1
Lσx 1
4
4
3
3
2
2
1
1
0
0
σ
L 1
σ
Ly’1
Lσ1
σ
x’
L 1
y’y’ Lσ1
x’y’
Lσx’x’
1
Lσ1
y’y’y’
Lσ1
x’y’y’Lσ1
σ
x’x’y’
Lx’x’x’
1
σ
L 2
σ
Ly’2
Lσ2
σ
x’
L 2
y’y’ Lσ2
σ
x’y’
L 2
x’x’ Lσ2
y’y’y’
Lσ2
x’y’y’Lσ2
σ
x’x’y’
L 2
x’x’x’ σ
L 3
σ
Ly’3
Lσx’3
Lσy’y’
3
σ
Lx’y’
3
Lσx’x’
3
Lσ3
σ
y’y’y’
L 3
x’y’y’Lσ3
σ
x’x’y’
Lx’x’x’
3
σ
L 4
σ
Ly’4
σ
L
4
σ
x’
L 4
y’y’ Lσ4
σ
x’y’
L 4
x’x’ Lσ4
σ
y’y’y’
L 4
x’y’y’Lσ4
σ
x’x’y’
Lx’x’x’
4
x’
y
σ
Ly 1
Lσyy1
Lσxx1
Lσxyy
1
Lσxxx
1
σ
Ly 2
σ
Lyy2
Lσxx2
Lσxyy
2
Lσxxx
2
σ
Ly 3
Lσyy3
Lσxx3
Lσxyy
3
σ
Lxxx
3
σ
Ly 4
σ
Lyy4
σ
Lxx4
Lσ4
xyy
σ
Lxxx
4
Counts
10
10
9
9
8
8
7
7
6
6
Counts
11
(a) Translation
4
4
3
3
2
2
1
1
0
0
φ
Counts
5
σ
L 1
σ
Ly’1
σ
L
1
x’
Lσy’y’
1
Lσ1
σ
x’y’
Lx’x’
1
Lσ1
σ
y’y’y’
Lx’y’y’
1
Lσx’x’y’
1
Lσ1
x’x’x’ σ
L 2
σ
Ly’2
Lσx’2
σ
L 2
y’y’ Lσ2
x’y’
Lσ2
x’x’ Lσ2
y’y’y’
Lσx’y’y’
2
σ
Lx’x’y’
2
σ
Lx’x’x’
2
Lσ3
σ
Ly’3
Lσx’3
Lσy’y’
3
Lσx’y’
3
Lσx’x’
3
Lσy’y’y’
3
σ
Lx’y’y’
3
Lσx’x’y’
3
σ
L 3
x’x’x’ σ
L 4
σ
Ly’4
Lσx’4
σ
Ly’y’
4
Lσ4
x’y’
Lσ4
x’x’ Lσ4
y’y’y’
Lσ4
x’y’y’Lσ4
x’x’y’
Lσx’x’x’
4
s
φ
Lσ1
φ
Lσφφ1
Lσss1
Lσsφφ
1
Lσsss1
σ
Lφ 2
σ
Lφφ2
Lσss2
Lσsφφ
2
Lσsss2
σ
Lφ 3
Lσφφ3
Lσss3
Lσ3
sφφ
σ
Lsss3
σ
Lφ 4
Lσφφ4
σ
Lss4
σ
L 4
sφφ
σ
Lsss4
11
5
(b) Similarity
5
(d) Hybrid
Figure 5.6: Histograms of the selected features, for the mammograms classified into
cancer and control groups, using the expert committee of 20 members. Lσxy1 denotes the
mixed second order Gaussian derivative feature in the directions of x and y on the scale
σ1 . For similarity-registered, non-linear and hybrid coordinate systems, histograms
are similar, while the most commonly occurring feature was the y′ or ϕ derivative on
the scale σ2 = 2mm in the 3-jet space; the translation-registered system favours the
coarsest scale σ4 = 8mm. The position features appear only in the translation-registered,
similarity-registered and the hybrid coordinate systems.
Algorithm 2 Our Evaluation Procedure
Require: Independent test 145-145 set S and the expert committee as the input
Ensure: The summary of the AUC scores as the output
for k = 1 to 100 do
Extract the set F of 42 features at 1000 random positions inside the mask in each
image
for l = 1 to 20 do
Select the feature subset corresponding to the member l in the expert committee
Compute the mean kNN score for the feature subset over the points in each image
Compute the AUC-score from the mean kNN scores, A(l, k) ← AUC
end for
end for
Summarise the AUC scores in A
Table 5.5: Classification scores for the cross-sectional study
Method
AUC ± SEM
p-value
Translation
Similarity
Non-linear
Hybrid
0.619 ± 0.007
0.626 ± 0.009
0.624 ± 0.005
0.632 ± 0.008
10−2
n.s.
n.s.
N/A
committee members; the results are collected into Table 5.5, where we also show the
p-value of the Student t-test by comparing the best method to the others. The mean over
all of the scores showed that the hybrid method yielded the best result; the similarity
registration yielded slightly better scores compared to the non-linear registration, but this
difference was not found to be statistically significant. The lowest score was provided
by the translation registration, as expected, and the difference between the translation
registration and the hybrid method was marginally significant. The corresponding
AUC scores for the radiologist-assisted scoring, i.e., the percent density and the BIRADS
(density) score, were 0.56 ± 0.03 and 0.59 ± 0.03, respectively, which are lower than any
of the four methods above.
5.6
Conclusions
We have presented an anatomical breast coordinate transform to facilitate computerised
analysis of mammograms. The transform defines a one-to-one correspondence between
2D points in mediolateral (ML) or mediolateral oblique (MLO) view mammograms
and the parameter space and can thereby be used both as an implicit and an explicit
mammogram registration method. Because the mammograms are 2D projections of
0.7
0.68
0.66
0.64
AUC
0.62
0.6
0.58
0.56
0.54
Translation
Similarity
Non−linear
Hybrid
0.52
0.5
0
2
4
6
8
10
12
14
16
18
20
Committee Member
Figure 5.7: Mean AUC scores in the function of the committee member. The mean score
is computed over the 100 sets of points, and the error bars indicate the sample standard
deviation around the mean. The plot is summarised in Table 5.5, which shows that the
hybrid method yielded the best mean result, after which came the similarity and the
non-linear registration; the translation registration performed the weakest.
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
Sensitivity
Sensitivity
1
0.5
0.4
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
0
1
0.1
0.2
0.3
1−Specificity
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
Sensitivity
Sensitivity
1
0.5
0.4
0.2
0.2
0.1
0.1
0.4
0.5
0.6
1−Specificity
(c) Similarity
0.8
0.9
1
0.7
0.8
0.9
1
0.4
0.3
0.3
0.7
0.5
0.3
0.2
0.6
(b) Translation
1
0.1
0.5
1−Specificity
(a) Unregistered
0
0
0.4
0.7
0.8
0.9
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
1−Specificity
(d) Non-linear
Figure 5.8: Mean ROC curves (solid line) and their 95% confidence intervals (dashed
line) computed over the 20 committee members.
deformable 3D shapes, the correspondence is approximate as far as individual localisable
3D features are concerned. However, the breast coordinate transform allows a statistical
comparison to be made between arbitrary breasts from similar views, which facilitates,
for example, breast cancer risk assessment.
The breast coordinate transform is constructed by setting the subset of second order
curves, parabolae, as the coordinate lines of the transform. The construction allows
numerical computation of the forward and inverse transforms as well as Jacobians of
the transforms at given positions of the image or the parameter space. The construction
thereby provides orientation correspondence in addition to point-wise correspondence,
which means that features can be implicitly extracted, i.e., without explicitly warping
the mammograms in anatomically registered directions. In our breast cancer riskassessment experiments, the Gaussian derivative features were extracted in this manner.
Our experimental evaluation suggests that the non-linear breast coordinate system
is able to perform anatomical registrations of breasts. This conclusion is based on the
following facts: (1) the intensity correlation between points inside the breast region is
improved in a longitudinal study if compared to cases where the points are not registered; direct intensity correlation-based registration yielded similar correlation scores
but with larger variance. (2) The orientation histograms showed that the registered
gradient directions comply with the anatomical breast tissue orientation; in addition,
the gradient orientation histograms were shown to be less random than they were with
the translation or similarity registration. (3) The registration location error of independently marked breast tissue structure points was smallest by using the breast coordinate
system in a longitudinal registration when compared with several other systems. (4) In
the breast cancer risk assessment experiment, which is essentially feature selection and
classification of the cross-sectional study, the best results were obtained by the method
that used the position features provided by the non-linear breast coordinate system.
In experiments in this paper, the breast parameters were computed from manually
given landmarks. The breast parameters are dependent, to a certain degree, on the points
that are selected e.g. on the breast boundary. This additional source of uncertainty could
be further evaluated and it should be taken into consideration during the selection of
the points. However, it is straightforward to automatically estimate the parameters in
future. In practice, one can use the existing techniques to find the nipple, pectoral line,
and breast–air boundary. The remaining task of estimating the breast parameters is then
to fit the breast air boundary onto the boundary parabolae. We suggest using a more
robust criterion such as M-estimators in this task rather than the least squares; moreover,
we would suggest using more heavy weighting near the nipple because the parabolic
approximation is often less viable on the upper portions of the mammograms.
From breast cancer risk assessment experiments, we made the following conclusions. (1) The hybrid method combining the similarity registration and the non-linear
breast coordinate system yielded the best result. This result suggests that the position correspondence of the non-linear coordinate system is stronger than that of the
similarity-transform-based system; however, the orientation correspondence provided
by the latter is more discriminative. This, in turn, suggests that it is more important to
preserve the linear structures of the breasts than to measure derivative information in the
direction of the coordinate lines of the non-linear system. (2) The similarity transformbased registration yielded slightly better results than the non-linear coordinate system.
The position features were not selected at all in the case of the non-linear system and
quite rarely for the similarity transform-based system, which indicates that the benefit
of the two coordinate systems against the translation registration came from the reference orientation provided by the system. (3) The translation-registration-based system
yielded the weakest result, as expected, because the orientation and position were the
most ambiguous for it.
To summarise, the anatomical breast coordinate system is applicable for breast cancer
risk assessment where the discriminative features are not rotation invariant but need to
be measured with respect to some anatomical reference orientation in the ML or MLO
mammograms. In addition, employing such coordinate transformations for classifying orientation features in mammograms yields better discrimination than radiologistassisted scoring such as BIRADS for density and the percentage density. In principle,
the breast coordinate transform could be additionally extended to cranial-caudal (CC)
views. In contrast to the ML and MLO views, this approach is problematic because of
the absence of the pectoral muscle, which we used as an anatomical landmark. The
extension of the coordinate system for the CC views is thus left for future work.
Chapter 6
A Framework to Determine
Mammographic Regions that Show
Early Changes Due to Development of
Breast Cancer: An Application in Risk
Assessment
Abstract
Recent studies have indicated that not just density but also texture in mammograms is associated
with risk. It is estimated that about ninety percent of breast cancers arise from the ductal and
lobular glands leading to calcification that appears as parallel lines associated with blood vessels.
As such it is worth looking into texture features describing the local orientation of breast tissue in
an anatomically oriented breast coordinate system that is more accurate than traditional image
coordinate system as seen from previous chapters. It is well understood that mammographic
parenchymal pattern change as described by Wolfe, Boyd is indicative of cancer; hence in this
chapter we aim to develop a framework that discovers the mammogram regions where changes due
to breast cancer are most likely to occur. Here, we propose a statistical framework that performs
an automatic scaling and selection of region of interest over score map which was computed with
respect to anatomical breast coordinate system developed in our previous work. This framework
uses nested cross- validation scheme for ROI optimization that makes it possible to investigate
the mammogram regions that show significantly different classification scores between the cancer
and control group. We use independent training and testing sets from the case-control study of
495 women. A subset of these women (245) was diagnosed with breast cancer 2-4 years after the
baseline mammograms. Our experiments suggest that significant regions/patterns that need to
be considered while risk assessment are the region behind the nipple (central part of the breast),
which can be justified by the previous findings by other research groups. We also show the new
sampling techniques called importance sampling guided by these regions/patterns that improve
the classification accuracy in both cross-sectional and temporal study design. In general, this
99
work suggest the region that need to be considered to improve both preclinical and follow-up
screening phases of cancer advancement. However, larger study population is warranted to
validate this hypothesis.
6.1 Introduction
Breast cancer is the most common cancer among women. Early detection of the cancer significantly improves conservative treatment. In recent years mammography has
proved invaluable in the detection and screening of breast cancer that has resulted in
national screening programs for all women in the high risk group [12].
Results from randomized clinical trials and other studies show that screening mammography can help reduce the number of deaths from breast cancer among women
in the age range of 40 to 74 years, especially for those over age 50 [22, 291, 292]. In
many studies, it has been shown that mammographic patterns and their visual assessment are significant indicators of risk for developing breast cancer. Mammographic
pattern is influenced by age, BMI, reproductive factors, and race/ethnicity. The interaction among these factors in predicting breast radiographic pattern, and their association
with the presence of histological markers of increased breast cancer risk is poorly defined [210, 211]. In recent years, parenchymal texture measures have been shown to be
an independent risk factor for breast cancer [26, 56, 58, 59, 179].
Many studies have shown the role of various texture features in applications aiming
at detecting diverse structures in mammograms: microcalcifications [293, 219], speculated lesions [294], tissue classification [295, 296] and tumor characterization as benign
or malignant [297, 298]. Very few studies have been published about the risk assessment
using parenchymal texture measure [59, 56, 58, 299, 300, 179] The studies conducted to
date have not shown specific regions on mammogram during screening that undergoes
changes leading to breast cancer. However, the importance of size and position of ROI
in specific high risk population (BRCA 1/2) have been investigated by Giger et al. [57]
and by Couto et al. in [301]. Frequency of geographical occurrence of tumors on the
mammograms on an interval database is studied by Brown et al. [302]. Meeson et al.
[303] studied the location of true positive and false negative in screen detected database.
Karssemeijer et al. [304] studied the suspicious location on current mammogram with
corresponding location on the prior mammogram. Recently, [305] discovered the significance of nipple-areolar region that induces benign process such as eczema, duct
ectasia, periductal mastitis, adenomas, papillomas, leiomyomas, and abscesses; malignant processes include Paget disease, lymphoma, and invasive and noninvasive breast
cancers.
The approaches mentioned above have the following limitations. (i) The mammographic parenchymal feature (texture) based on breast anatomy is not considered. Also
they consider global texture feature and do not take local information into account.
Texture analysis is performed with respect to the x,y coordinate system, either on the
full segmented breast tissue region [304] or a sub region specified by a rectangular window of the mammogram [57]. It is well known that the parenchymal texture is highly
dependent on the orientation of fibroglandular tissues and anatomy of breast but x and
y axis directions do not have direct anatomical meaning. Due to variability between the
shapes of breast, a fixed direction in one mammogram may anatomically correspond to
a completely different direction in another. Even after image registration, the explicit
warping of images can produce image re-sampling artifacts leading to undesirable results [178]. (ii) Automatic selection of desirable scale (resolution) and size of ROI should
be adjusted according to the location of breast region in the mammogram, as the breast
tissue thickness is variable across the regions due to the compression of breast during
scanning, thereby leading to variable tissue texture orientation [306]. (iii) All these studies were conducted either on diagnostic mammograms or on high risk populations such
as BRCA 1/2. There are relatively fewer studies that consider screening mammograms
for risk assessment; it is clinically more relevant to investigate the region that shows
early changes due to cancer progression within the screening mammograms that are
later found to be cancerous. Early detection of breast cancer with screening mammography implies that treatment can be started earlier in the course of the disease, possibly
before it has spread.
In this paper we propose a statistical framework based on nested cross-validation
for determining region of interest (patterns) in mammograms that undergo structural
changes in breast parenchyma during the development of breast cancer. This framework performs an automatic scaling and ROI selection over the score map which was
computed with respect to anatomical breast coordinate system. We employ nested
cross-validation scheme for ROI optimization in an anatomical breast coordinate system, developed in our previous work.
In addition, we show how these patterns enhance the performance of risk assessment
discussed in previous chapters. We discuss and interpret the anatomical relevance of
resultant patterns. Further, we investigate the potential of these discriminative patterns
by validating them on widely used datasets in mammographic CAD community i.e.
mini-MIAS [188] and DDSM [190, 192]. Building on our previous longitudinal study
[53, 52], we extend the use of discriminant patterns for improving the quantification
of drug treatments with HRT. The chapter is organized as follows: In Section 6.2 we
provide the background of the risk assessment study that motivates this project. In
Section 6.3, we present detailed description of our theory and methods, while Section
6.5 investigates the application of discovered regions on various other studies. We
present our conclusions and discussion in the final section.
6.2 Materials
6.2.1 A Case-Control Study
Our research was motivated by a study population of 495 women derived from a previously published case-control study on the effect of recall rate in the Dutch biennial
screening program [220]. Methodologies for detecting regions that undergo greatest
change in carcinogenesis induced parenchymal patterns hold the key for estimating the
localization of carcinoma within the mammogram. A cornerstone of this work is to find
the regions that show early changes in the mammogram due to development of breast
cancer. In the literature on mammogram image analysis most of the studies are con-
ducted on the following two datasets: DDSM [190] and MIAS [188]. These datasets are
not suitable to investigate early changes in tissue pattern because the mammograms are
collected after cancer detection which implies that the mammographic texture patterns
have already changed. Our experiments warrant that the mammograms be collected
before the histopathological detection (before metastasis). Only pre-metastatic mammograms can allows us to extract patterns that may help in understanding and predicting
future risk of mammograms in screening studies.
In the present study, participants were aged between 49 and 81 years. Of these
women 245 were subsequently diagnosed with breast cancer (123 interval and 122
screen-detected cancers). Mammograms were used from the screening 4 years before
diagnosis for screen-detected cancers and 2-4 years before diagnosis for the interval
cancers. Mammograms of 250 women without breast cancer diagnosis in the subsequent
4 years were used as control. It was subsequently checked that cases and controls had
similar age distributions at the last screening mammogram before detection (controls
61.3 0.4 years, interval cancers 61.8 0.6 years, screen-detected cancers 61.7 0.5 years). The
design of the original study implied that the first available mammogram was 4 years
before this for control and screen-detected cancers and 2 years before the last screening
mammography (hence 2-4 years before diagnosis) for interval cancers. The film-based
mammograms were digitized using a Vidar scanner providing an image resolution of
1500x2500 pixels on 12-bit gray scale and size 50m x 50 m. A contra lateral mediolateral
oblique view was analyzed. Radiologists were blinded to subject outcome. The breast
region was automatically outlined including the boundary to the pectoral muscle [219].
6.3 Computation of Scores
In this section we explain how the mammogram is scored for risk assessment. Section
6.3.1 describes a routine to register all mammograms in a unique breast coordinate
system. Section 6.3.2 presents feature sampling in breast coordinates. In Section 6.3.3
we describe how the parenchymal texture features using 3-jet with respect to breast
coordinate system is extracted and later scored using k-NN classifier.
6.3.1 Registering All Mammograms in an Anatomically Oriented Breast
Coordinate System
In order to find the region of interest that shows early changes due to cancer, one needs
to register all mammograms into a common coordinate system. X-ray mammograms
are 2D projections of 3D volumes which makes it demanding to establish a point correspondence across the mammograms in image coordinates. A common solution to this
problem is mammogram registration, where the nature of the images as 3D projections is
disregarded and the mammogram registration handled as non-linear mapping problem
between 2D images. Most of the previous approaches for the automated analysis of 2D
mammograms, however, first segment the breast region and then conduct the analysis
B
B
φ
|BD| = |BC|
π
D
(x,y)
φ
s|AD|
A
φ0
A
C
C
(a)
(b)
Figure 6.1: (a) The breast parameters are the landmarks A, B, and C, and the breast
boundary normal at A. The points B and C are the intersections of the pectoral line
and the parabolic breast boundary approximations; (b)The breast coordinates s, φ of
the point (x,y) in the Cartesian coordinate frame are defined as the relative distance
from the nipple along the parabolic line and the direction of the parabola at the nipple,
respectively. The parabola is computed from the nipple point A, the direction angle φ
at A, and the point D on the pectoral line, Where |BD|=φ/|BC|.
within the breast region in the x,y coordinate system. However, the x and y-axis directions do not have a direct anatomical meaning, and due to the variability between
the shapes of the breasts, a fixed direction in one mammogram may anatomically correspond to a completely different direction in another. In addition, the obvious warping
of the images due to registration techniques can produce image artifacts due to image
re-sampling, a result that would not be desirable. To address the problems above, we
use the anatomical breast coordinate system [178] that identifies corresponding positions
and locations among arbitrary mediolateral oblique (MLO) view mammograms (see in
Figure 7.1).
6.3.2 Feature Sampling in a Breast Coordinate System
All mammograms are registered intrinsically into a common coordinate system determined by one to one mapping from (x , y) to (s , ϕ). Thus (s , ϕ) define the registered
coordinates across all mammograms. To assess the importance of mammogram regions
as coordinate confederate as possible, we should sample the mammograms at uniformly
3
1000
2.5
Directional angle (Phi)
1200
Y−axis
800
600
400
1.5
1
0.5
200
0
0
2
400
800
1000
X−axis
(a)
1400
1600
0
0
0.2
0.4
0.6
Geodesic distance (S)
0.8
1
(b)
Figure 6.2: (a) A set of n points of sampled uniformly on the mean breast plane in
Cartesian coordinates; (b) The points mapped onto the parameter space that illustrates
the nonlinearity of the coordinate system.
distributed points in the mammograms (not uniformly in the breast coordinates) and we
need to use point sets that are registered across mammograms. An inherent problem in
this task is that the homogeneous point distribution in one mammogram is not uniformly
distributed in another since the mapping provided by the breast coordinate system is
nonlinear. Our solution to this problem is to construct a reference coordinate frame
that is a good compromise across all the mammograms; thus, we compute the mean of
the landmark points (see Figure 7.1) over all the mammograms including both cancer
and control populations and then compute the corresponding mean/average breast parameters. We use mean breast as a reference coordinate frame in such a way that we
generate uniformly distributed samples in the mean coordinate image, which can then
be transferred to the breast coordinates (see Figure 6.2) using the inverse coordinate
transform [178].
6.3.3 Parenchymal Texture Features and Scoring
Every pixel at every (s, ϕ) location within the segmented breast region is scored on
the basis of texture, specifically, mammographic texture resemblance (MTR) measure
[179, 178]. MTR is a collection of Gaussian multi-scale features recorded at scales 1
mm, 2 mm, 4 mm, and 8 mm with respect to anatomical breast coordinate system.
Standard sequential forward selection [246] is used as a feature selection algorithm
with recognition rate quantified as area under ROC curve [200]. The resulting reduced
dimensional feature vectors from feature selection were used in classification. We then
identify how many of the 100 most alike features originated from cases versus controls
using approximate k nearest neighbor classifier [247] with k = 100. These counts acted
as votes for case and control groups. For an individual mammogram, the votes from
all s and ϕ locations represent a score map as shown in Figure 6.3. Image analysis and
calculations were performed using Matlab Software [307].
As a result for each image, we obtain a uniformly distributed score map for all
mammograms in the mean coordinate frame, as Figure 6.3 illustrates.
6.4 Learning of the Relevant Regions
Once we have a score map for all mammograms in a common coordinate frame, a
conventional way of computing scores per mammogram is to take the mean of uniformly
distributed scores within the mammograms, hence making no preference over locations
on the mammograms as described in preceding chapters. However, being agnostic
to the locations reduces the discrimination of the data. A natural question is, which
locations/regions should be taken into account? Therefore, in this section, we present a
method of score selection based on locations i.e. bucketing which is described in Section
6.4.1 and a nested cross-validation scheme in Section 6.4.2.
6.4.1 Bucket Representation
In order to represent relevant regions on a score map, a systematic measure is needed.
To determine the locations that are maximally separable, one straight forward way is
to compare the scores between cancer and control groups, one to one over all possible
s and ϕ locations in mean breast coordinate. However, in this approach we are not
considering the contextual neighborhood scores. In previously published studies, using
spatial-statistical texture measures with contextual pixel classification techniques as described in the review chapter of this dissertation, incorporating spatial information from
neighborhood pixels (long range order interaction) within mammogram have shown a
significant improvement in classification. This motivates us to use some representation
with a specific capacity of holding a score from neighborhood pixels; this is solved by
dividing the mean coordinate frame into rectangular regions, the ”buckets”. Obviously,
next question is the selection of optimal bucket size/scale. We believe that the scale is not
constant throughout the mammogram region. Hence, it is clear that, different bucket
scales are needed for different locations. To circumvent this problem, we introduce the
typical sizes of buckets a priori i.e. 1x1, 2x2, 4x4, 8x8, 16x16, and 32x32 ...nxn pixels,
for example bucket of scale 4x4 means, each mammogram score map is divided into
different buckets of size 4x4 i.e. 16 scores in an parametric space s and ϕ that gives rise
to n/16 buckets over n scores. Similarly, scale size of 1 indicates 1 score per bucket i.e. n
buckets. Since the principal aim of this study is to find out the important region/buckets
across the cancer and control groups, we use the performance criterion as area under
ROC curves between the buckets with same locations on mean breast coordinates. A
typical area under ROC decides the number of buckets to be considered significant ie,
buckets that have area under ROC above a certain number; the threshold, are selected.
Hence, by selecting different scale and threshold, different bucket size with different
locations are considered. Effect of Scale and threshold on bucket selection is shown in
Figure 6.4 and 6.5. Hence, there are two free parameters in the bucket representation of
a score map, scale and threshold, that need to be optimized.
6.4.2 Nested Cross-Validation (Optimizing Scale and Threshold)
In this section, we introduce a nested cross-validation scheme to optimize the scale and
threshold of the bucketing representation to obtain the significant and relevant region
called ’mask’ in mean breast coordinates.
Finding an optimal threshold and scale is equivalent to finding significant buckets
that experience maximum discrimination between cancer and control group. It is worth
noting that, we have three parameters to optimize namely, scale, threshold and the mask.
The Mask is a byproduct of scale and threshold when applied to the particular data with
class labels. From Figure 6.4 and Figure 6.5, we have learned that different masks are
generated by different combination of scale and threshold.
Usually, parameter selection is done in training phase and its evaluation is done in
testing phase. In present study, we have only 125 score map each from cancer and control
set. One way to get the optimal values for given parameters i.e. scale, threshold and
mask is to divide the dataset into training and test sets so that, training set is used to learn
these optimal parameters that can be validated on test set. With sample size of 125 each
per group, it is not satisfactory to divide it into training and testing set considering three
free parameters to be optimized. Moreover, we want these parameters to generalize
to an independent data set in future to guard against Type III error [308, 309]. To
circumvent this problem, a common solution is to use cross validation, thereby data
is used in different partitions, and the validation results are averaged over the rounds.
Optimization of model parameters by generalized cross-validation has its own limitation
[310]. According to the theory of model selection, it is always beneficial to optimize the
complex model for the parameters sequentially. In another words, training data can be
subdivided into two set, where one set is used to optimize for the scale and threshold,
while the other is used to optimize for the mask using optimum value of scale and
threshold obtained from first set.
Thus, we need some framework where procedure for selecting parameter values is
itself a part of optimizing algorithm, hence we propose following nested cross validation
scheme, termed as nested because one cross validation runs within another.
Let Data D be divided into three sets, where first set is used to learn the scale (S) and
threshold (T), The second set is used to learn mask with the help of S and T as obtained
from Set 1, while the third one is used independently to evaluate the performance of
obtained mask. This process mainly involves three steps as follows,
Let data D be divided into three subsets: Dtrain1 , Dtrain2 and Dtest ,
Step 1: if Dtrain1 = (X1 , Y1 ), find (S, T | Dtrain1 )
Step 2: if Dtrain2 = (X2 , Y2 ), find (mask | Dtrain2 , S, T)
Step 3: if Dtest = (X3 ), find (Y3 | X3 , mask)
1
0.8
0.6
0.4
0.2
0
(a)
(b)
1
0.8
0.6
0.4
0.2
0
(c)
(d)
Figure 6.3: (a) An example mammogram from the control group; (b) Corresponding
score map representing the cancer probabilities (likelihood) illustrated in the mean coordinate frame; (c)An example mammogram from the cancer group; (b) Corresponding
score map representing the cancer probabilities (likelihood) illustrated in the mean coordinate frame
0.68
0.68
0.66
0.66
0.64
0.64
0.62
0.62
0.6
0.6
0.58
(a)
(d)
(b)
0.58
(c)
0.68
0.68
0.68
0.66
0.66
0.66
0.64
0.64
0.64
0.62
0.62
0.62
0.6
0.6
0.6
0.58
0.58
0.58
(e)
(f)
Figure 6.4: Figures showing the mask created by selected buckets of varying size
(1,2,4,8,16, and 32)on a typical mammogram score map with respect to constant threshold of area under ROC 0.58
0.68
0.68
0.68
0.66
0.66
0.66
0.64
0.64
0.64
0.62
0.62
0.62
0.6
0.6
0.58
0.6
0.58
0.56
0.58
0.54
0.56
0.52
0.54
(a)
(b)
0.68
(c)
0.68
0.67
0.675
0.66
0.67
0.65
0.665
0.64
0.66
0.63
0.655
0.62
0.65
0.61
0.645
0.6
(d)
0.56
0.68
0.675
0.67
0.665
0.64
(e)
0.66
(f)
Figure 6.5: Figure showing the masks created by buckets of size 4 on a typical mammogram score map with respect to varying threshold of area under ROC from 0.52 to
0.66
Algorithm 3 Nested cross-validation for finding optimal scale and threshold for buckets
selection
Input: Data D divided into 5 disjoint subset D1 , D2 ...D5
Output: WeightMap W, cross-validation scores
Initialize: M = acctrain = acctest = 0
for k = 1 to 5C4 ∗ 4C3 do
Let i1 , i2 ...i5 are the subset indices corresponding to the kth permutation
Strain1 = {Di1 , Di2 , Di3 }
Strain2 = {Di4 }
Stest = {Di5 }
(Ŝ, T̂) = argmax(S,T) AUC(Strain1 , Mask(Strain1 , S, T))
acctrain1 (k) = AUC(Strain1 , Mask(Strain1 , Ŝ, T̂))
acctrain2 (k) = AUC(Strain2 , Mask(Strain2 , Ŝ, T̂))
acctest (k) = AUC(Stest , Mask(Strain2 , Ŝ, T̂))
Mval (k) = Mask(Strain2 , Ŝ, T̂)
end for
WeightMap = Mval
where X and Y represent the data and class labels respectively.
Now let data D of size 125 score maps from each group be divided into 5 disjoint
subsets represented by index {I1 , I2 , I3 , I4 , I5 }. Keeping the size of training set larger than
that of test set we can select 1 disjoint subset as test set and remaining 4 subset as training
set 1 and 2 together. This can be done by selecting 4 subset out of 5 in 5C4 different ways.
Out of 4 disjoint subset, we can select 1 disjoint subset as a training set 2 and remaining
3 subset as a training set 1, ie we can have 4C3 different ways of making training subsets.
Thereby, we can have 5C4 * 4C3 equal to 20 different runs of unique combination of
training set 1, training set 2 and test set. However, there are many possible way to
divide data D into three subsets of different size.
For example, an arbitrary combination can have following subsets
Strain1 = {Di5 , Di1 , Di3 }
Strain2 = {Di2 }
Stest = {Di4 }
The reason for having bigger size of training set 1 than 2 is, training set 1 is use to
optimize for 2 free parameter while training set 2 is use to get a single optimal mask.
For each of these 20 iterations, mask obtained from training set 2 is evaluated on an
independent test set to get test accuracy. Test accuracy is averaged over all runs which
will provide an independent measure of how well the mask with an optimal S and T, fit
on future data. Bucket sizes following octaves are selected such as 1, 2, 4, 8, 16, and 32.
Since the area under ROC can never be less than 0.5 and maximum AUC will be always
lower than 0.70 (previous experience with the data [178, 179]), threshold is initialized
between 0.5 to 0.68, with 0.02 increments.
Algorithm 3 represent the procedure for nested cross validation where, some of the
abbreviations in above algorithms are as fallows
Mask (Data, Scale, Threshold) : This function takes three input i) a data, ii) threshold,
iii) size of buckets. This function provides the binary mask as an output by computing
a selected region govern by threshold and scale of buckets on a given data as shown in
Figure 6.4 and 6.5.
AUC (Data, Mask) : This function computes the area under ROC (Az) on the data
using the mask created by particular scale and threshold.
acctrain = Accuracy on training dataset.
acctest = Accuracy on test dataset.
Steps corresponding to particular iteration of cross-validation is shown as a block
diagram in Figure 6.6.
6.5 Experiments
6.5.1 Nijemengen Study
The dataset used for breast cancer screening study as described in Section 6.2 is considered for evaluating the proposed framework. Score maps from 125 images each from
cancer and control groups are generated by sampling 5000 points in a mean breast coordinate system. Formation of weight map by union of masks obtained in all iteration
of crossvalidation is shown in Figure 6.7 followed by anatomical relevance of weight
map for Nijmegen study. As seen from Figure 6.6, each iteration of cross validation produces a single mask obtained from Strain1 and Strain2 . The performance of each iteration
of nested cross validation on Stest is shown in Figure 6.8. Here, even if we consider the
scores corresponding to relevant region described by the obtained mask, it is important
to note that, these scores were generated from the k-NN (k-d tree) which was trained
on all 5000 locations distributed over the entire mean breast. In other words, merely
averaging the scores of Stest within the mask will not provide an accurate evaluation
but we need to retrain the k-d tree using the points sampled only within the mask and
generate the score of Stest accordingly. We call this new sampling of points in mean
breast as a Importance Sampling, the word importance because some regions are given
more weight (importance) while re-sampling. It is very similar to the term importance
sampling used in statistics where, the idea behind importance sampling is that certain
values of the input random variables in a simulation have more impact on the parameter
being estimated than others. It is a classical variance reduction techniques for increasing
the efficiency of Monte Carlo algorithms for estimating integrals [311]. It is different
from the previously used uniform sampling throughout the mean breast coordinate.
From Figure 6.8, it is also important to note that, in each iteration the performance on
Stest after importance sampling was better than the uniform sampling. Also the training
accuracy of set 2 is lower than that of set 1 since optimization of S and T is done only on
training set 1 while optimal S and T is validated on training set 2.
Training accuracy
Optimal S and T
Test accuracy
Step 2: Selecting optimal S & T
pair corresponding to maximum
classification accuracy
Step 4: Generating mask
using optimal S & T pair
on training set 2 along
with training accuracy
Figure 6.6: Flow diagram of steps involved in a particular iteration of a nested crossvalidation
Table 6.1: Effect of importance sampling on test set of Nijmegen study
Method
a
AUC ± SEMb
95œCIc
With uniform samplingd
0.54 ± 0.002
[0.537 0.544]
With importance samplingd
0.59 ± 0.010
[0.570 0.610]
With uniform samplinge
0.63 ± 0.001
[0.631 0.634]
With importance samplinge
0.65 ± 0.001
[0.646 0.651]
a
Areas under the ROC curve (Az) are given to indicate the performance of classification between cancer
and control of test set with uniform sampling and with importance sampling using weight map. It is
average over all performances obtained in all iterations of cross-validation. b Standard error of mean. c
95 Confidence interval. d Performance on test set averaged over all 20 iterations of cross validation. e
Performance on test set when acting as an independent data ; averaged over all committee members as
described in [178]
In our previous work [178], we reported the highest AUC of 0.632 with standard error
of mean 0.008 amongst four suggested breast coordinate systems for a set of images from
Nijmegen study. That experiment was done using uniform random sampling with 1000
points within the individual breast coordinate system and evaluated on independent test
set consisting of 145 cases each from cancer and control. To benchmark the performance
of our importance sampling with respect to uniform random sampling we repeated
the experiment on same test set for various number sampling points starting from
1000, 2000...10000 points and compared their performance with Area under ROC (AUC)
with standard error. In each iteration, AUC for importance sampling is significantly
more than that for uniform sampling. Here, it is important to note that, results with
importance sampling is slightly biased since weight map is a union of all masks taken
from 20 iterations of cross-validation over test set consisting of 125 cases each from
cancer and control set which was also a part of test set that was used in previous study.
It is noteworthy that the test accuracy using importance sampling is lower than that of
previously published result (see Figure 6.8); this may be due to the smaller sample size,
as in each cross-validation iteration test accuracy is computed over only 25-25 set. It is
also evident that the improvement in test accuracy is consistent and independent of the
number of sampling points. This may help in understanding the trends of improvement
in the performance due to importance sampling for future studies.
6.5.2 mini-MIAS dataset
mini-MIAS database [188] is composed by the medio-lateral oblique (MLO) views of
both breasts. The MIAS database provides annotations for each mammogram, and
one of them is micro-calcification. 23 mammograms with pixel resolution 200 micron
each from normal and micro calcified subjects are taken. The reason for including
only micro-calcification subjects is that we are interested in patterns which may have
discrepancies in early stage of metastasis in the breast, and micro-calcification is one
of them. We are interested in investigating the performance of the patterns learned
1
0.8
0.6
0.4
0.2
0
(a)
Upper
retroglandular
region
Pectoral
muscle
region
Central region
Lower
retroglandular
region
Skin edge
region
Chest wall
region
(b)
Figure 6.7: (a) Union of all masks obtained in individual iteration of cross validation
forms estimated weight map with probabilities of important region of maximum separation between cancer and control within breast region in MLO view of mammograms;
(b) Anatomical locations on the breast in MLO view of mammograms
Accuraccy measure as a area under ROC
0.75
Training accuracy for set 1
Validation accuracy for set 2
Test accuracy using importance sampling
Test accuracy using uniform sampling
0.7
0.65
0.6
0.55
0.5
2
4
6
8
10
12
14
16
18
20
Iteration number during nested cross−validation
(a)
Accuracy measure as a area under ROC
0.7
Test accuracy using importance sampling
Test accuracy using uniform sampling
0.69
0.68
0.67
0.66
0.65
0.64
0.63
0.62
0.61
0.6
1000
2000
3000
4000
5000
6000
7000
8000
9000 10000
Number of sampling points
(b)
Figure 6.8: (a)Training and test performance over each iterations of cross validation;
(b) Performance using previously published uniform random sampling and proposed
importance sampling on 145-145 test set sampled with various number points with error
barsa
a
Error bars indicate standard error as computed by DeLong test[249]
Table 6.2: Effect of importance sampling on mini-MIAS dataset
a
AUC (SE)b
Method
95œCIc
With uniform sampling
0.89 (0.046)
[0.76 0.96]
With importance sampling
0.92 (0.040)
[0.79 0.97]
a
Areas under the ROC curve (Az) are given to indicate the performance of classification between mammograms from micro-calcifications and control populations with uniform sampling and with importance
sampling using weight map. b Delong test for the calculation of the Standard Error of the Area Under the
Curve (AUC)[249] c Binomial exact Confidence Interval for the AUC[312]
Table 6.3: Effect of importance sampling on DDSM dataset
Method
a
AUC (SE)b
95œCIc
With uniform sampling
0.63 (0.049)
[0.54 0.71]
With importance sampling
0.60 (0.051)
[0.50 0.68]
a
Areas under the ROC curve (Az) are given to indicate the performance of classification between mammograms from micro-calcifications and control populations with uniform sampling and with importance
sampling using weight map. b Delong test for the calculation of the Standard Error of the Area Under the
Curve (AUC)[249] c Binomial exact Confidence Interval for the AUC[312]
from Nijemegen study on subjects with micro-calcification and normal populations.
Images are preprocessed and annotated with landmark points to form breast coordinate
system. Score maps within breast coordinates are obtained with both uniform sampling
and importance sampling as done in Nijmegen study. The performance of classification
between normal and cancer subjects with micro-calcification for uniform and importance
sampling are shown in Table 6.2.
6.5.3 DDSM Study
The primary purpose of DDSM database [190] is to facilitate a sound research on the
development of computer algorithms to aid in screening. We use a set which consists
of 366 (183 each from normal and cancer subjects) mammograms with MLO views from
HOWTEKTM scanner with 12-bit pixel depth and 43.5 microns pixel resolution. Normal
cases are formed for patients with normal exam results that have had previous normal
exams in the last four years. Cancer cases are formed from screening exams in which at
least one pathology proven cancer is found. Images were preprocessed and provided by
[192]. Images were annotated for landmarks to form breast coordinate system followed
by score maps in parametric breast coordinate frame with respect to Nijmegen dataset.
The performance of classification with uniform sampling and with importance sampling
is shown in Table 6.3.
6.5.4 Longitudinal Study
The benefits of hormone replacement therapy (HRT) in postmenopausal women are
well known. However, some studies have reported a link between long-term HRT
use and cancer risk [14, 313, 15, 209]. This motivates us to see the applicability of the
pattern that show early changes in Nijmegen study that may affect the performance
of detecting the pattern change during the HRT treatment. Our longitudinal double
blind placebo controlled HRT study includes 36 volunteers for treated with transdermal
estradiol two years and monitored from baseline to follow-up. Right MLO views with
pixel resolution 200 micron are taken. Images were annotated for landmarks to form
breast coordinate system followed by score maps in parametric breast coordinate frame
with respect to Nijmegen dataset. Computation of score maps is the same as described
in [186, 178]. The performance of classification between baseline and follow-up for
uniform and importance sampling is shown in Table 6.4.
6.6 Discussion and Conclusion
The main contribution of this chapter is a statistical method that learns the weight map
with an automatic scale selection over score map, stating how different regions should be
weighted in cancer-control classification tasks with importance sampling. The novel use
of nested cross-validation scheme makes no assumptions about the distribution of the
data unlike other methods that rely on untenable assumptions about statistical distributions which makes this method generally applicable to different kinds of discrimination
image analysis tasks, where the training class labels are available.
However, others have investigated the significance of different regions of interest
on mammograms in more conventional way. Giger et al. [57] detected regions by
dividing mammograms in to five compartments by a rectangular bounding box in
image coordinates. They showed with fractal features, the region behind nipple is more
discriminative between high risk patient (BRCA 1/2) and controls, while [303] divided
the breast into different region by the frequency of occurring of tumors and, found that
the occurrence of tumor is more in the central region i.e. behind the nipple-areolar region
in MLO views. [302] also had similar findings. [303] showed that the central part of
Table 6.4: Effect of importance sampling on longitudinal HRT study
Method
a
AUC (SE)b
95œCIc
With uniform sampling
0.55 (0.07)
[0.43 0.67]
With importance sampling
0.57 (0.06)
[0.44 0.68]
a
Areas under the ROC curve (Az) are given to indicate the performance of classification between mammograms from micro-calcifications and control populations with uniform sampling and with importance
sampling using weight map. b Delong test for the calculation of the Standard Error of the Area Under the
Curve (AUC)[249] c Binomial exact Confidence Interval for the AUC[312]
the breast on MLO view of mammograms contributes to the frequency of 63% in screen
and detected cancers followed by upper retroglandular region, chest wall band and skin
edge. Interestingly, the weight map (see Figure 6.7) generated from the present study
strongly supports these findings where the region behind nipple-areolar tissue in MLO
view is most discriminative. We believe that the proposed method is more descriptive
and indicative than the previous findings due to the anatomical correspondence of each
and every location across mammograms in the breast coordinate system. The reason for
the central part being the most discriminative could be the presence of constant thickness
region under the compression plate on the breast while acquiring a mammogram. This
might influence the parenchymal texture within the central part to be more indicative
and consistent. Constant thickness region (CTR) is also reported by Manduca et al.
and Heine et al. [164, 314] being the most important while extracting various texture
features from screening mammograms. Giger et al. [57] also demonstrated the statistical
decrease of performance as the ROI location was varied from central region immediately
behind the nipple.
This work also shows the improvement in the performance of discrimination between
cancer and control in Nijmegen study than in our previously published results [178].
This improvement is due to the importance sampling and motivated by the discovery of
patterns generated by nested cross validation. This suggests that the anatomical correspondence plays an important role while considering the mammographic parenchymal
texture analysis which currently an interesting topic within the mammogram image
analysis community for developing various imaging biomarkers.
In this chapter we have verified the general applicability of the discovered pattern on
several datasets, widely used in mammogram image analysis community. This method
showed the trends of improvement in discriminating between normal and cancer cases
with microcalcification in mini-MIAS study as discussed in Section 6.5.2. Though this
improvement was not statistically significant and this may be due to the limited sample
size as limited sample size has been reported to affect the comparison between the
AUC as suggested by Hanely et al. [315]. It is worth noting that, cancer cases in
mini-MIAS study are taken from those cases for which mammograms are detected
with microcalcification only. Recent findings [316] has shown the strong correlation
between the microcalcification and early stage of metastasis in the breast and explores
the hypothesis that breast calcification composition is directly related to the local tissue
pathological state. Similarly [317] support the theory that breast tumors associated with
casting-type calcifications at mammography comprise a disease entity which exhibits
significantly more aggressive behavior and a poorer outcome than do cancers with
other mammographic tumor features. Therefore, it is probable that mini-MIAS dataset
with cancer cases exhibiting microcalcification will have parenchymal texture pattern
similar to cancer population in Nijmegen study. This is a likely explanation for the
improvement in performance. Our result on mini-MIAS study resembles with findings
by [124] where texture analysis of tissue surrounding microcalcification in mini-MIAS
data shown promising results in computer-aided diagnosis of breast cancer.
On the contrary, in DDSM dataset the performance deteriorated with importance
sampling as shown in Section 6.5.3. However, this drop in performance is not statistically significant. The mammograms from cancer population within the DDSM study
are collected after the detection of tumor and majority of the histopathology results
are malignant (>80 %). The DDSM was tested and scored based on the parameters
(patterns) learned from Nijmegen study which only includes mammograms collected
2 years prior to metastasis. As such we believe that any changes in mammographic
parenchymal texture pattern that might have occurred and progressed (metastasized)
in other locations of the breast might not show up in pre-metastasis mammograms (Nijmegen study). This can be a reason for the performance drop on the DDSM dataset.
However, this hypothesis must be validated on other studies similar to DDSM.
In the longitudinal study, our results show an improvement in detecting the significant change of parenchymal texture from baseline to follow-up during in the population
undergoing HRT treatment than the placebo. This result also supports the hypothesis
that HRT may influence the tissue structure in the breast. However, whether this change
of tissue structure is related to breast cancer risk is not clear. Similar finding is suggested by other research groups [318, 313]. This result also warrants that the regions be
monitored in CAD systems while considering the parenchymal texture pattern in future
studies involving temporal drug treatments.
We hope our study result will support the general application of this framework, and
extension thereof, to the diverse image analysis applications where textures related to
anatomical correspondence are significant. We believe this contribution will improve the
mammographic image processing especially in quantifying the risk assessment using
parenchymal textures.
Part II
Chapter 7
Quantitative Imaging and Visualization
Through Structure Enhancing Diffusion
Applied to Longitudinal Study
Involving Hormone Replacement
Therapy (HRT)
Abstract
Breast density is considered as a structural property of mammogram that can change in various ways explaining different effects of medicinal treatments. Short term hormone replacement
therapy (HRT) use is well established for menopausal symptom relief while the benefits and risks
of long term HRT remain controversial. Previously our mammographic parenchymal texture
measure has been validated on various studies involving HRT such as raloxefene, estradiol,
trimegestone (oral HRT), progesterone (nasal HRT) [230, 52, 53]. The aim of this chapter is to
provide a framework for obtaining more accurate and sensitive measurements of mammographic
parenchymal pattern change that relate to specific effects like Hormonal Replacement Therapy
(HRT) and aging. Given effect-grouped patient data, we demonstrated how the structure tensor and structure enhancing diffusion with its coherence features computed in an anatomically
oriented breast coordinate system followed by a statistical learning scheme provides a non subjective and reproducible measure, as compared to the traditional BIRADS and computer aided
percent density measure. We also demonstrate how the orientation of breast parenchyma changes
in population undergoing HRT treatment vs. placebo over time. This framework facilitates
radiologist to assess longitudinal changes in mammographic parenchymal pattern in one to one
correspondence across temporal mammograms of a subject thereby guide them to evaluate an
individual risk.
122
7.1 Introduction
Several approaches to the automatic methods of assessing mammographic breast density
have been suggested [242, 40] All of these aim either at reproducing the radiologist’s
categorical rating system or at segmenting the dense tissue to get a percentage density
score. Our approach differs from existing methods in three ways. (i) Breast density is
considered a structural property of the mammogram that can change in various ways
explaining different effects. (ii) The measure is derived from observing a specific effect
in a controlled study. (iii) The measure is invariant to affine intensity changes and
more accurate since it consider the tissue orientation of breast parenchyma visible on
mammogram with respect to anatomical breast coordinate system. It is worth noting
that, we do not aim at measuring what is traditionally called breast density, i.e. the
relative amount of fibro-glandular tissue. Since the term mammographic density is most
often used for this type of measure (see [313, 319]), we will use the term mammographic
pattern to describe more general properties of the mammogram. We will show that
mammographic changes can be perceived as a structural matter that may be accessed
ignoring the actual brightness of the images and that it changes differently under the
physiological processes of aging and HRT. The chapter is organized as follows, Section
7.1, gives an introduction of various methods related to proposed work and motivation.
In Section 7.2, gives a description of data to which we apply our proposed framework.
Section 7.3, deals with construction of breast coordinate system followed by proposed
feature extraction techniques such as Structure tensor and diffusion tensor coherence.
In Section 7.6, we discuss the result followed by application of proposed framework to
the breast cancer risk assessment and its significance to radiologist. In Section 7.7, we
provide conclusions and delineate some possible directions for future research.
7.2
Material
The data used in this work is from a 2-year randomized, double-blind, placebo-controlled
clinical trial by Nordic Bioscience A/S [320, 321], in which the participants received either 1 mg 17b-estradiol continuously combined with 0.125 mg trimegestone (n=36), or
placebo (n=36) for 2 years. At entry into the study, women were between 52 and 65
years of age, at least 1 year postmenopausal with a body mass index less than or equal
to 32 kg/m2. Breast images were acquired at the beginning (t0) and the end of the 2-year
treatment period (t2) using a Planmed Sophie mammography X-ray unit. The images
were then scanned using a Vidar scanner to a resolution of approximately 200 microns
with 12 bit gray-scales. Delineation of the breast boundary on the digitized image was
done manually by an expert using 10 points along the boundary connected with straight
lines. Only the right mediolateral oblique view was used, since it has been shown previously that a reliable measure of the breast density can be accessed from any one view
[322]. We denote the patient groups P0, P2, H0, and H2 for placebo and treatment (HRT)
at t0 and t2 time point respectively.
7.3 Methods
For all methods involving human interaction, the reading radiologist was blinded with
respect to treatment and the images were presented in random order. The same radiologist (Paola Pettersen) made all readings. All images undergone through the basic
preprocessing steps such as removal of border artifacts; and segments breast tissue
and pectoral muscle from digital mammograms. Images are normalized using Z-score
normalization technique [193].
7.3.1 Construction of Breast Coordinate System
In usual practice, we assign image coordinate in relation to some orthonormal base
vectors, typically aligned with the rows and columns of the image. We have proposed
a unique breast coordinate system, where shape of the breast in mammogram is given
importance (see Chapter 5). Here the breast is considered as an intersection of two
parabolas at nipple point and these parabolas later meet the pectoral muscle as shown
in Figure 7.1 (a). As a result, each point on the mammogram is given the coordinate
with respect to the new parameter space represented by geodesic distance s and angle
ϕ as shown in Figure 7.1 (b). The significance of breast anatomy based coordinate
system is discussed in previous Chapters 5 and 6. We sample uniformly the given breast
coordinate in parametric space and divide each region in parametric space in such a
way that each of them contains at least 600 pixels when transferred back to Cartesian
space (image coordinate) as shown in Figure 7.1 (c)(d). It is worth noting that, we could
have divided regions in parametric space only, but this will have non-uniform effect
when transffered back to Cartesian coordinate due to non-linearity between parametric
space and Cartesian space (see Chapter 5). Hence to ensure the uniform sampling in
Cartesian space (image coordinate) this step is required. We believe that 600 pixels
are sufficient enough to describe the combine textural properties of a particular region.
Also the reason to divide parametric space into different region is to learn local textural
properties within temporal mammograms. For temporal mammograms, a position of
features play an important role to monitor the specific change of tissue structure with or
without HRT treatment, hence independent training-test dataset per region is a certain
course of action.
7.4
Feature Extraction
For every pixels within each region, a set of textural features based on Coherence
properties of an image are extracted. The reason for selecting these category of texture
features is that, the Eigen values of the structure tensor has been used extensively in
application consisting of spatio-temporal video data [323]. We believe that the coherence
properties of temporal mammograms will also provide significant information about
the temporal change over time, which is a prime requirement in this particular dataset.
B
B
φ
|BD| = |BC|
π
D
(x,y)
φ
s|AD|
A
φ0
A
C
C
(a)
φ
(b)
Y
S
(c)
X
(d)
Figure 7.1: (a) The breast parameters are the landmarks A, B, and C, and the breast
boundary normal at A. The points B and C are the intersections of the pectoral line and
the parabolic breast boundary approximations; (b)The breast coordinates s, φ of the point
(x,y) in the Cartesian coordinate frame are defined as the relative distance from the nipple
along the parabolic line and the direction of the parabola at the nipple, respectively. The
parabola is computed from the nipple point A, the direction angle φ at A, and the point
D on the pectoral line, where |BD|=φ/|BC| a (c) Division of parametric space s, φ into 24
different region considering the uniform distributions of samples (pixel locations) in each
region; (d) Reverse mapping of sampling pixels from parametric space s, φ to Cartesian
space x, y in order to ensure the meaningful division of regions on mammogram.
a
Please refer to Chapter 5 of this dissertation for more details on construction of breast coordinate system
Moreover, image enhancement based on image structure (structure enhancing diffusion)
may also help in enhancing vasculature structure of the breast parenchyma that will
improve detection of changes across temporal mammograms. We will discuss these
texture features in following sections.
7.4.1 Structure Tensor
Structure tensor is a second-moment matrix, derived from the gradient of a function.
It summarizes the predominant directions of the gradient in a specified neighborhood
of a point, and the degree to which those directions are coherent [324]. Features based
on structure tensors are invariant to affine intensity transformation, in addition , point
wise robustness is provided through convolution with Gaussian kernel of scales σ. The
structure tensor for a mammogram image I(x,y) is
 ∂I2

∂2 I
 ∂x2 ∂x∂y



(7.1)
Sσ (I(x,y) ) = Gσ ∗ 


 ∂2 I
∂I2 
∂x∂y
∂y2
7.4.2 Structure Tensor Construction within Breast Coordinate System
As seen from Equation 8.1, the traditional way of computing Gaussian derivatives
considering rectangular image coordinate (x,y) was straight forward. But, in case of
breast coordinate system computing Gaussian derivatives with respect to(s, ϕ) isn’t
simple. Since non-orthogonality is inherent due to shape of breast on mammogram.
Therefore, we derived that the mixed Gaussian derivatives of an arbitrary order in the
directions v1 and v2 can be computed as a contraction of Gaussian derivative tensor and
unit vectors pointing at the directions (see Chapter 5).
In general, we are interested in an arbitrary mixed derivative which can be represented as follows
Dθ1 · · · Dθ1 Dθ2 · · · Dθ2 (g ∗ f ) ≡ Dkθ11 Dkθ22 (g ∗ f )
(7.2)
| {z }| {z }
k1 times
k2 times
where the derivative is computed k1 times corresponding to the direction u1 and k2 times
in the direction u2 , where θ1 and θ2 are the polar angles of the direction vectors v1 and
v2 , respectively. It is important to note that since our breast coordinate is not perfectly
orthogonal, structure tensor and its coherence properties is rotationally variant but
rotational invariance is intrinsically achieved by developing a breast coordinate system
with manual/semi automatic geometric landmarks as shown in Figure 7.1. The equation
for structure tensor in Cartesian coordinate changes to following Equation 7.3
 ∂I2

∂2 I
 ∂s2 ∂s∂ϕ



(7.3)
Sσ (I(x,y) ) = Gσ ∗ 

 ∂2 I

∂I2 
∂s∂ϕ
∂ϕ2
7.4.3 Structure Enhancing Diffusion
This Diffusion tensor employs spatial filtering in which image intensities in a local neighborhood are utilized to compute new intensity values and smooth along orientation of
image structure guided by structure tensor. It act as a de-noising model that suppresses the noise as well as preserves the flow-like structure, which has special interest
in mammography, since mammographic parenchymal pattern has flow-like, thin, linear
structures within breast vasculature representing the significant textural information
[325, 124]. Petroudi and her colleagues have shown the effect of isotropic diffusion and
the maximum responses of the anisotropic diffusion at various scale being significant
while evaluating the effect of HRT [69, 70, 71] on mammograms. Structure Enhancing
Diffusion adapts its Eigenvalues to enhance the structure hence the Eigenvalues are related to the anisotropy of the image represented by two conductivity terms β1 and β2 in
the direction of gradient and isophote at a given scale respectively, Detailed information
can be found in [324, 326]. The structure enhancing diffusion D is defined as
 ∂I2
∂I2
∂I ∂I
(β2 − β1 ) ∂s
 β1 ∂s2 + β2 ∂ϕ
2
∂ϕ

1

Dσ (I(s,ϕ) ) = Gσ ∗ √


∂I2
∂I ∂I
∂I2
l2 − norm(Isσ , Iϕσ )  (β2 − β1 ) ∂s
β1 ∂ϕ
2 + β2 ∂s2
∂ϕ
−



 ,


(7.4)
∂I2 + ∂I2
∂s2 ∂ϕ2
η2
, β1 = 15 ∗ β2 ., and Gσ denotes the Gaussian with standard deviation σ
where β2 = e
(aperture size over which the orientation information is averaged).
7.4.4 Curvature Anisotropic Diffusion
The breast is a heterogeneous composition of adipose tissue, epithelial cells (parenchymal), and fibrous connective tissue (stromal), and most breast cancers arise from the
ductal epithelial cells [55, 26]. Brady and his colleagues [327, 328] have consistently
shown the significance of Curvilinear Structures (CLS) in mammograms. These structures are physically corresponding to milk ducts, blood vessels, Cooper’s ligaments and
spicules in the breast. All of these structures, bar spicules, are features of normal breast
tissue [327]. In order to improve the performance of structure enhancing diffusion so
as to extract noticeable and significant orientation of breast tissue, we adopt a curvature anisotropic diffusion on an image using a modified curvature diffusion equation
(MCDE) [329]. However, there are many methods based on diffusive filtering [330, 331]
has been used for improvement of mammogram quality in CAD application. MCDE
does not exhibit the edge enhancing properties of classic anisotropic diffusion, but instead consider image as a manifold defined by graph of function embedded in some
Euclidian space. Mean curvature motion of these graphs is considered as an underlying
model for diffusion. This facilitates the natural geometric way to treat the image in order
to extract their anatomical structural information. Following mean curvature described
by [329] was adopted to evolve an image (I) during diffusion as,
It (s, ϕ) =
7.5
Iss (1 + (Iϕ )2 ) − 2Is Iϕ Isϕ + (Iϕ )2 (1 + (Is )2 )
2(1 + (Is )2 + (Iϕ )2 )1.5
(7.5)
Pixel Based Classification by k-NN
Structure enhancing diffusion is applied to the mammogram enhanced by above Equation 7.5 to obtained DCAD . S,D and DCAD can be decompose by Eigen analysis. Eigensystem of these 2D tensors carries orientation information of image, it allows us to separate
image into constant areas, corners and straight edges according to number of non-zero
Eigenvalues. The parameter to measure the spread of the Eigenvalues is the coherence
C.
For every sampled pixel, coherence features C based on Eigenvalues of structure
tensor matrix S at four different scales σ of 1, 2, 4, and 8 mm are computed as shown in
Equation 8.3
Cσ = (
λ1 − λ2 2
)
λ1 + λ2 + η
(7.6)
Where, λ1 and λ2 eigen values of tensor at specific scale σ and λ1 >λ2 . η is a small
positive number to avoid numerical stability problems in a the plannar region of an
image where λ1 ≈ λ2 ≈ 0.
After extracting the features i.e. coherence at all 600 pixels each from 24 possible
regions, mammographic pattern measure is derived by training a pixel classifier on
subsets of images from the available data. These subsets are chosen to represent the
potential differences in patterns to be detected by the method. As an example, one
subgroup may be the H2 images from hormone treated patients and the other the
P2 images from the placebo group. Leave 2 out validation methodology is used and
followed by rank based feature selection procedure [203]. Each mammogram is scored
using voting based k-NN classifier [247] as described in our previously published work
[68, 179] (see Chapter 4). Four sets of coherence features are used for classifier training
and subsequently tested in the experiments as follows
STC: Features using Structure Tensor Coherence as described in Section 7.4.2.
SEDC: Features using Structure Enhancing Diffusion Coherence as described in Section
7.4.3.
SEDCADC: Features using Structure Enhancing Diffusion after Curvature Anisotropic
Diffusion Coherence as described in Section 7.4.4.
Combined: Combined features including all coherence features from STC, SEDC and
SEDCADC.
In addition to feature extraction, here we extract the tensor field with a principal
eigenvectors which is supposed to be aligned with the direction of the tissue orientation.
This can be achieved using the structure tensor field, which remove the sign ambiguity
by tensorizing the gradient. This will help in comparing the structure change at a
particular location between temporal mammograms, anatomic correspondence will be
provided by breast coordinate system intrinsically.
7.6 Result
Table 7.1 shows a comparative performance of all feature extraction techniques with
respect to radiologist assisted density scores. Features using proposed techniques show
better capability to separate the HRT patients from the placebo patients at end of the
study, than the categorical BIRADS [50] methodology and PD [40] (percentage density).
This was expected due to the fact that, during post menopausal age, breast tissue changes
their structure which may not necessarily be a density therefore it can’t not be picked
up by BIRADS or PD measure, similar finding is observed in our previously published
work [52, 53]. However, our features are able to pick up the orientation of the breast not
only during the HRT treatment but also during Placebo treatment showing quantitative
analysis to the radiologist about the heterogeneity of tissue structure (parenchymal patterns). Figure 7.2, Shows how structure tensor field is helpful in the task of visualization
of breast tissue structure over the treatment and in placebo. In placebo it is not expected to change the orientation of breast tissue significantly from baseline to follow-up
(P0 to P2). Looking at difference field of structure tensor in Figure 7.2, It is evident
that breast tissue density may change due to age but its orientation remains similar in
placebo group. Also from Table 7.1 , it is observed that, Coherence feature of Structure
Enhancing Diffusion after Curvature Anisotropic Diffusion outperforms over all other
coherence based techniques since area under ROC in separating H0 to H2 was maximum
i.e. 0.73. Also it is evident that, when all these features are combined, performance of
the ROC under logistic regression was 0.74 , statistically highest amongst individual
features. These finding once again justify the significance of considering the anatomy of
breast on mammogram especially for quantifying the changes in tissue pattern during
HRT follow-up as seen in Chapter 5. This improvement is due to the intrinsic registration across the mammogram in an anatomically oriented breast coordinate system. As
we have seen from the result in Chapter 5, the registration error using breast coordinate
system was lowest compare to other image registration techniques.
7.7
Conclusion
In conclusion, we have shown that based on the various tensor techniques it is possible to
differentiate between patients receiving HRT and patients receiving placebo treatments.
The proposed mammographic pattern score is an automated method, able to quantify the
effect of HRT as a structural change in the breast tissue. To our knowledge the coherence
based calculation has not been used in connection with mammographic parenchymal
analysis in any previous work. We believe that, this framework assist radiologist to
see the structural pattern that may undergo changes during the follow-up of patients
(a) Placebo Baseline Mammogram
(b) Placebo Follow-up Mammogram
(c) Placebo Baseline Structure Tensor Field
(d) Placebo Follow-up Structure Tensor Field
Figure 7.2: Placebo: Baseline and Follow-up mammograms and their corresponding
structure tensor field
Figure 7.3: Placebo: Difference field of structure tensor between Follow-up and Baseline
(a) HRT Baseline Mammogram
(b) HRT Follow-up Mammogram
(c) HRT Baseline Structure Tensor Field
(d) HRT Follow-up Structure Tensor Field
Figure 7.4: HRT: Baseline and Follow-up mammograms and their corresponding structure tensor field
Figure 7.5: HRT: Difference field of structure tensor between Follow-up and Baseline
Table 7.1: Performance characteristics of various texture measures in comparison to
breast density measures in longitudinal study stratified by populations undergoing HRT
treatment (H) and placebo (P) with a duration from 0(Baseline) to 2years(Follow-up)
Method/Test
BI-RADS
PD
STC
DTC
CADTC
Combined
P0 vs P2a
H0 vs H2a
AUCb
SEc
N.S.
N.S.
N.S.
N.S.
N.S.
N.S.
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
0.61
0.66
0.72
0.72
0.73
0.74
0.06
0.07
0.05
0.03
0.01
0.01
a
b
p-value shown using Wilcoxon-Ranksum test[233]
Areas under the ROC curve (Az) are given to indicate the performance of classification between H0 Vs H2
c
Delong test for the calculation of the Standard Error (SE) of the Area Under the Curve (AUC)[249]
involving HRT trial to assess the risk.
Part III
Chapter 8
Computer-Aided Parenchymal Texture
Analysis in Digital Mammograms: The
Potential for Estrogen-Receptor Specific
Breast Cancer Risk Estimation
Abstract
We investigate the potential of mammographic parenchymal texture as a surrogate marker of the
risk to develop Estrogen Receptor (ER) subtype-specific breast cancer compared to the standard
mammographic density measures, in a case-control study design. Digital mammographic (DM)
images were retrospectively collected and analyzed under HIPAA and IRB approval. Cases
included the contralateral (i.e., unaffected) images of women diagnosed with unilateral breast
cancer (n = 118), stratified by ER-positive (n = 88) and ER-negative (n = 30) receptor status
after pathology confirmation. Controls included DM images randomly selected at 1:3 ratio to
cases (n = 354) and age-matched based on 5-yr intervals. Both post-processed PremiumViewTM
(GE Healthcare) and raw images with MLO views were analyzed. Multiple texture features
including, Gaussian derivatives, coherence feature of structure and structure enhancing diffusion
representing the orientation and heterogeneity of the parenchymal structure were extracted using
validated algorithms developed in our laboratory. Texture features were extracted independently
from various regions of the breast such as dense and non-dense region. The dimensionality of
the features was reduced by a ranking algorithm. Breast percent density (PD) was estimated
by a computerized thresholding technique. Logistic regression was performed with leave-twoout cross validation to evaluate the classification accuracy of the extracted texture features and
breast PD to distinguish between (i) cancer cases and controls, and (ii) ER+ and ER- cancer
cases. Performance was evaluated by area under Receiver Operator Characteristic curve analysis
(AUC). The Delong test was used to compare the various AUCs.
The overall performance of post-processed images was better than raw images. The AUCs
for classifying between cancer cases and controls were equal to 0.70 (p <0.05) for PD, 0.75 (p
<0.001) when combined with texture features. Texture feature alone gave AUC of 0.72 for both
136
dense and nondense region. When classifying between the ER+ and ER- cases ROC AUCs were
equal to 0.61 for PD (p <0.001), 0.71(p <0.001) when combined with texture feature. Texture
feature in dense region alone gave AUC of 0.70 (p <0.001) while nondense region gave 0.56
(N.S.). Texture feature from both dense and non dense region were positively correlated with PD
0.40 (p <0.001).
Breast PD and parenchymal texture can both distinguish between cancer cases and controls.
However, for ER subtype-specific classification, PD alone does not provide sufficient information,
while texture features have significant classification accuracy. Combining breast PD with texture
features achieves the best performance. Through our investigations we also found that the
population undergoing HRT has a more tendacy of developing ER + breast cancer than that of
ER - as compare to placebo.
8.1 Introduction
Breeding evidences suggest that the etiologic and risk profile differences between women
who tend to evolve ER+ and ER- breast cancer. Enlarged risk of ER+ breast cancer
appears to be associated with increased endogenous overall exposure to estrogen and
cycling regenerative hormones [61, 332, 333]. Biomarkers of such regenerative hormone
exposure could be used during screening procedures to recognize woman at high risk
of ER+ breast cancer implementing targeted SERM chemoprevention strategies [334].
Increase of Breast density is strongly associated with breast cancer risk for both ER +
and ER- but it is not distinct [335, 333]. Mammographic parenchymal pattern are shown
to reflect the change of their structure in response to hormonal exposure [52, 211].
[299, 57] shown the discrimination between BRCA 1and 2 using parenchymal texture
measure. Moreover, [26] shown that, the inherent biological factors associated with
breast cancer risk are expressed in a parenchymal tissue and subsequently manifested
in her mammographic parenchymal pattern. Growing evidence in literature shows a
potential casual association between risk and mammographic texture [56, 57, 58, 179, 59,
211, 52] This motivates us to explore the possibility of our texture techniques developed
in our laboratory to discriminate between ER+ and ER- mammographic parenchymal
pattern. In this study we investigated the potential of mammographic parenchymal
texture as a surrogate marker of the risk to develop Estrogen Receptor (ER) subtypespecific breast cancer, compared to the standard mammographic density measures, in a
case-control study design.
This Chapter is organized as fallows. In Section 8.3, we describes various texture
methods employed in this study, Section 8.4 shows we present a scoring methodology
k-NN classifier. In Section 8.6, we show the potential of texture scores in different
experiments consisting of various dataset of clinical importance. In Section 8.8, we
discuss the result and its clinical significance.
8.2
Materials
Digital mammographic (DM) images were retrospectively collected and analyzed under
HIPAA and IRB approval. Cases included the contralateral (i.e., unaffected) images
of women diagnosed with unilateral breast cancer (n = 118), stratified by ER-positive
(n = 88) and ER-negative (n = 30) receptor status after pathology confirmation. Controls
included DM images randomly selected at 1:3 ratio to cases (n = 354) and age-matched
based on 5-yr intervals. Both post-processed PremiumViewTM (GE Healthcare) and raw
images with MLO views were analyzed. The study demographics is shown in Figure 8.1.
It is worth noting that, both Clause and Gail risks are not discriminative in ER-subtype
specific populations. This motivates us to investigate the potential of mammographic
parenchymal textures to discriminate this dataset between ER-subtype specific breast
cancers.
Age
Clause
Risk
Gail
Gail
Risk
Risk
(5 yrs) (Lifetime)
Figure 8.1: Demographics of cancer cases stratified by ER positive and ER negative
receptor status
Table 8.1: List of jet features up to third order expressed in x-y coordinates.
Number
∂x order
∂y order
1 2
0 0
0 1
3
1
0
4
0
2
5 6
1 2
1 0
7
0
3
8
1
2
9
2
1
10
3
0
8.3 Method: Texture Feature Extraction
For each mammogram, three broad families of texture features are extracted namely
Gaussian derivatives (n-jet), coherence properties of structure tensor and structure enhancing diffusion tensor representing the orientation and heterogeneity [179] of the
parenchymal tissue within breast. The principal reason for selecting these particular
set of texture feature is due to the fact that, Gaussian derivatives and coherence based
features have shown better performance in Case-Control studies [178, 179] and longitudinal studies involving various HRT treatments [186, 52, 53] as discussed in previous
chapter of this dissertation.
Gaussian Derivatives
Physiological evidence is presented that the visual receptive fields in the primate eye
are shaped like the sum of a Gaussian function and its Laplacian generating Gaussian
derivative-like fields. Based on these fields, it can be expected to provide human visual
system in image processing algorithms [336]. For every pixel in the mammogram
Gaussian derivative features are extracted at four different Gaussian scales 2, 4, 8, and
16 mm considering typical resolution of mammogram i.e. 10 pixel/mm. 10 different
combination of partial derivatives of image intensities with respect to x-y coordinate at
particular scale σ as shown in Table 8.1. This contributes 40 jet features per pixel for four
different scales in mammogram.
Structure Tensor and Structure Enhancing Diffusion
Structure tensor is a second-moment matrix, derived from the gradient of a function.
It summarizes the predominant directions of the gradient in a specified neighborhood
of a point, and the degree to which those directions are coherent [324]. Features based
on structure tensors are invariant to affine intensity transformation and rotationally
invariant, in addition , point wise robustness is provided through convolution with
Gaussian kernel of scales σ. Computation of structure tensor S for mammogram image
I( x, y) is shown in Equation 8.1



Sσ (I(x,y) ) = Gσ ∗ 

∂I2
∂x2
∂2 I
∂x∂y
∂2 I
∂x∂y
∂I2
∂y2






(8.1)
This Diffusion tensor employs spatial filtering in which image intensities in a local
neighborhood are utilized to compute new intensity values and smooth along orientation
of image structure guided by structure tensor. It act as a denoising model that suppresses
the noise as well as preserves the flow-like structure, which has special interest in
mammography, since mammographic parenchymal pattern has flow-like, thin, linear
structures within breast vasculature representing the significant textural information
[325, 124]. It adapts its Eigenvalues to enhance the structure hence the Eigenvalues are
related to the anisotropy of the image represented by two conductivity terms β1 and β2 in
the direction of gradient and isophote at a given scale respectively, detailed information
can be found in [324, 326]. Structure enhancing diffusion tensor D is defined in following
Equation 8.2 as

 ∂I2
∂I2
∂I ∂I

 β1 ∂x2 + β2 ∂y
(β2 − β1 ) ∂x
2
∂y 


1


(8.2)
Dσ (I(x,y) ) = Gσ ∗ √


σ σ 

∂I2 
∂I2
∂I ∂I
l2 − norm(Ix , Iy ) (β2 − β1 ) ∂x ∂y β1 ∂y2 + β2 ∂x2 
−
∂I2 + ∂I2
∂x2 ∂y2
η2
where β2 = e
, β1 = 15 ∗ β2 , and Gσ denotes the Gaussian with standard deviation σ
(aperture size over which the orientation information is averaged).
Both S and D can be decomposed by Eigen analysis. Eigensystem of these 2D
tensors carries orientation information of the image that allows us to separate image into
constant areas, corners and straight edges according to number of non-zero Eigenvalues.
The parameter to measure the spread of the Eigenvalues is the coherence C. For every
sampled pixel, coherence features C based on Eigenvalues of structure tensor matrix S
at four different scales σ of 2, 4, 8, and 16 mm are computed as shown in Equation 8.3
λ1 − λ2 2
)
(8.3)
λ1 + λ2 + η
Where, λ1 and λ2 eigen values of tensor at specific scale σ and λ1 >λ2 . η is a small
positive number to avoid numerical stability problems in a the planner region of an
image where λ1 ≈ λ2 ≈ 0. [h]
In this way, the extracted texture features includes 48 features in total for each pixel
location from three aforementioned feature categories ie contributing 40 features for
Gaussian derivative, 4 coherence features each for Structure tensor and Structure enhancing diffusion are computed as shown in Figure 8.3. In addition to 48 feature a
position feature of each pixels from centroid of the breast is added. The typical computation time required to extract all texture features at all scales from one mammogram
was ≈ 60 sec using a Pentium IV processor running at 3 GHz. Extracted features are
then scored and classified as discussed in next section.
Cσ = (
x 10
x 10
6
3
5
4
2
3
2
x 10
1.4
3.5
1.2
3
1
2.5
0.8
2
0.6
1.5
0.4
1
0.2
0.5
1
1
(a) σ = 2mm
x 10
1.6
0
(b) σ = 4mm
0
(c) σ = 8mm
0
(d) σ = 16mm
0
0.9
0.8
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0.7
0.6
0.5
0.4
0.3
0.2
0.1
(e) σ = 2mm
(f) σ = 4mm
0
(g) σ = 8mm
0
(h) σ = 16mm
0
Figure 8.2: (a-d) Arbitrary 3-jet features at four different scale, (e-h) Arbitrary Coherence
feature map of structure tensor at four different scale
8.4 Feature Classification and Scoring
Pixel based approximate k-nearest neighbor (k-NN) classifier [247] is used for the classification of texture features. Dimensionality of feature space is reduced to maximum
feature of 6 from 48 features by using a rank based feature selection algorithm [196, 310]
with recognition rate quantified as area under the receiver operating characteristic (AUC)
[315].Hence each mammogram has a feature vector of size px6 , where p is number of
pixel locations within mammogram.
Here, the k-NN performs pixel classification based on local features that describe the
mammogram structure in the vicinity of every pixel to be classified. Generally, the features extracted per pixel are expected to exhibit large similarity for every mammogram
even though they may come from two different subgroups of mammograms. Therefore,
for individual pixels, it is difficult to decide which of the subsets it belongs. Fusing
all weak local decisions, however, into a global overall score per mammogram ensures
that sufficient evidence in favor of one of the two groups is accumulated and allows
for a more accurate decision. Considering this aspect, a simple fusion strategy is employed. After every pixel has been provided with a posterior probability of belonging
to one of the two classes by the classifier, the average probability per pixel in the image
is determined. The average value is then taken as the final score for a mammogram.
Obviously, several other fusion strategies are possible [196]. The detailed description of
scoring strategy is explained in our previously published work [179], [186], [178]. The
Algorithm 4 Mammogram scoring procedure
Input: P = {500, 1000, 2000, 3000}, Training set DTR , k = 100, SCR = 0
Output: The summery of mammogram score
for p = 1 to size of P do
for n = 1 to size of p do
Extract 50 texture features and 2 position of feature nth pixel location within
specified region of given mammogram
Do Rank based feature selection on DTR
Compute the class label probability of nth pixel using k-NN with k number of
nearest neighbour.
Store the class label probability in array SC
end for
SCRp = SC
end for
SCR = SCRp
training and testing of the classifier was performed using the leave-two-out methodology [310, 53], meaning leaving one mammograms out from each class. The performance
of classifier was evaluated by means of Receiver operative characteristics curve (ROC)
(AUC) [315].
Let P be the array of point set with number of pixel location considered within
mammogram region, DTR as a training set and k be the number of nearest neighbor in
k-NN , then the procedure to compute score SCR for a mammogram is explained below
Input
A Mammogram
Preprocessing
Histogram
equalization and
z-score
normalization
Extracting Texture
Features
i) 3-jet
ii) Structure Tensor
iii) Structure Enhancing
Diffusion
Feature Classification
Scoring each candidate with
k-NN, and assigning probabilty of a class label.
Scoring mammogram by averaging the
probalities over all candidates within breast
region
Feature Sampling and
Fusing
Selecting n number of
candidate points on
random location within
breast region on above
computed feature map
Feature Ranking
Selecting important features per
candidate using rankbased
fetaure selction.
Figure 8.3: Block diagram of mammogram scoring methodology
(a) A Mammogram
(b) Feature
within Breast
sampling (c) Feature
Sampling (d) Feature
sampling
within dense region
within nondense region
Figure 8.4: Feature sampling within various region of breast
8.5 Estimation of PD
Breast density is computed by a multi-class fuzzy c-means (FCM) algorithm based on an
optimal number of clusters derived by the tissue properties of the specific mammogram
as described in keller et al. [2]. A mammogram with a segmented breast quantified as
dense tissue is shown in Figure 8.5
Figure 8.5: A mammogram with a segmented breast quantified as dense tissue by our
fully automated software[2]
8.6 Experiments: General Risk and ER-Subtype Specific
Risk Estimation
In this section we describe the task of classification stratified by cancer Vs control and
ER+ Vs ER- cancer cases. In both these experiment we sample pixel location from three
different region of mammogram namely, (i) Entire breast region, (ii) Dense breast region
delineated by our automatic method [2], and (iii) Non-dense breast region, non-dense
region is calculated as the total breast area minus the dense region. Ideally one should
sample all available pixel locations within the region but machine memory allowed
maximum of 3000 pixel locations per region per mammogram due to increase in feature
space and dimensionality. We take a particular set of points consisting 500, 1000, 2000
and 3000 number of pixels in each region. We average the score from all set of points as
explained in Algorithm 8.4. An equivalent k=100 is used, to reflect the total number of
feature vectors in the training set of k-NN. Pixel locations are selected randomly across
the region and in addition to their texture features the position of individual pixel from
the centroid of the breast boundary is added as an extra feature to the classifier. The
reason for doing this is, if the changes we are investigating mainly occur in specific
regions this knowledge will help reduce noise from changes in unimportant regions. If
there are important changes in one region simultaneous with important, but manifested
inversely in the conventional features, in another region, this knowledge might improve
classification dramatically. Pixel locations selected for feature extraction from various
breast regions are shown in Figure 8.4.
Scores obtained from each region of a mammogram is fused together with a PD and a
series of logistic regression is done to identify features that were associated with the class
label in each experiments. Initial analysis were done within each region of the breast
(entire breast, dense region, non-dense region and PD), and later analysis were done
across all region with PD as a combine logistic model. To measure the sensitivity and
specificity of each region, the c-statistics i.e. area under receiver operator characteristic
(ROC) curve for logistic regression model was calculated. Standard error of AUC is
computed using the methods of Hanley and McNeil [315], which guide in determining
the size of the sample required to provide a sufficiently reliable estimate of this area.
Statistical analysis is done using [307, 337]
8.6.1 Result: Raw Data
Raw image acquisition was performed with a GE Healthcare DS full-field DM system as
discussed in Section 8.2 and scored using the method discussed above. Figure 8.6 shows
the performance of texture measures extracted from various region of mammogram for
the task of both Cancer Vs Control and ER subtype specific discrimination. Correlations
of texture scores for various regions with breast density (PD) are shown in Table 8.2 for
Cancer Vs. Control Experiments and in Table 8.3 for ER + Vs. ER - subtype populations.
Scatter plot between PD and Texture scores representing correlation stratified by different
Table 8.2: Pearson Correlations of density with texture measures with raw images in the
Cancer cases Vs Control discrimination experiments
Percent Density
Breast Region
Dense Region
Non-Dense Region
Percent Density
Breast Region
Dense Region
Non-Dense Region
1
0.01 (N.S.)
1
0.38 (p<0.001)
0.76 (p<0.001)
1
0.30 (p<0.001)
0.73 (p<0.001)
0.70 (p<0.001)
1
1
1
0.8
0.8
0.6
0.6
Sensitivity
Sensitivity
experiments are shown in Figure 8.7.
0.4
Percent density Az=0.58, SE=0.324
Breast region Az=0.63, SE=0.0325
Dense region Az=0.68, SE=0.029
Non−dense region Az=0.69, SE=0.030
Combine (Logit Model) Az=0.69, SE=0.026
0.2
0
0
0.2
0.4
0.6
1−Specificity
0.8
(a) Cancer vs Control Raw Images
0.4
Percent density Az=0.56, SE=0.061
Breast region Az=0.57, SE=0.065
Dense region Az=0.66, SE=0.056
Non−dense region Az=0.51, SE=0.062
Combine (Logit Model) Az=0.68, SE=0.060
0.2
1
0
0
0.2
0.4
0.6
1−Specificity
0.8
1
(b) ER+ vs ER- Raw Images
Figure 8.6: Area Under ROC Performance
8.6.2 Result: Processed Data
The post-processed PremiumViewTM (GE Healthcare) MLO images (1147x957x12bit) as
described in Section 8.2 were analyzed preprocessed with Z-score normalization in order
to bring the intensity ranges of two populations as shown in Figure 8.8. Images are then
scored using the method discussed above, Figure 8.9 shows the performance of texture
measures extracted from various region of mammogram for the task of both Cancer
Vs Control and ER subtype specific discrimination. Correlations of texture scores for
various regions with breast density (PD) are shown in Table 8.4 for Cancer Vs. Control
Experiments and in Table 8.5 for ER + Vs. ER - subtype populations. Scatter plot between
PD and Texture scores representing correlation stratified by different experiments are
shown in Figure 8.10.
Table 8.3: Pearson Correlations of density with texture measures with raw images in the
ER + Vs ER - cases discrimination experiments
Percent Density
Breast Region
Dense Region
Non-Dense Region
Percent Density
Breast Region
Dense Region
Non-Dense Region
1
-0.19 (p <0.05)
1
0.11 (N.S.)
0.47 (p<0.001)
1
0.15 (N.S.)
0.60 (N.S.)
0.46 (p<0.001)
1
0.8
0.84
Cancer Cases
0.7
ER + Cases
0.82
Control
ER − Cases
Texture Measure
Texture Measure
0.8
0.6
0.5
0.4
0.3
0.78
0.76
0.74
0.72
0.7
0.2
0.1
0
0.68
0.2
0.4
0.6
Percent Density
0.8
(a) Pearson’s r = 0.69 (p <0.001)
1
0.66
0
0.2
0.4
0.6
Percent Density
0.8
1
(b) Pearson’s r = 0.50 (p <0.001)
Figure 8.7: Scatter plot between Texture scores and Percent Density in dataset with raw
images
8.7 Experiments: ER-subtype specific risk and Hormone
Replacement Therapy (HRT)
Observational studies and randomized trials have demonstrated that hormone replacement therapy (HRT) increases the recipient’s risk of developing breast carcinoma. Because it is known that some breast malignancies are hormonally responsive and that others are not, it has been hypothesized that HRT may be associated with the development
of estrogen receptor (ER)-positive/progesterone receptor (PR)-positive breast carcinoma
more so than with the development of ER-negative/PR-negative breast carcinoma [338].
The relative effects of postmenopausal hormone replacement therapy (HRT) with estrogen alone vs. estrogen + progestin on breast cell proliferation and on breast cancer
risk are controversial [339]. Also in our previously published work [53, 52], we have
learned that neither raloxifene nor low dose transdermal estradiol treatment increases
the general breast cancer risk. This motivates us to investigate whether the population
undergoing HRT treatment have a tendency to develop ER subtype specific breast can-
(a) Before
(b) After
Figure 8.8: Cummulative distribution plot of intensities before and after Z-score normalization in processed data population
Table 8.4: Pearson Correlations of density with texture measures with processed images
after Z-score normalization in the Cancer cases Vs Control discrimination experiments
Percent Density
Breast Region
Dense Region
Non-Dense Region
Percent Density
Breast Region
Dense Region
Non-Dense Region
1
0.28 (p<0.001)
1
0.74 (p<0.001)
0.37 (p<0.001)
1
0.53 (p<0.001)
0.56 (p<0.001)
0.68 (p<0.001)
1
cer as compared to placebo in our 2-year randomized, double-blind, placebo-controlled
clinical trial by Nordic Bioscience A/S [321]. In this study participants received either 1
mg 17b-estradiol continuously combined with 0.125 mg trimegestone (n=36), or placebo
(n=36) for 2 years. At entry into the study, women were between 52 and 65 years of age,
at least 1 year postmenopausal with a body mass index less than or equal to 32 kg/m2.
Breast images were acquired at the beginning (t0) and the end of the 2-year treatment
period (t2) using a Planmed Sophie mammography X-ray unit. The images were then
scanned using a Vidar scanner to a resolution of approximately 200 microns with 12
Table 8.5: Pearson Correlations of density with texture measures with processed images
after Z-score normalization in the ER + Vs ER - cases discrimination experiments
Percent Density
Breast Region
Dense Region
Non-Dense Region
Percent Density
Breast Region
Dense Region
Non-Dense Region
1
0.10 (N.S.)
1
0.40 (p<0.001)
0.32 (p<0.001)
1
0.40 (p<0.001)
-0.13 (N.S.)
0.13 (N.S.)
1
1
0.8
0.8
0.6
0.6
Sensitivity
Sensitivity
1
0.4
Percent density Az=0.70, SE=0.027
Breast region Az=0.65, SE=0.030
Dense region Az=0.72, SE=0.027
Non−dense region Az=0.72, SE=0.028
Combine (Logit Model) Az=0.75, SE=0.023
0.2
0
0
0.2
0.4
0.6
1−Specificity
0.8
0.4
Percent density Az=0.61, SE=0.061
Breast region Az=0.56, SE=0.061
Dense region Az=0.70, SE=0.054
Non−dense region Az=0.51, SE=0.064
Combine (Logit Model) Az=0.71, SE=0.058
0.2
1
0
0
(a) Cancer vs Control Processed Images
0.2
0.4
0.6
1−Specificity
0.8
1
(b) ER+ vs ER- Processed Images
Figure 8.9: Area Under ROC Performance
Table 8.6: Performance of Texture measure on self ER-subtype specific data using leave2-out cross validation
ER + (n = 30)
ER - (n = 30)
ER-subtype Specific Measure
0.49 ± 0.01
0.50 ± 0.01 †
Data shown Mean ± Standard Error of Mean (SEM), † (p < 0.05) indicate significantly larger absolute
effect between ER + and ER - group with Two-sample T-test
bit gray-scales. Similar texture features as described in Section 8.3 are extracted from
these study and trained on dataset stratified by ER+ and ER- (processed). Later they
are scored using k-NN classifier as discussed in Section 8.4, this measure we call it as
”ER-subtype specific measure”. Table 8.7 shows the performance of ER-subtype specific
measure trained on dataset consisting of ER + and ER - population with leave-2-out cross
validation. It is observed that ER-subtype specific measure is lower in ER + group than
ER -. When same texture measure is use to score mammograms from both treatment
and placebo groups, ER subtype specific measure reduces from baseline to follow-up
in HRT group while in Placebo it remains unchanged (see Table 8.7). Therefore it is
worth noting that, HRT shows the trend of developing ER + breast cancer than that of
ER - subtype specific breast cancer and however, this trend is marginally significant (p
<0.05).
8.8 Discussion and Conclusion
We have demonstrated the potential of including parenchymal textures measure in addition to available PD to discriminate between cancer cases and control population.
0.8
0.84
Cancer Cases
0.7
ER + Cases
0.82
Control
ER − Cases
Texture Measure
Texture Measure
0.8
0.6
0.5
0.4
0.3
0.78
0.76
0.74
0.72
0.7
0.2
0.1
0
0.68
0.2
0.4
0.6
Percent Density
0.8
(a) Pearson’s r = 0.70 (p <0.001)
1
0.66
0
0.2
0.4
0.6
Percent Density
0.8
1
(b) Pearson’s r = 0.52 (p <0.001)
Figure 8.10: Scatter plot between Texture scores and Percent Density in dataset with
processed images
Table 8.7: Demographics of Texture measure trained for ER-subtype specific discrimination on longitudinal study evolving placebo and HRT groups at baseline and after 2
years of hormone treatment
Placebo (n = 36)
HRT (n = 36)
Baseline
0.66 ± 0.01
0.65 ± 0.01
Follow up
0.66 ± 0.01
0.64 ±0.01 ⋆ †
Data shown Mean ± Standard Error of Mean (SEM), ⋆ (p < 0.05) indicates significant difference
compared to baseline with paired T-test,† (p < 0.05) indicate significantly larger absolute effect compared
with Placebo or HRT group with Two-sample T-test
ER-subtype Specific Measure
However, for ER subtype-specific discrimination, PD alone does not provide sufficient
information, while texture features independently discriminate with significant classification accuracy. Combining breast PD with texture features achieves the best performance. In this study we observed that the discrimination between ER subtype specific
populations becomes better while considering dense region only than the non-dense
region in both Raw (see Figure 8.6) and Processed data (see Figure 8.9). This hypothesis
supports previous research findings by Kerlikowske et al. [335] where women with
high mammographic density is reported to have increased risk of both ER-positive and
ER-negative breast cancers. The association between mammographic density and breast
cancer may be due to factors besides estrogen exposure. On the Similar line, Roubidoux
et al. [340] had shown the association of ER negative population with increased breast
density. This might indicate the link between density, ER status and parenchymal texture features. Overall performance of post-processed data was better than the raw one,
similar finding is also observed in our previously published study [341].
It is also worth noting that combine texture feature from both dense and nondense
region shows improvement when used in logistic regression. It is evident that, fibroglandular and breast fat tissue have independent effects on breast cancer risk. This indicates
that adjustment for non-dense tissue should be considered when studying associations
between dense area and breast cancer risk using texture measures. Similar finding is
also supported by van Gils et al. [54] in their recently published study.
From the scatter plot of both Raw (see Figure 8.7) and Processed (see Figure 8.10)
, it is worth noting that texture scores have positive correlation with a density and
correlation is more in Cancer Vs. Control experiments than in ER + Vs. ER - population.
This explains why, the discrimination is better in Cancer versus control than in ER
subtype specific classification. Since PD also shows the same profile which is quite
matured hypothesis since PD has been shown the independent marker for breast cancer
by many studies [12, 75, 342] But association of PD with ER-subtype specific risk is
not clear yet, hence it is hard to distinguish between ER + and ER - by texture alone,
even though texture carries different information than that of PD in ER subtype specific
experiment. However, this gives an important clue to understand the link between
parenchymal texture features and risk of developing ER subtype specific breast cancer
risk. Heine et al. [26] has shown that, the inherent biological factors associated with
breast cancer risk are expressed in a parenchymal tissue and subsequently manifested
in her mammographic parenchymal pattern. Growing evidence in literature shows a
potential casual association between risk and mammographic texture [56, 57, 58, 179, 59]
Our analysis in present study also shows the similar association.
For both raw and processed data, texture features from dense and non dense regions
are positively correlated with each other. This correlation is higher in Cancer Vs. Control
than ER + Vs. ER - experiment as shown in Tables 8.2, 8.3, 8.4, and 8.5. This suggests
that, dense and non dense tissue carries different texture information and should be
considered especially for ER subtype specific risk estimation.
To the best of our knowledge our study is first to explore the potential of mammographic parenchymal texture analysis for ER specific breast cancer risk assessment.
This could have significant impact in personalized, ER specific risk-reduction interventions, such as SERMs and aromatase inhibitors. In present protocol, evaluation of the
ER-status is performed by means of immunohistochemistry (IHC) which has some limitation being invasive [60]. However many studies has shown the association of different
factors including breast density with ER status [61, 62, 63] ,till date, in our knowledge no
study has shown the association with mammogram texture and ER status on contra-later
breasts. If present study perform consistent over other study population, this may have
potential to predict the ER positive status prior to carcinogenesis and may help in better
treatment such as SERMs [64].
Currently, ER status can only be assessed invasively at the time that breast cancer is
diagnosed and no accurate method exists to estimate the a priori risk. SERMs play an
important role in the primary prevention of ER+ breast cancer, having the potential to
reduce the incidence of these cancers by 48 % [334]. However, SERM chemoprevention
can also expose women to undesired side-effects such as stroke, endometrial cancer, and
formation of cataract. Therefore, effective use of SERMs requires identifying women at
the highest risk of developing ER+ breast cancer. Currently no accurate method exists.
It is estimated that from the 10 million US women that are considered eligible by FDA
standards for SERM chemoprevention, only about 2.5 million would actually benefit
[334]. If our hypothesis proves to be true, mammographic texture can be used as a noninvasive biomarker during screening procedures to identify women who would benefit
most from SERM chemoprevention. Our study suggests that mammographic texture
potentially has value for ER specific breast cancer risk assessment. Larger prospective
clinical studies are warranted, with patient follow-up, to prospectively validate these
findings considering additional risk factors [343, 334, 64].
Part IV
Chapter 9
Conclusions
This chapter contains a summary of the dissertation, discussion of its findings, several
of their implications and possible future work. Finally a short conclusion is given.
9.1 Summary
In Chapter 1 we present the background, introduction and motivation that justify the
rationale of this dissertation. We describe current and past practices in evaluating breast
cancer risk using screening mammograms. We discuss advantages, disadvantages and
controversies over screening mammogram practices. We also discuss the potentials
and limitations of breast density being an independent risk factor. Later we lay down
the foundation of this dissertation by generating a hypothesis i.e. ”Can mammographic
parenchymal texture measure perform better or at least as good as breast density which currently
is a well established link for risk assessment”, which will become a motivation for rest of the
chapters in this dissertation.
In Chapter 2 we summarizes and compares the mammographic parenchymal texture
techniques used in various applications such as, microcalcification detection, mass characterization and tissue characterization based on available literatures. Emphasis is given
on the techniques that have been used for risk assessment application on screening mammograms. In meticulous, we divide the texture techniques based on (i) Statistical: 1st
and 2nd order statistics (ii) Spatial-Statistical: Fractal properties, Laws texture feature,
Scale space, Wavelet, Gabor, Fourier. We evaluate and compare their performances by
FROC analysis on one of the most commonly used database available in public domain,
such as mini-MIAS and DDSM. We found that each measure has a unique property to
describe the complexity of mammographic parenchymal pattern and can provide good
classification accuracy when combined together.
Taking into account the importance of texture features, in Chapter 3 we investigate
whether texture properties characterized by local Fractal Dimension (FD) and Lacunarity
contribute to assess breast cancer risk in both case-control and temporal study involving
population that undergo HRT treatments. We were interested in fractal properties since
154
this category of texture features had been used by many researchers for risk assessment
task [66, 67, 11, 57, 136, 135] . Methods of computing FD and Lacunarity using box
counting are discussed. In our experiments, we found that fractal dimension does not
exhibit difference between cancer and control while Lacunarity shows no significant
change in either of the studies. We concluded that the BIRADS, percentage density, and
to some degree Fractal dimension may broader relate to changes in parenchymal tissue
structure.
In Chapter 4 we investigate the potential of our breast cancer risk marker called
mammographic texture resemblance MTR marker. Various mammographic parameters
were analyzed for relation to breast cancer risk: (C) categorical parenchymal pattern
scores; (R) radiologist’s percentage density, (P) computer-based percentage density; (H)
computer-based breast cancer risk MTR marker; (E) computer-based hormone replacement treatment MTR marker; and (A) an aggregate of P and H. We found positive
correlation between density scores, C, R, and P, no other pair showed significant correlation. In this experiment we found that, the FROC performance of the aggregate marker
(A) surpasses others significantly except H. We concluded that the MTR marker is an
independent and stronger related to risk than density scorings, and as such provided
additional information.
In order to improve the performance of MTR further, in Chapter 5 we develop a novel
Breast Coordinate System that is based on breast anatomy to register female breasts into a
common coordinate frame in 2D mediolateral (ML) or mediolateral oblique (MLO) view
mammograms. On the basis of some geometric landmarks, we have constructed a nonlinear mapping between the parameter frame and the breast region in the mammogram.
This mapping makes it possible to identify the corresponding positions and orientations among all of the ML or MLO mammograms, which facilitates an implicit use of
the registration, i.e., no explicit image warping is needed. In addition, we show how
the proposed coordinate system can be used in temporal studies to pin-point anatomically equivalent locations between the mammograms of each woman and among the
mammograms of all of the women in the study. Also in the cross-sectional study, it is
observed that the classification between cancer and control groups can be improved by
using the new coordinate system with Committee Based Learning, compared to other systems evaluated such as our old MTR measure discussed in Chapter 4. This coordinate
system makes an accurate anatomical registration of breasts possible, which suggests its
wide applicability wherever 2D mammogram registration is required.
In Chapter 6, taking into account of breast coordinate system, we develop a framework that discovers the mammogram regions where changes due to breast cancer are
most likely to occur. Here, we propose a Statistical Framework that performs an automatic scaling and selection of region of interest over score map which was computed
with respect to anatomical breast coordinate system developed in chapter 5. This framework uses nested cross-validation scheme for ROI optimization that makes it possible
to investigate the mammogram regions that show significantly different classification
scores between the cancer and control group. Furthermore, we show the new sampling
techniques called Importance Sampling guided by these regions/patterns that improve the
classification accuracy in both cross-sectional (Nijemegn, DDSM, MIAS) and temporal
study (HRT) design.
In Chapter 7 we provide a Framework for obtaining more accurate and sensitive measurements of mammographic parenchymal pattern change that relate to specific effects
like Hormonal Replacement Therapy (HRT) and aging. We demonstrated how the structure tensor and structure enhancing diffusion with its coherence features computed in an
anatomically oriented breast coordinate system followed by a statistical learning scheme
provides non subjective and reproducible measure, as compared to the traditional BIRADS and computer aided percent density measure. We also demonstrated how the
orientation of breast parenchyma changes in population undergoing HRT treatment vs.
placebo through Difference Field Visualization. This framework facilitates radiologist to
assess changes in mammographic parenchymal pattern in one to one correspondence
across temporal mammograms of a subject thereby guide them to evaluate an individual
risk.
In Chapter 8 we investigate the potential of mammographic parenchymal texture as
a surrogate marker of the risk to develop Estrogen Receptor (ER) subtype-specific breast
cancer compared to the standard mammographic density measures, in a case-control
study design. Various texture features as learnt from previous chapters were extracted
independently from various regions of the breast such as dense and non-dense region of
both raw and processed images in case-control study design. We found that breast density and parenchymal texture can both distinguish between cancer cases and controls.
However, for ER subtype-specific classification, PD alone does not provide sufficient
information, while texture features have significant classification accuracy. Combining
breast PD with texture features achieves the best performance. Through our investigations we also found that the population undergoing HRT has a more tendency of
developing ER + breast cancer than that of ER - as compared to placebo. This investigation will help in establishing a non-invasive biomarker during screening procedures
to identify women who would benefit most from SERM (Selective Estrogen Receptor
Modulator) chemoprevention such as Raloxefene and Estradiol.
9.2 Discussion
The fundamental goal of this dissertation was to investigate the potential of Mammographic Parenchymal Texture (MPT) as an imaging biomarker of (i) General risk of
developing breast cancer (ii) Effect specific drugs involving various HRT treatments (iii)
Estrogen Receptor sub type specific risk.
From all our experiments, in retrospect, we have achieved our goal in discovering the
significance of Mammographic Parenchymal Texture (MPT) being an independent surrogate
marker of (i) General Risk (see Chapter 2, 3, 4, 5, 6) ,(ii) Risk in HRT populations (see
Chapter 2, 7), and (iii) Estrogen receptor subtype specific risk (see Chapter 8).
We would like to take readers attention to the Figure 9.1 that motivates this disser-
Figure 9.1: The block diagram explaining the different factors influencing parenchymal
change that results in breast carcinogenesis: A motivation behind this dissertation
tation (also discussed in Chapter 1), where we initially believed that the three different
ways by which the parenchymal tissue structure may experience change during the
carcinogenesis and we succeed in showing this from our findings (i) Exposure to HRT
(see results from Chapter 3 and 7) (ii) Endogenous Hormone Exposure (ER + risk) (see
results from Chapter 8) (iii) Change of Genetic Makeup (BRCA 1/2) or unknown factors/General risk (see results from Chapter 2, 4, 5 and 6). Our observation, ”Just like
density, mammographic parenchymal texture measure also has an ability to detect these
changes comparable to breast density” is proved.
However, the relationship between parenchymal pattern and breast cancer risk has
been studied and debated for past three decades, with many subsequent reviews [33,
34, 35, 36, 37, 38, 39, 40, 12, 11, 26]. It is now clear that there is an increased breast cancer
risk associated with certain breast tissue compositions and that other known risk factors
may exert some influence on breast tissue, which causes long-and short-term changes
evident on mammogram. Our findings also correlates with Wolfe’s analysis for pattern
based risk assessment which he initiated in 1976. In his consistent experiments [33, 34] ,
he observed a relationship between the prominence of ductal patterns and breast cancer
in xeroradiographs. He classified the pattern based on their complexity. Later, Boyd and
others [44, 45, 46, 47] found that this complexity can be quantified as a breast density on
mammogram. In spite of being well studied and established link between breast density
and cancer risk, it has some discrepancies such as; (i) To which degree changes in density
reflects changes in risk, (ii) Whether changes in density caused by intervention (HRT) or
not has any relation to changes in breast cancer risk. It is observed in many studies that,
even though two mammograms with matched age has same PD (percent density), may
have different Gail risk; this is due to the fact that breast density proportion changes
with time; however it is not clear whether the breast cancer risk changes accordingly.
We believe that our findings with MPT represented by our marker MTR in this
dissertation has provided an insight to solve these discrepancies in some extent because
of facts summarized as follows
• An anatomically oriented breast coordinate system, this coordinate makes it possible to identify the corresponding position and orientations among MLO mammograms, which facilitates an implicit use of registration in both cross- sectional
and longitudinal studies.
• Development of texture features such as Gaussian derivatives, structure and diffusion tensors with respect to breast coordinate system, that enhances the orientation
information of breast parenchyma.
• Use of committee based machine learning techniques in addition to most validated
texture features that further improves the performance of MTR.
• A statistical framework that ensures the automatic selection of inner and outer scale
of MTR scores, which further enhances the performance of MTR by the iterative
process of importance sampling.
Our scoring methodology is fully automated and has the clinical advantages in
terms of reproducibility, objectivity, and scalability, potentially leading to cost effective and efficient screening of women. However, use of quantitative texture measure
representing parenchymal (epithelial) tissue structure on mammogram is not unique.
Many researchers [55, 26, 344, 11, 80, 124, 69, 164] across mammographic image analysis
community are working on developing an imaging biomarker for risk assessment in
screening mammograms.
9.3 Future Work and Implications
Possible implications and future prospects to the methodology presented in this dissertation are discussed as follows,
• Currently MTR is computed by manual landmark selection to construct a breast
coordinate system, in future it could be made fully automatic, so that we can use
MTR as a supportive marker for huge screening trials across hospitals.
• Further research is warranted in scoring methodology of MTR such as developing
an adaptive metric for k-NN classifier, fast and robust feature selection methodology.
• Breast coordinate transform could be additionally extended to cranial-caudal (CC)
views so that combine anatomical information of tissue structure in both MLO and
CC can be utilized.
• The region that showed early changes due to development of breast cancer in
Nijmegen study must be considered while sampling and scoring methodology in
future studies.
• Confounders such as ethnicity, body mass index, age, earlier hormone treatment,
menopause status, mammographic and digitalization technology and calibration
must be examined and potentially compensated for all future studies while quantifying mammographic parenchymal pattern.
• Robust preprocessing steps for normalization of mammograms such as calibration
of thickness of the compressed breast between mediolateral oblique and craniocaudal mammograms as suggested by Brady et al. [345] should be considered.
• Recently, Crandall et al. [346] has shown an association between breast tenderness
and change in mammographic density. In future the method of computing tissue
tenderness with other parameters such as pressure between compression plates
during mammography may be considered.
• Since we have established an anatomical breast coordinate system for MLO views,
its application can be considered in other breast modalities such as MRI and
tomosynthesis.
• SMF as suggested by Highnam et al. [347] shows considerable promise in being
of major use in large epidemiological studies related to breast cancer, hence this
could be considered.
• Improved version of interactive threshold measurement representing breast density as suggested by Aitken et al. [348] could be considered in addition to texture
measure.
• Researchers are studying various tumor markers such as kinetic features of breast
MRI [349], optical pathology in blood, urine or in fluid from breast (nipple aspirate)
[350, 351, 352, 353]. These features can be incorporated to existing methodology to
build an efficient and more personalized risk assessment model.
9.4 Conclusion
In retrospect, mammographic parenchymal texture analysis does not seem such a complex problem in today’s world of computer vision and machine learning field. It is
possible in some extend to learn the complexity of Wolfe’s pattern (developed in late
seventies) using advanced pattern recognition techniques. A fast, robust, and more importantly reproducible mammographic scoring methodology is found. We have shown
that mammographic parenchymal texture (MPT) has a potential to discriminate between
various populations of clinical importance and can be used by radiologist as a supportive tool. Our long term hypothesis is to establish a non-invasive biomarker during
screening procedures to identify women who would benefit most from SERM (Selective
Estrogen Receptor Modulator) chemoprevention and also to predict her general risk.
No doubt other methodology for the breast cancer risk assessment using advance imaging modalities will be found, but the concept of Mammographic Parenchymal Texture
(MPT) patterns and its application in breast cancer risk assessment is firmly established.
Chapter 10
List of Publications
161
[1] Gopal Karemore and Mads Nielsen. Mammographic parenchymal texture techniques in application to breast cancer risk assessment: A review. Invited : Biomedical
Imaging and Intervention Journal, 2011.
[2] Mads Nielsen, Gopal Karemore, M Loog, J Raundahl, N Karssemeijer, J D M Otten,
M A Karsdal, C M Vachon, and C Christiansen. A novel and automatic mammographic texture resemblance marker is an independent risk factor for breast cancer.
Cancer epidemiology, 35(4):381–387, 2011.
[3] Sami S Brandt, Gopal Karemore, Nico Karssemeijer, and Mads Nielsen. An anatomically oriented breast coordinate system for mammogram analysis. IEEE Transactions
on Medical Imaging, 30(10):1841–51, 2011.
[4] Gopal Karemore, Sami Brandt, Nico Karssemeijer, and Mads Nielsen. Discovery
of mammogram regions that show early changes due to the development of breast
cancer: A preliminary work. In Elliot Fishman, editor, 97th Scientific Assembly and
Annual Meeting of Radiological Society of North America-LL-INE1154-WEB, Chicago,
December 2011. RSNA.
[5] Gopal Karemore, Brad Keller, Huen Oh, Julia Tchou, Mads Nielsen, Emily Conant,
and Despina Kontos. Computer-aided parenchymal texture analysis in digital
mammograms: The potential for estrogen-receptor specific breast cancer risk estimation. To be submitted: Medical Physics, 2011.
[6] Jakob Raundahl, Marco Loog, Mads Nielsen, Sami S. Brandt, Gopal R. Karemore.
Breast tissue density measure. US Patent Applicaton-20110013819, 2008.
Breast tissue density measure
[7] Gopal Karemore, Brad Keller, Huen Oh, Julia Tchou, Mads Nielsen, Emily Conant,
and Despina Kontos. Computer-aided parenchymal texture analysis in digital
mammograms: The potential for estrogen-receptor specific breast cancer risk estimation. In Jay Alan Baker and Thomas Hans Helbich, editors, 97th Scientific
Assembly and Annual Meeting of Radiological Society of North America-Oral Session
SSG01, Chicago, December 2011. RSNA.
[8] Gopal Karemore, Sami Brandt, Nico Karssemeijer, and Mads Nielsen. A framework
to determine mammographic regions that show early changes due to development
162
of breast cancer: An application in risk assessment. To be submitted: Physics in
Medicine and Biology, 2011.
[9] Gopal Karemore, Sami Brandt, N. Karssemeijer, and Mads Nielsen. Automatic
breast cancer risk assessment from digital mammograms. In European Congress of
Radiology, Vienna, December 2011. ECR.
[10] Gopal Karemore, Sami Brandt, Nico Karssemeijer, and Mads Nielsen. Anatomic
breast coordinate system for mammogram analysis. In 5th International Workshop
on Breast Densitometry and Breast Cancer Risk Assessment, San Francisco, December
2011.
[11] Shen Sun, Gopal Karemore, Nico Karssemeijer, and Mads Nielsen. Combining
different views of mammographic texture resemblance (mtr) marker of breast cancer risk. In 5th International Workshop on Breast Densitometry and Breast Cancer Risk
Assessment, San Francisco, December 2011.
[12] Gopal Karemore, Sami Brandt, Jon Sporring, and Mads Nielsen. Anisotropic diffusion tensor applied to temporal mammograms: an application to breast cancer risk
assessment. Conference Proceedings of the International Conference of IEEE Engineering
in Medicine and Biology Society, pages 3178–3181, 2010.
[13] Gopal Karemore and Mads Nielsen. An automatic framework for assessing breast
cancer risk due to various hormone replacement therapies (hrt): A novel cad application in digital mammography. In 96th Scientific Assembly and Annual Meeting
of Radiological Society of North America, Chicago, December 2010. RSNA.
[14] Mads Nielsen, Paola C Pettersen, Peter Alexandersen, Gopal Karemore, Jakob
Raundahl, Marco Loog, and Claus Christiansen. Breast density changes associated
with postmenopausal hormone therapy: post hoc radiologist- and computer-based
analyses. Menopause New York Ny, 17(4):772–778, 2010.
[15] Chen Chen, Konstantin Chernoff, Gopal Karemore, Pechin Lo, Mads Nielsen, and
Francois Lauze. Classification in medical images using adaptive metric k-nn. Proceedings of SPIE, 7623:76230S–76230S–9, 2010.
[16] Gopal Karemore, J.B. Mullick, Mads Nielsen, S. Chidangil, and K.V. Rajagopal. Relevance of echo-structure and texture features: An application in ultrasound breast
tumor classification. In European Federation of Societies for Ultrasound In Medicine and
Biology, page Oral Presentation, Copenhagen, 2010. EUROSON 2010.
[17] Gopal Karemore, J.B. Mullick, R Sujatha, Mads Nielsen, and C Santhosh. Classification of protein profiles using fuzzy clustering techniques: an application in
early diagnosis of oral, cervical and ovarian cancer. Conference Proceedings of the
International Conference of IEEE Engineering in Medicine and Biology Society, pages
6361–6364, 2010.
[18] Gopal Karemore, I Arganda-Carreras, and Mads Nielsen. Automatic consistent
registration framework for temporal pairs ofmamogram: In application to breast
cancer risk assessment due to hrt (hormone replacementtherapy). International
Journal of Computer Assisted Radiology and Surgery, 4(S1):356–357, 2009.
[19] Mads Nielsen, Jakob Raundahl, Paola C Pettersen, Marco Loog, Gopal Karemore,
Morten A Karsdal, and Claus Christiansen. Low-dose transdermal estradiol induces breast density and heterogeneity changes comparable to those of raloxifene.
Menopause New York Ny, 16(4):785–791, 2009.
[20] Gopal Karemore and Mads Nielsen. An automatic framework for assessing breast
cancer risk due tovarious hormone replacement therapies (hrt). In 4th International
Workshop on Breast Densitometry and 1st International Workshop on Mammographybased Assessment of Breast Cancer Risk, San Francisco, 2009.
[21] Gopal Karemore and Mads Nielsen. Fractal dimension and lacunarity analysis of
mammographic patterns in assessing breast cancer risk related to hrt treated population: a longitudinal and cross-sectional study. Proceedings of SPIE, 7260:76230S–
76230S–9, 2009.
[22] Gopal Karemore and Mads Nielsen. Yet another mammography measure to evaluate breast cancer risk. In 4th International Workshop on Breast Densitometry and 1st
International Workshop on Mammography-based Assessment of Breast Cancer Risk, San
Francisco, 2009.
[23] Gopal Karemore, Lavanya Rai, Keerthilatha M Pai, and V B Kartha. Serum protein
profile study of clinical samples using high performance liquid chromatographylaser induced fluorescence: case of cervical and oral cancers. Proceedings of SPIE,
7182:71820J–71820J–9, 2009.
[24] Gopal Karemore, Sujatha N Raja, Lavanya Rai, V B Kartha, and Santhosh Chidangil.
Protein profile study of clinical samples using laser induced fluorescence as the
detection method: case of malignant and normal cervical tissues. Proceedings of
SPIE, 7169:71691I–71691I–8, 2009.
[25] Gopal Karemore, M. Nielsen, K.K. Mascarenhas, K.S. Choudhary, A. Patil, V.K.
Unnikrishnan, V. Prabhu, A. Chowla, and C. Santhosh. Classification of laser induced fluorescence spectra from normal and malignant tissues using learning vector quantization neural network in bladder cancer diagnosis. 8th IEEE International
Conference on BioInformatics and BioEngineering, 7169:1–6, 2008.
[26] Jakob Raundahl, Marco Loog, Mads Nielsen, Sami S. Brandt, Gopal R. Karemore.
Breast tissue density measure. US Patent Applicaton-20110013819, 2008
Chapter 11
Acknowledgement
First I would like to thank my supervisor Mads Nielsen; his positive outlook and ingenuity contributed throughout the progress of my PhD work. Mads always encouraged
and inspired me in understanding both technical and clinical aspects of this project. He
is not only a talented mentor, but a good friend, almost like a life coach for me. I have
learned a lot from him. My co-supervisor Sami Brandt has managed to continuously
provide sharp minded and focused feedback to the endless requests for comments and
suggestions. Especially from Sami I have learned how to report the achieved scientific
results clearly and comprehensively. I would like to thank Nordicbioscience A/S director
Dr.Claus Christiansen and radiologist Paola Pettersen, for providing the opportunity to
make this investigation. I would also like to thank Nico Karssemeijer (Radboud University), who is an expert in the field of mammographic image analysis and who give me an
opportunity to work on his dataset which has great clinical importance. Furthermore,
Prof. Despina Kontos for providing me scholarship and showing me great hospitality
on my visit to University of Pennsylvania,USA and Dr. David Liu at Siemens Corporate
Research, USA for partial scholarship and support. I also would like to thank Prof.
James Sethian,Prof. Ruzena Bajscy (University of California, Berkeley), Prof. Celine
Vachon, Prof. Armando Manduca (Mayo Clinic), Julio E. Celis (Danish Cancer Society)
and Prof. Morten Karsdal (Nordic Bioscience A/S) for allowing me to visit their labs and
exchange the ideas.
Finally, I would like to thank my friends and colleagues (nearest neighbors) for helping
me without whom these years would have felt a lot longer, with no particular order:
Jhinuk Basu Mullick , Saurabh Gupta, Shruti Agarwal, Kersten Pettersen, Melanie Ganz,
Aditya Tatu, Bjorn Karstens, Prof. Santhosh Chidangil, Prof. Dr. Martin HofmannApitius, Prof. Marc Zimmerman, Dr. Ravi Malladi, Prof. Emily Conant, Prof. Hebbar,
Prof. Mohan AY, Prof. Maria Montoya Sanchez, Aarish Qazi, Nazish Qazi, Bala Krishna Prabhala, Chen Chen, Konstantin Chernoff, Rajeev Sonuwar, Aditya Bharadwaj,
Allesandro Crimi, Erik Dam, Martin Lillholm, Lene Larsen, Rabia Granlund, Joselene
Marques ,Jon Sporring, Vladlena Gorbunova, Francois Lauze, Kim Steenstrup Pedersen,
Camilla Jrgensen, Dina Riis Johannessen, Lauge Srensen, Marleen De Bruijne, Dan Jrgensen, Peter Mysling,Antonio Segovia-Silvestre, Diana Julie Leeming, Ulla Krogshede,
165
Pallavi Balabhadrapatruni, Naga Dandu, Sudhakar Tummala, Adhish Prasoon, Ahmed
Ashraf Billal, Linda Kitts, Brad Keller, Terri Astrin, Sren Hauberg, Aasa Feragen, Pechin
Lo Chien Pau, Jakob Raundahl, Prasad Raju, Lakshmi Raju, Deepak Bhatt, Ashwini
Joshi, Nidhi Gupta, Dhara Raijada, RK Shetty, Roshni Ramchandran, Arun Menon, Sujatha Bhatt, Chandra Shekar Kenchappa, Navin Sharma, Manasi Datar, Prasanna Joshi,
Prachi Dandekar, Sushil Kadu, Prasad Kamdi, Sandeep Dixit, Vishal Koradia, Kinjal Koradia, Deepak-Surekha Amrutkar, Akriti Sood, Sharat Varma, Pallavi Pratap, Devdatt
Kawathekar, Dharmendra Rai, Dr. Vishwas Zade,Dr. Nandali Zade, Dr. Kishor Taori,
Raju Chichkhede, Dhananjay Ragit, Manoj Wandile, Nikhil Wandile, Adwait Kamat,
Amit Patil, Rahul Karan, Ashish Khante, Ankush Karemore, Sidharth Vikal, Yogish
Mallya, Rushali Parkhi, late Abhishek Parkhi and others who I forgot.
Chapter 12
Disclosure
Chapter 2: Mammographic Parenchymal Texture Techniques in Application to Breast
Cancer Risk Assessment: A Review
Disclaimer:
Gopal Karemore is a prime authour and conducted the programming, experiments,
and writing; MN has supervised this work. This chapter is recycled from [354]
Chapter 3: Fractal Dimension and Lacunarity in Cross-sectional and Longitudinal
Population
Disclaimer:
Gopal Karemore is a prime authour. He conducted programming, experiments, and
writing; Mads Nielsen has supervised this work. This chapter is recycled from [184]
Chapter 4: Mammographic Texture Resemblance Marker is an Independant Risk
Factor
Disclaimer:
Mads Nielsen is a prime authour and done writting of this work[179]; Gopal Karemore conducted experiments.
This chapter is recycled from mainly [179] and [183, 182, 180, 355]. In [179] all
co-authors no objection certificate is obtained.
Chapter 5: An Anatomically Oriented Breast Coordinate System for Mammogram
Analysis
Disclaimer:
Construction of Breast Coordinate and computation of Gaussian derivatives with
respect to Coordinate is completely designed and implemented by Sami Brandt who
is a principal and first author of this paper. Gopal has conducted image registration
experiemnts in Section V. Experiments (All registration techniques). and Section B
(Feature selection algorithm, Histograms of the selected features, Committee based
learning , Evaluation Algorithm, ROC plots and classification scores). N. Karssemeijer
has provided dataset and Mads Nielsen has mentored this work.
This chapter is recycled from [178].
Chapter 6: A Framework to Determine Mammographic Regions that Show Early
Changes Due to Development of Breast Cancer: An Application in Risk Assessment
167
Disclaimer:
Gopal is a prime author who conducted the programming, experiments, and writing.
Sami developed Anatomical Breast coordinate system. N. Karssemeijer has provided
dataset and Mads Nielsen has mentored this work. This chapter is recycled from [356,
185, 357]
Chapter 7: Anisotropic Diffusion Applied to Temporal Mammograms: An Application to Breast Cancer Risk Assessment
Disclaimer:
Gopal is a prime author who conducted the programming, experiments, and writing.
Sami developed Anatomical Breast coordinate system. Jon Sporring mentored STI and
DTI concepts, Mads supervised this work.
This chapter is recycled from [186, 182, 52, 53].
Chapter 8: Computer-Aided Parenchymal Texture Analysis in Digital Mammograms: The Potential for Estrogen-Receptor Specific Breast Cancer Risk Estimation
Disclaimer:
Gopal is a prime author who conducted the programming, experiments, and writing. Despina Kontos provided the data and concepts; Emily Conant provided clinical
inputs, Others mentored this work.This work was entirely conducted at University of
Pennsylvania during visiting scholarship and confidential (currently under IP norms
and review process). University of Pennsylvania reserve all rights.
This chapter is recycled from [358, 187]
1
1
Reprint permission is obtained from TMI-IEEE, SPIE and all co-authors no objection certificate is
issued
[1] J.N. Wolfe. Risk for breast cancer development determined by mammographic
parenchymal pattern. Cancer, 37(5):2486–92, 1976.
[2] Keller B, Nathan D, Wang Y, Zheng Y, Gee J, Conant E, and Kontos D. Adaptive
multi-cluster fuzzy c-means segmentation of breast parenchymal tissue in digital
mammography. Med Image Comput Comput Assist Interv., 14(3):562–9, 2011.
[3] D M Parking, P Pisani, and J Ferlay. Global cancer statistics. CA A Cancer Journal
for Clinicians, 49(1):33–64, jan-feb 1999.
[4] F. Michor, Y. Iwasa, and M.A. Nowak. Dynamics of cancer progression. Nat Rev
Cancer, 4(3):197–205, 2004.
[5] C. Desantis, R. Siegel, P. Bandi, and A. Jemal. Breast cancer statistics, 2011. CA
Cancer J Clin, 2011.
[6] J. Russo and I.H. Russo. Biological and molecular bases of mammary carcinogenesis. Lab Invest, 57(2):112–37, 1987.
[7] S. Park, J.S. Koo, M.S. Kim, H.S. Park, J.S. Lee, J.S. Lee, S.I. Kim, and B. Park.
Characteristics and outcomes according to molecular subtypes of breast cancer
as classified by a panel of four biomarkers using immunohistochemistry. Breast,
2011.
[8] M.H. Gail, L.A. Brinton, D.P. Byar, D.K. Corle, S.B. Green, C. Schairer, and J.J.
Mulvihill. Projecting individualized probabilities of developing breast cancer for
white females who are being examined annually. J Natl Cancer Inst, 81(24):1879–86,
1989.
[9] http://www.cancer.gov/cancertopics/pdq/screening/breast/HealthProfessional.
National cancer institute: Breast cancer screening. 2010.
[10] R.A. Smith, V. Cokkinides, A.C. von Eschenbach, B. Levin, C. Cohen, C.D. Runowicz, S. Sener, D. Saslow, and H.J. Eyre. American cancer society guidelines for the
early detection of cancer. CA Cancer J Clin, 52(1):8–22.
[11] H. Li, M.L. Giger, O.I. Olopade, A. Margolis, L. Lan, and M.R. Chinander. Computerized texture analysis of mammographic parenchymal patterns of digitized
mammograms. Acad Radiol, 12(7):863–73, 2005.
169
[12] NF Boyd, JW Byng, and RA Jong. Quantitative classification of mammographic
densities and breast cancer risk: results from the canadian national breast screening study. J Natl Cancer Inst, 87:670–5, 1995.
[13] Daniel B. Kopans. Breast Imaging. Lippincott - Raven, second edition, 1998.
[14] Catherine Schairer, Jay Lubin, Rebecca Troisi, Susan Sturgeon, Louise Brinton, and
Robert Hoover. Menopausal estrogen and estrogen-progestin replacement therapy
and breast cancer risk. Journal of the American Medical Association, 283(4):485–491,
January 2000.
[15] R. K. Ross, A. Paganini-Hill, P. C. Wan, and M. C. Pike. Effect of hormone replacement therapy on breast cancer risk: Estrogen versus estrogen plus progestin.
Journal of the National Cancer Institute, 92(4):328–332, February 2000.
[16] N. Hamajima, K. Hirose, and K. et al Tajima. Alcohol, tobacco and breast cancer–
collaborative reanalysis of individual data from 53 epidemiological studies, including 58,515 women with breast cancer and 95,067 women without the disease.
Br J Cancer, 87(11):1234–45, 2002.
[17] K.A. Brown and E.R. Simpson. Obesity and breast cancer: progress to understanding the relationship. Cancer Res, 70(1):4–7, 2010.
[18] J. Brisson, B. Brisson, G. Cot, E. Maunsell, S. Brub, and J. Robert. Tamoxifen and
mammographic breast densities. Cancer Epidemiology Biomarkers and Prevention,
9(9):911–915, September 2000.
[19] Matthew Freedman, Javier San Martin, John O’Gorman, Stephen Eckert, Marc E.
Lippman, Shih-Chung B. Lo, Erin L. Walls, and Jianchao Zeng. Digitized mammography: a clinical trial of postmenopausal women randomly assigned to receive
raloxifene, estrogen, or placebo. Journal of the National Cancer Institute, 93(1):51–56,
January 2001.
[20] Katrina Armstrong, Andrea Eisen, and Weber Barbara. Assessing the risk of breast
cancer. The New England Journal of Medicine, 342:564–571, Feb 2000.
[21] E.J. Feuer, L.M. Wun, C.C. Boring, W.D. Flanders, M.J. Timmel, and T. Tong. The
lifetime risk of developing breast cancer. J Natl Cancer Inst, 85(11):892–7, 1993.
[22] K. Kerlikowske, D. Grady, S.M. Rubin, C. Sandrock, and V.L. Ernster. Efficacy of
screening mammography. a meta-analysis. JAMA, 273(2):149–54, 1995.
[23] G. van Schoor, S.M. Moss, J.D.M. Otten, R. Donders, E. Paap, G.J. den Heeten,
R. Holland, M.J.M. Broeders, and A.L.M. Verbeek. Increasingly strong reduction
in breast cancer mortality due to screening. Br J Cancer, 104(6):910–4, 2011.
[24] M.J.M. Broeders, A.L.M. Verbeek, H. Straatman, P.G.M. Peer, P.C.M.P. Jong,
L.V.A.M. Beex, J.H.C.L. Hendriks, and R. Holland. Repeated mammographic
screening reduces breast cancer mortality along the continuum of age. J Med
Screen, 9(4):163–7, 2002.
[25] F. Jafri Nazia and J. Slanetz Priscilla. The shrinking breast: An unusual mammographic finding of invasive lobular carcinoma. Radiology Case Reports, 2(3):94,
2007.
[26] JJ Heine and P Malhotra. Mammographic tissue, breast cancer risk, serial image
analysis and digital mammography. part 1 tissue and related risk factors. Academic
radiology, 9(3):115–122, 2002.
[27] Edwin F Daily. The health insurance plannew york city welfare department project.
American Journal Of Public Health And The Nations Health, 53(9):1353–1360, 1963.
[28] John A Shepherd, Serghei Malkov, Bo Fan, Aurelie Laidevant, Rachel Novotny, and
Gertraud Maskarinec. Breast density assessment in adolescent girls using dualenergy x-ray absorptiometry: a feasibility study. Cancer epidemiology biomarkers
prevention a publication of the American Association for Cancer Research cosponsored by
the American Society of Preventive Oncology, 17(7):1709–1713, 2008.
[29] K. Kerlikowske, D. Grady, J. Barclay, E.A. Sickles, A. Eaton, and V. Ernster. Positive
predictive value of screening mammography by age and family history of breast
cancer. JAMA, 270(20):2444–50, 1993.
[30] P. Salzmann, K. Kerlikowske, and K. Phillips. Cost-effectiveness of extending
screening mammography guidelines to include women 40 to 49 years of age. Ann
Intern Med, 127(11):955–65, 1997.
[31] K.J. Jrgensen. Flawed methods explain the effect of mammography screening in
nijmegen. Br J Cancer, 105(4):592–3, 2011.
[32] K.J. Jrgensen, J.D. Keen, and P.C. Gtzsche. Is mammographic screening justifiable considering its substantial overdiagnosis rate and minor effect on mortality?
Radiology, 260(3):621–7, 2011.
[33] JN Wolfe. Mammography: ducts as a sole indicator of breast carcinoma. Radiology,
89:206–210, 1967.
[34] JN Wolfe. A study of breast parenchyma by mammography in the normal woman
and those with benign and malignant disease. Radiology, 89:201–205, 1967.
[35] J N Wolfe. Risk for breast cancer development determined by mammographic
parenchymal pattern. Cancer, 37(5):2486–2498, 1976.
[36] P.M. Krook, T. Carlile, W. Bush, and M.H. Hall. Mammographic parenchymal
patterns as a risk indicator for prevalent and incident cancer. Cancer, 41(3):1093–7,
1978.
[37] L. Tabar and P.B. Dean. Mammographic parenchymal patterns. risk indicator for
breast cancer? JAMA, 247(2):185–9, 1982.
[38] J. Brisson, R. Verreault, A.S. Morrison, S. Tennina, and F. Meyer. Diet, mammographic features of breast tissue, and breast cancer risk. Am J Epidemiol, 130(1):14–
24, 1989.
[39] A.M. Oza and N.F. Boyd. Mammographic parenchymal patterns: a marker of
breast cancer risk. Epidemiol Rev, 15(1):196–208, 1993.
[40] J. W. Byng, N. F. Boyd, E. Fishell, R. A. Jong, and M. J. Yaffe. The quantitative
analysis of mammographic densities. Physics in Medicine and Biology, 39:162938,
1994.
[41] A.F. Saftlas, J.N. Wolfe, R.N. Hoover, L.A. Brinton, C. Schairer, M. Salane, and
M. Szklo. Mammographic parenchymal patterns as indicators of breast cancer
risk. Am J Epidemiol, 129(3):518–26, 1989.
[42] E. Warner, G. Lockwood, D. Tritchler, and N.F. Boyd. The risk of breast cancer
associated with mammographic parenchymal patterns: a meta-analysis of the
published literature to examine the effect of method of classification. Cancer Detect
Prev, 16(1):67–72, 1992.
[43] N.F. Boyd, G.A. Lockwood, J.W. Byng, D.L. Tritchler, and M.J. Yaffe. Mammographic densities and breast cancer risk. Cancer Epidemiol Biomarkers Prev,
7(12):1133–44, 1998.
[44] J. Brisson, F. Merletti, N.L. Sadowsky, J.A. Twaddle, A.S. Morrison, and P. Cole.
Mammographic features of the breast and breast cancer risk. Am J Epidemiol,
115(3):428–37, 1982.
[45] N.F. Boyd, J.M. Rommens, K. Vogt, V. Lee, J.L. Hopper, M.J. Yaffe, and A.D.
Paterson. Mammographic breast density as an intermediate phenotype for breast
cancer. Lancet Oncol, 6(10):798–808, 2005.
[46] C. Byrne, C. Schairer, L.A. Brinton, J. Wolfe, N. Parekh, M. Salane, C. Carter, and
R. Hoover. Effects of mammographic density and benign breast disease on breast
cancer risk (united states). Cancer Causes Control, 12(2):103–10, 2001.
[47] L. Martin and N. Boyd. Mammographic density. potential mechanisms of breast
cancer risk associated with mammographic density: hypotheses based on epidemiological evidence. Breast Cancer Res, 10(1):201, 2008.
[48] E.J. Roebuck. The importance of mammographic parenchymal patterns. Br J
Radiol, 55(654):387–98, 1982.
[49] H. Lee-Han, G. Cooke, and N.F. Boyd. Quantitative evaluation of mammographic
densities: a comparison of methods of assessment. Eur J Cancer Prev, 4(4):285–92,
1995.
[50] American College of Radiology. Illustrated Breast Imaging Reporting and Data System.
American College of Radiology, third edition, 1998.
[51] C.H. van Gils, J.H. Hendriks, R. Holland, N. Karssemeijer, J.D. Otten, H. Straatman,
and A.L. Verbeek. Changes in mammographic breast density and concomitant
changes in breast cancer risk. Eur J Cancer Prev, 8(6):509–15, 1999.
[52] Mads Nielsen, Paola C Pettersen, Peter Alexandersen, Gopal Karemore, Jakob
Raundahl, Marco Loog, and Claus Christiansen. Breast density changes associated
with postmenopausal hormone therapy: post hoc radiologist- and computerbased analyses. Menopause New York Ny, 17(4):772–778, 2010.
[53] M Nielsen, J Raundahl, PC Pettersen, M Loog, G Karemore, MA Karsdal, and
C. Christiansen. Low-dose transdermal estradiol induces breast density and heterogeneity changes comparable to those of raloxifene. Menopause, 16:785–91, 2009.
[54] Lokate Mariette, HM Peeters Petra, M Peelen Linda, Haars Gerco, B Veldhuis
Wouter, and H van Gils Carla. Mammographic density and breast cancer risk:
the role of the fat surrounding the fibroglandular tissue. Breast Cancer Research,
13(R103), 2011.
[55] C. Byrne, C. Schairer, J. Wolfe, N. Parekh, M. Salane, L.A. Brinton, R. Hoover, and
R. Haile. Mammographic features and breast cancer risk: effects with time, age,
and menopause status. J Natl Cancer Inst, 87(21):1622–9, 1995.
[56] Wei J, Chan HP, Wu YT, Zhou C, Helvie MA, Tsodikov A, Hadjiiski LM, and
Sahiner B. Association of computerized mammographic parenchymal pattern
measure with breast cancer risk: a pilot case-control study. Radiology, 260:42–9,
2011.
[57] H Li, ML Giger, Z Huo, OI Olopade, L Lan, BL Weber, and I. Bonta. Computerized
analysis of mammographic parenchymal patterns for assessing breast cancer risk:
effect of roi size and location. Med Phys, 31:549–55, 2004.
[58] A Manduca, MJ Carston, JJ Heine, CG Scott, VS Pankratz, KR Brandt, TA Sellers,
CM Vachon, and JR. Cerhan. Texture features from mammographic images and
risk of breast cancer. Cancer Epidemiol Biomarkers Prev, 18:837–45, 2009.
[59] D Kontos, LC Ikejimba, PR Bakic, AB Troxel, EF Conant, and AD. Maidment.
Analysis of parenchymal texture with digital breast tomosynthesis: comparison
with digital mammography and implications for cancer risk assessment. Radiology,
261:80–91, 2011.
[60] Spiros Kostopoulos, Dionisis Cavouras, Antonis Daskalakis, Ioannis Kalatzis,
Panagiotis Bougioukos, George C. Kagadis, Panagiota Ravazoula, and George
Nikiforidis. Assessing estrogen receptors’ status by texture analysis of breast tissue specimens and pattern recognition methods. In Computer Analysis of Images
and Patterns, pages 221–228. Springer Berlin / Heidelberg, 2007.
[61] Lisa M. Hines, Betsy Risendal, and Martha L. Slattery. Differences in estrogen
receptor subtype according to family history of breast cancer among hispanic,
but not non-hispanic white women. Cancer Epidemiol Biomarkers Prev, 17:2700–06,
2008.
[62] Maki DD and Grossman RI. Patterns of disease spread in metastatic breast carcinoma: influence of estrogen and progesterone receptor status. AJNR Am J
Neuroradiol, 21:1064–6, 2000.
[63] Erin J. Aiello, Diana S.M. Buist, and Emily White. Association between mammographic breast density and breast cancer tumor characteristics. Cancer Epidemiol
Biomarkers Prev, 14:662–68, 2005.
[64] Althuis MD, Fergenbaum JH, Garcia-Closas M, Brinton LA, Madigan MP, and
Sherman ME. Etiology of hormone receptor-defined breast cancer: a systematic
review of the literature. Cancer Epidemiol Biomarkers Prev, 13(10):1558–68, 2004.
[65] C H van Gils, J H C L Hendriks, R Holland, N Karssemeijer, J D M Otten, H Straatman, and A L M Verbeek. Changes in mammographic breast density and concomitant changes in breast cancer risk. European Journal of Cancer Prevention, 8:509–515,
1999.
[66] Z Huo, M L Giger, D E Wolverton, W Zhong, S Cumming, and O I Olopade.
Computerized analysis of mammographic parenchymal patterns for breast cancer
risk assessment: feature selection. Medical Physics, 27(1):4–12, 2000.
[67] Hui Li, Maryellen L Giger, Zhimin Huo, Olufunmilayo I Olopade, Michael R
Chinander, and Li Lan. Computerized analysis of mammographic parenchymal patterns
using fractal analysis, volume 5032, pages 90–93. 2003.
[68] Jakob Raundahl and et al. Understanding hessian-based density scoring. In Digital
Mammography, volume 4046, pages 447–452, 2006.
[69] S Petroudi, T Kadir, and M Brady. Automatic classification of mammographic
parenchymal patterns: a statistical approach. Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society IEEE Cat
No03CH37439, pages 798–801, 2003.
[70] S Petroudi, K Marias, and M Brady. Evaluation of effect of hrt on breast density.
Lecture Notes in Comp. Sci., 4046:39, 2006.
[71] Y Gong, Michael Brady, and Styliani Petroudi. Texture based mammogram classification and segmentation. Digital Mammography, page 616625, 2006.
[72] J.N. Wolfe, A.F. Saftlas, and M. Salane. Mammographic parenchymal patterns and
quantitative evaluation of mammographic densities: a case-control study. AJR Am
J Roentgenol, 148(6):1087–92, 1987.
[73] Norman F Boyd, Lisa J Martin, Qing Li, Limei Sun, Anna M Chiarelli, Greg Hislop, Martin J Yaffe, and Salomon Minkin. Mammographic density as a surrogate
marker for the effects of hormone therapy on risk of breast cancer. Cancer epidemiology biomarkers prevention a publication of the American Association for Cancer
Research cosponsored by the American Society of Preventive Oncology, 15(5):961–966,
2006.
[74] N F Boyd, B O’Sullivan, J E Campbell, and et al. Mammographic signs as risk
factors for breast cancer. British Journal of Cancer, 45:185–193, 1982.
[75] Boyd NF, Martin LJ, Bronskill M, Yaffe MJ, Duric N, and Minkin S. Breast tissue
composition and susceptibility to breast cancer. J Natl Cancer Inst, 102:1224–37,
2010.
[76] N. Boyd, L. Martin, A. Gunasekara, O. Melnichouk, G. Maudsley, C. Peressotti,
M. Yaffe, and S. Minkin. Mammographic density and breast cancer risk: evaluation
of a novel method of measuring breast tissue volumes. Cancer Epidemiol Biomarkers
Prev, 18(6):1754–62, 2009.
[77] M. Yaffe. Mammographic density. measurement of mammographic density. Breast
Cancer Res, 10(3):209, 2008.
[78] John A Shepherd, Lionel Herve, Jessie Landau, Bo Fan, Karla Kerlikowske, and
Steve R Cummings. Novel use of single x-ray absorptiometry for measuring breast
density. Technology in cancer research treatment, 4(2):173–182, 2005.
[79] Melanie R Palomares, Joelle R B Machia, Constance D Lehman, Janet R Daling,
and Anne McTiernan. Mammographic density correlation with gail model breast
cancer risk estimates and component risk factors. Cancer epidemiology biomarkers
prevention a publication of the American Association for Cancer Research cosponsored by
the American Society of Preventive Oncology, 15(7):1324–1330, 2006.
[80] Despina Kontos, Predrag R Bakic, Ann-Katherine Carton, Andrea B Troxel, Emily F
Conant, and Andrew D A Maidment. Parenchymal texture analysis in digital
breast tomosynthesis for breast cancer risk estimation: a preliminary study. Academic Radiology, 16(3):283–298, 2009.
[81] A.P. Dhawan, Y. Chitre, and C. Kaiser-Bonasso. Analysis of mammographic microcalcifications using gray-level image structure features. IEEE Trans Med Imaging,
15(3):246–59, 1996.
[82] H.P. Chan, B. Sahiner, N. Petrick, M.A. Helvie, K.L. Lam, D.D. Adler, and M.M.
Goodsitt. Computerized classification of malignant and benign microcalcifications
on mammograms: texture analysis using an artificial neural network. Phys Med
Biol, 42(3):549–67, 1997.
[83] H.P. Chan, B. Sahiner, K.L. Lam, N. Petrick, M.A. Helvie, M.M. Goodsitt, and D.D.
Adler. Computerized analysis of mammographic microcalcifications in morphological and texture feature spaces. Med Phys, 25(10):2007–19, 1998.
[84] J.C. Fu, S.K. Lee, S.T.C. Wong, J.Y. Yeh, A.H. Wang, and H.K. Wu. Image segmentation feature selection and pattern classification for mammographic microcalcifications. Comput Med Imaging Graph, 29(6):419–29, 2005.
[85] S. Singh, V. Kumar, H. Verma, and D. Singh. Svm based system for classification
of microcalcifications in digital mammograms. Conf Proc IEEE Eng Med Biol Soc,
1, 2006.
[86] A.N. Karahaliou, I.S. Boniatis, S.G. Skiadopoulos, F.N. Sakellaropoulos, N.S.
Arikidis, E.A. Likaki, G.S. Panayiotakis, and L.I. Costaridou. Breast cancer diagnosis: analyzing texture of tissue surrounding microcalcifications. IEEE Trans
Inf Technol Biomed, 12(6):731–8, 2008.
[87] ML Giger, F. Yin, K. Doi, CE Metz, R A Schmidt, and CJ Vyborny. Investigation of
methods for the computerised detection and analysis of mammographic masses.
SPIE Conference Medical Imaging IV - Image Processing SPIE, 1233:183–184.
[88] P Miller and S Astley. Classification of breast tissue by texture analysis. Image and
Vision Computing, 10:277–283, 1992.
[89] R. Gupta and P.E. Undrill. The use of texture analysis to delineate suspicious
masses in mammography. Phys Med Biol, 40(5):835–55, 1995.
[90] B. Sahiner, H.P. Chan, N. Petrick, M.A. Helvie, and M.M. Goodsitt. Computerized characterization of masses on mammograms: the rubber band straightening
transform and texture analysis. Med Phys, 25(4):516–26, 1998.
[91] N.R. Mudigonda, R.M. Rangayyan, and J.E. Desautels. Gradient and texture
analysis for the classification of mammographic masses. IEEE Trans Med Imaging,
19(10):1032–43, 2000.
[92] R. Bellotti, F. De Carlo, S. Tangaro, G. Gargano, G. Maggipinto, M. Castellano,
R. Massafra, D. Cascio, F. Fauci, R. Magro, G. Raso, A. Lauria, G. Forni, S. Bagnasco,
P. Cerello, E. Zanon, S.C. Cheran, E. Lopez Torres, U. Bottigli, G.L. Masala, P. Oliva,
A. Retico, M.E. Fantacci, R. Cataldo, I. De Mitri, and G. De Nunzio. A completely
automated cad system for mass detection in a large mammographic database. Med
Phys, 33(8):3066–75, 2006.
[93] H. Georgiou, M. Mavroforakis, N. Dimitropoulos, D. Cavouras, and S. Theodoridis. Multi-scaled morphological features for the characterization of mammographic masses using statistical classification schemes. Artif Intell Med, 2007.
[94] M. Masotti, N. Lanconelli, and R. Campanini. Computer-aided mass detection in
mammography: false positive reduction via gray-scale invariant ranklet texture
features. Med Phys, 36(2):311–6, 2009.
[95] Tuceryan Mihran and Anil Jain. The Handbook of Pattern Recognition and Computer
Vision, 2nd Edition, chapter Texture Analysis. World Scientific Publishing Co, 1998.
[96] Hideyuki Tamura, Shunji Mori, and Takashi Yamawaki. Textural features corresponding to visual perception. IEEE Transactions on Systems, Man and Cybernetics,
8(6):460–473, 1978.
[97] R. M. Haralick. Statistical and structural approaches to texture. Proceedings of the
IEEE, 67(5):786–804, 1979.
[98] IE Magnin, F Cluzeau, CL Odet, and A. Bremond. Mammographic texture analysis: an evaluation of risk for developing breast cancer. Opt Eng, 25:780–784,
1986.
[99] H P Chan, D Wei, M A Helvie, B Sahiner, D D Adler, M M Goodsitt, and N Petrick.
Computer-aided classification of mammographic masses and normal tissue: linear
discriminant analysis in texture feature space. Physics in Medicine and Biology,
40(5):857–876, 1995.
[100] A Petrosian, H P Chan, M A Helvie, M M Goodsitt, and D D Adler. Computeraided diagnosis in mammography: Classification of mass and normal tissue by
texture analysis. Physics in Medicine and Biology, 39(12):2273–88, 1994.
[101] B Sahiner, H P Chan, N Petrick, D Wei, M A Helvie, D D Adler, and M M Goodsitt.
Classification of mass and normal breast tissue: a convolution neural network
classifier with spatial domain and texture images. IEEE Transactions on Medical
Imaging, 15(5):598–610, 1996.
[102] P Taylor, S Hajnal, Mh Dilhuydy, , and B Barreau. Using computers to separate
difficult from easy mammograms. The British journal of radiology, 67(797):456–463,
1994.
[103] B Verma and J Zakos. A computer-aided diagnosis system for digital mammograms based on fuzzy-neural and feature extraction techniques. IEEE transactions on information technology in biomedicine a publication of the IEEE Engineering in
Medicine and Biology Society, 5(1):46–54, 2001.
[104] A Karahaliou, I Boniatis, P Sakellaropoulos, S Skiadopoulos, G Panayiotakis, and
L Costaridou. Can texture of tissue surrounding microcalcifications in mammography be used for breast cancer diagnosis? Nuclear Instruments and Methods
in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated
Equipment, 580(2):1071–1074, 2007.
[105] J C Fu, S K Lee, S T C Wong, J Y Yeh, A H Wang, and H K Wu. Image segmentation
feature selection and pattern classification for mammographic microcalcifications.
Computerized medical imaging and graphics the official journal of the Computerized
Medical Imaging Society, 29(6):419–429, 2005.
[106] Anna N Karahaliou, Ioannis S Boniatis, Spyros G Skiadopoulos, Filippos N Sakellaropoulos, Nikolaos S Arikidis, Eleni A Likaki, George S Panayiotakis, and Lena I
Costaridou. Breast cancer diagnosis: analyzing texture of tissue surrounding microcalcifications. IEEE transactions on information technology in biomedicine a publication of the IEEE Engineering in Medicine and Biology Society, 12(6):731–738, 2008.
[107] J K Kim and H W Park. Statistical textural features for detection of microcalcifications in digitized mammograms. IEEE Transactions on Medical Imaging, 18(3):231–
238, 1999.
[108] D L Thiele, C Kimme-Smith, T D Johnson, M McCombs, and L W Bassett. Using
tissue texture surrounding calcification clusters to predict benign vs malignant
outcomes. Medical Physics, 23(4):549–555, 1996.
[109] N R Mudigonda, R M Rangayyan, and J E Desautels. Gradient and texture
analysis for the classification of mammographic masses. IEEE Transactions on
Medical Imaging, 19(10):1032–1043, 2000.
[110] Tingting Mu, Asoke K Nandi, and Rangaraj M Rangayyan. Classification of breast
masses using selected shape, edge-sharpness, and texture features with linear and
kernel-based classifiers. Journal of digital imaging the official journal of the Society for
Computer Applications in Radiology, 21(2):153–169, 2008.
[111] Z Huo, M L Giger, C J Vyborny, D E Wolverton, and C E Metz. Computerized
classification of benign and malignant masses on digitized mammograms: a study
of robustness. Academic Radiology, 7(12):1077–1084, 2000.
[112] Yi-Ta Wu, Jun Wei, Lubomir M Hadjiiski, Berkman Sahiner, Chuan Zhou, Jun Ge,
Jiazheng Shi, Yiheng Zhang, and Heang-Ping Chan. Bilateral analysis based false
positive reduction for computer-aided mass detection. Medical Physics, 34(8):3334–
3344, 2007.
[113] P G Tahoces, J Correa, M Souto, L Gmez, and J J Vidal. Computer-assisted diagnosis: the classification of mammographic breast parenchymal patterns. Physics
in Medicine and Biology, 40(1):103–117, 1995.
[114] M L Giger, C J Vyborny, F I Olopade, and D E Wolverton. Computer-aided
diagnosis: analysis of mammographic parenchymal patterns and classification of
masses on digitized mammograms. Proceedings of the 20th Annual International
Conference of the IEEE Engineering in Medicine and Biology Society Vol20 Biomedical
Engineering Towards the Year 2000 and Beyond Cat No98CH36286, (2):1017–1020,
1998.
[115] J J Heine and R P Velthuizen. A statistical methodology for mammographic density
detection. Medical Physics, 27(12):2644–2651, 2000.
[116] Shalini Gupta and Mia K Markey. Correspondence in texture features between
two mammographic views. Medical Physics, 32(6):1598–1606, 2005.
[117] H S Sheshadri and A Kandaswamy. Experimental investigation on breast tissue
classification based on statistical feature extraction of mammograms. Computerized
medical imaging and graphics the official journal of the Computerized Medical Imaging
Society, 31(1):46–48, 2007.
[118] Laws K. Textured image segmentation. Ph.D. Dissertation: University of Southern
California, 1980.
[119] Laws K. Rapid texture identification. In SPIE Vol. : Image Processing for Missile
Guidance, 238:1490–500, 1980.
[120] Peter Miller and Sue Astley. Classification of breast tissue by texture analysis.
Image and Vision Computing, 10(5):277–282, 1992.
[121] R Gupta and P E Undrill. The use of texture analysis to delineate suspicious
masses in mammography. Physics in Medicine and Biology, 40(5):835–855, 1995.
[122] W E Polakowski, D A Cournoyer, S K Rogers, M P DeSimio, D W Ruck, J W
Hoffmeister, and R A Raines. Computer-aided breast cancer detection and diagnosis of masses using difference of gaussians and derivative-based feature saliency.
IEEE Transactions on Medical Imaging, 16(6):811–819, 1997.
[123] R Pfisterer and F Aghdasi. Tumor detection in digitized mammograms by image
texture analysis. Optical Engineering, 40(2):209–216, 2001.
[124] Karahaliou A., Skiadopoulos S., Boniatis I., Sakellaropoulos P., Likaki E., Panayiotakis G., and Costaridou L. Texture analysis of tissue surrounding microcalcifications on mammograms for breast cancer diagnosis. Br J Radiol, 2007.
[125] Shantanu Banik, Rangaraj M Rangayyan, and J E Leo Desautels. Detection of architectural distortion in prior mammograms. IEEE Transactions on Medical Imaging,
30(2):279–294, 2011.
[126] Maria Petrou. Image Processing: Dealing with Texture. Wiley, 1 edition, 2006.
[127] B Mandelbrot. The fractal geometry of nature. W.H. Freemann and Company, 1983.
[128] P. Soille and J.F. Rivest. On the validity of fractal dimension measurements in image
analysis. Journal of Visual Communication and Image Rep- resentation, 7(3):217–229,
1996.
[129] J. Keller and S. et al Chen. Texture description and segmentation through fractal
geometry. Computer Vision, Graphics, and Image Processing, 45:150166, 1989.
[130] P Gabriel, S Lovejoy, D Schertzer, and G L Austin. Multifractal analysis of resolution dependence in satellite imagery. Geophysical Research Letters, 15(12):13731376,
1988.
[131] T Parrinello and R A Vaughan. Multifractal analysis and feature extraction in
satellite imagery. International Journal of Remote Sensing, 23(9):1799–1825, 2002.
[132] F Arduini, S Fioravanti, and D D Giusto. Natural surface characterization by
multifractals. IAPR Workshop on Machine Vision Applications, pages 295–298, 1990.
[133] C J G Evertsz and B B Mandelbrot. Multifractal measures, volume 372, pages
921–953. Kluwer Academic Publishers Group, Dordrecht, The Netherlands, 1992.
[134] Irini S Reljin and Branimir D Reljin. Fractal geometry and multifractals in analyzing and processing medical data and images. Archive of Oncology, 10(4):283–293,
2002.
[135] C B Caldwell, S J Stapleton, D W Holdsworth, R A Jong, W J Weiser, G Cooke,
and M J Yaffe. Characterization of mammographic parenchymal pattern by fractal
dimension. Physics in Medicine and Biology, 35(2):235–247, 1990.
[136] J W Byng, N F Boyd, L Little, G Lockwood, E Fishell, R A Jong, and M J Yaffe.
Symmetry of projection in the quantitative analysis of mammographic images. European journal of cancer prevention the official journal of the European Cancer Prevention
Organisation ECP, 5(5):319–327, 1996.
[137] V Velanovich. Fractal analysis of mammographic lesions: a feasibility study
quantifying the difference between benign and malignant masses. The American
journal of the medical sciences, 311(5):211–214, 1996.
[138] L Zheng and A K Chan. An artificial intelligent algorithm for tumor detection in
screening mammogram. IEEE Transactions on Medical Imaging, 20(7):559–567, 2001.
[139] Predrag R Bakic, Michael Albert, Dragana Brzakovic, and Andrew D A Maidment. Mammogram synthesis using a 3d simulation. ii. evaluation of synthetic
mammogram texture. Medical Physics, 29(9):2140–2151, 2002.
[140] V Oktem and I Jouny. Automatic detection of malignant tumors in mammograms.
Conference Proceedings of the International Conference of IEEE Engineering in Medicine
and Biology Society, 3:1770–1773, 2004.
[141] Thanh Nguyen and Rangaraj Rangayyan. Shape analysis of breast masses in
mammograms via the fractal dimension. Conference Proceedings of the International
Conference of IEEE Engineering in Medicine and Biology Society, 3:3210–3213, 2005.
[142] Gopal Karemore and Mads Nielsen. Fractal dimension and lacunarity analysis
of mammographic patterns in assessing breast cancer risk related to hrt treated
population: a longitudinal and cross-sectional study. In Medical Imaging 2009:
Computer-Aided Diagnosis, volume 7260 of Proceedings of the SPIE, pages 72602F–
72602F–9, 2009.
[143] Gabriela Torres-Meja, Bianca De Stavola, Diane S Allen, Juan J Prez-Gaviln,
Jorge M Ferreira, Ian S Fentiman, and Isabel Dos Santos Silva. Mammographic
features and subsequent risk of breast cancer: a comparison of qualitative and
quantitative evaluations in the guernsey prospective studies. Cancer epidemiology
biomarkers prevention a publication of the American Association for Cancer Research
cosponsored by the American Society of Preventive Oncology, 14(5):1052–1059, 2005.
[144] Deepa Sankar and Tessamma Thomas. A new fast fractal modeling approach for
the detection of microcalcifications in mammograms. Journal of digital imaging the
official journal of the Society for Computer Applications in Radiology, 23(5):538–546,
2010.
[145] Shantanu Banik and Rangaraj M Rangayyan. Correction to detection of architectural distortion in prior mammograms using gabor filters, phase portraits, fractal
dimension, and texture analysis [1]. International journal of computer assisted radiology and surgery, 5(4):421–423, 2010.
[146] Despina Kontos, Predrag R Bakic, and Andrew D A Maidment. Texture in digital
breast tomosynthesis: a comparison between mammographic and tomographic
characterization of parenchymal properties. Proceedings of SPIE, 6915:69150A–
69150A–11, 2008.
[147] Lynda C Ikejimba, Andrea B Troxel, Emily F Conant, and Andrew D A Maidment.
Analysis of parenchymal texture with digital breast tomosynthesis : Comparison
with digital mammography and implications for cancer risk purpose : Methods :
Results. Radiology, 261(1):80–91, 2011.
[148] L. Shen, R.M. Rangayyan, and J.L. Desautels. Application of shape analysis to
mammographic calcifications. IEEE Trans Med Imaging, 13(2):263–74, 1994.
[149] M. Kallergi. Computer-aided diagnosis of mammographic microcalcification clusters. Med Phys, 31(2):314–26, 2004.
[150] Harris Georgiou, Michael Mavroforakis, Nikos Dimitropoulos, Dionisis Cavouras,
and Sergios Theodoridis. Multi-scaled morphological features for the characterization of mammographic masses using statistical classification schemes. Artificial
Intelligence in Medicine, 41(1):39–55, 2007.
[151] Rangaraj M Rangayyan, Shantanu Banik, and J E Leo Desautels. Computer-aided
detection of architectural distortion in prior mammograms of interval cancer.
Journal of digital imaging the official journal of the Society for Computer Applications in
Radiology, 23(5):611–631, 2010.
[152] Shantanu Banik, Rangaraj M Rangayyan, and J E Leo Desautels. Detection of architectural distortion in prior mammograms. IEEE Transactions on Medical Imaging,
30(2):279–294, 2011.
[153] M.R. Turner. Texture discrimination by gabor functions. Biol Cybern, 55(2-3):71–82,
1986.
[154] A Kaewlium and H Longbotham. Application of gabor transform as texture discriminator of masses in digital mammograms. Biomedical Sciences Instrumentation,
29:183–190, 1993.
[155] Rangaraj M Rangayyan and Fbio J Ayres. Gabor filters and phase portraits for the
detection of architectural distortion in mammograms. sdsdsdsd, 44(10):883–894,
2006.
[156] Yufeng Zheng. Breast cancer detection with gabor features from digital mammograms. Algorithms, 3(1):44–62, 2010.
[157] Daniel D Costa, Lcio F Campos, and Allan K Barros. Classification of breast tissue
in mammograms using efficient coding. BioMedical Engineering Online, 10(1):55,
2011.
[158] A Mencattini, M Salmeri, and P Casti. Bilateral asymmetry identification for the
early detection of breast cancer. IEEE International symposium on medical measurements and applications, 2011.
[159] B Zheng, W Qian, and L P Clarke. Digital mammography: mixed feature neural
network with spectral entropy decision for detection of microcalcifications. IEEE
Transactions on Medical Imaging, 15(5):589–597, 1996.
[160] C M Kocur, S K Rogers, L R Myers, T Burns, M Kabrisky, J W Hoffmeister, K W
Bauer, and J M Steppe. Using neural networks to select wavelet features for breast
cancer diagnosis. IEEE Engineering in Medicine and Biology Magazine, 15(3):95–102,
108, 1996.
[161] R N Strickland and H I Hahn. Wavelet transforms for detecting microcalcifications
in mammograms. IEEE Transactions on Medical Imaging, 15(2):218–229, 1996.
[162] C Ferreira. Analysis of mammogram classification using a wavelet transform
decomposition. Pattern Recognition Letters, 24(7):973–982, 2003.
[163] H Soltanianzadeh. Comparison of multiwavelet, wavelet, haralick, and shape
features for microcalcification classification in mammograms. Pattern Recognition,
37(10):1973–1986, 2004.
[164] A. Manduca, M.J. Carston, J.J. Heine, C.G. Scott, V.S. Pankratz, K.R. Brandt, T.A.
Sellers, C.M. Vachon, and J.R. Cerhan. Texture features from mammographic
images and risk of breast cancer. Cancer Epidemiol Biomarkers Prev, 2009.
[165] Bart M Ter Haar Romeny. Front-end vision and multi-scale image analysis. Physics,
Vi(xiii):2002–2002, 2002.
[166] Tony Lindeberg. Scale-Space Theory in Computer Vision. Kluwer Academic Publishers, 1994.
[167] Tony Lindeberg. Scale-space: A framework for handling image structures at multiple scales. CERN EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHREPORTSCERN, 96(8):1–12, 1996.
[168] Alfredo Petrosino and Michele Ceccarelli. A scale-space approach to preattentive
texture discrimination. Proceedings 10th International Conference on Image Analysis
and Processing, pages 162–167, 1999.
[169] Bart Ter Haar Romeny, Luc Florack, and Mads Nielsen. Scale-Space and Morphology
in Computer Vision, volume 2106. Springer Berlin Heidelberg, 2006.
[170] J. J. Koenderink. The structure of images. Biological cybernetics, 50(5):363–370, 1984.
[171] N Karssemeijer and G M Te Brake. Detection of stellate distortions in mammograms. IEEE Transactions on Medical Imaging, 15(5):611–619, 1996.
[172] Nico Karssemeijer. Local orientation distribution as a function of spatial scale for
detection of masses in mammograms. Distribution, 1613:280–293, 1999.
[173] Thomas Netsch and H O Peitgen. Scale-space signatures for the detection of
clustered microcalcifications in digital mammograms. IEEE Transactions on Medical
Imaging, 18(9):774–786, 1999.
[174] Jakob Raundahl. Mammographic density measured as changes in tissue structure
caused by hrt. Proceedings of SPIE, 6144:61440G–61440G–8, 2006.
[175] Jakob Raundahl, Marco Loog, Paola Pettersen, and Mads Nielsen. Quantifying
effect-specific mammographic density. Medical Image Computing and ComputerAssisted Intervention, 10(Pt 2):580–587, 2007.
[176] Jakob Raundahl, Marco Loog, Paola Pettersen, and Mads Nielsen. Evaluation of four mammographic density measures on hrt data. Proceedings of SPIE,
6512:65121F–65121F–6, 2007.
[177] Jakob Raundahl, Marco Loog, Paola Pettersen, Laszlo B Tanko, and Mads Nielsen.
Automated effect-specific mammographic pattern measures. IEEE Transactions on
Medical Imaging, 27(8):1054–1060, 2008.
[178] S. S. Brandt, G. Karemore, N. Karssemeijer, and M. Nielsen. An anatomically
oriented breast coordinate system for mammogram analysis. IEEE Trans Med
Imaging, 30(10):1841–1851, 2011.
[179] Nielsen M, Karemore G, Loog M, Raundahl J, Karssemeijer N, Otten JD, Karsdal
MA, Vachon CM, and Christiansen C. A novel and automatic mammographic
texture resemblance marker is an independent risk factor for breast cancer. Cancer
Epidemiol., 35:381–7, 2011.
[180] Gopal Karemore and Mads Nielsen. An automatic framework for assessing breast
cancer risk due to various hormone replacement therapies (hrt): A novel cad
application in digital mammography. In 96th Scientific Assembly and Annual Meeting
of Radiological Society of North America, Chicago, December 2010. RSNA.
[181] Gopal Karemore, Sami Brandt, N. Karssemeijer, and Mads Nielsen. Automatic
breast cancer risk assessment from digital mammograms. In European Congress of
Radiology, Vienna, December 2011. ECR.
[182] Gopal Karemore and Mads Nielsen. An automatic framework for assessing breast
cancer risk due tovarious hormone replacement therapies (hrt). In 4th International
Workshop on Breast Densitometry and 1st International Workshop on Mammographybased Assessment of Breast Cancer Risk, San Francisco, 2009.
[183] Gopal Karemore and Mads Nielsen. Yet another mammography measure to evaluate breast cancer risk. In 4th International Workshop on Breast Densitometry and 1st
International Workshop on Mammography-based Assessment of Breast Cancer Risk, San
Francisco, 2009.
[184] Gopal Karemore and Mads Nielsen. Fractal dimension and lacunarity analysis of
mammographic patterns in assessing breast cancer risk related to hrt treated population: a longitudinal and cross-sectional study. Proceedings of SPIE, 7260:76230S–
76230S–9, 2009.
[185] Gopal Karemore, Sami Brandt, Nico Karssemeijer, and Mads Nielsen. Discovery
of mammogram regions that show early changes due to the development of breast
cancer: A preliminary work. In Elliot Fishman, editor, 97th Scientific Assembly and
Annual Meeting of Radiological Society of North America-LL-INE1154-WEB, Chicago,
December 2011. RSNA.
[186] Karemore G, Brandt S, Sporring J, and Nielsen M. Anisotropic diffusion tensor applied to temporal mammograms: an application to breast cancer risk assessment.
In Conf Proc IEEE Eng Med Biol Soc, 2010.
[187] Gopal Karemore, Brad Keller, Huen Oh, Julia Tchou, Mads Nielsen, Emily Conant, and Despina Kontos. Computer-aided parenchymal texture analysis in digital mammograms: The potential for estrogen-receptor specific breast cancer risk
estimation. In Jay Alan Baker and Thomas Hans Helbich, editors, 97th Scientific
Assembly and Annual Meeting of Radiological Society of North America-Oral Session
SSG01, Chicago, December 2011. RSNA.
[188] J Suckling. The mammographic image analysis society digital mammogram
database. In Exerpta Medica International Congress Series 1069, pages 375–378, 1994.
[189] N Ibrahim, H Fujita, T Hara, and T Endo. Automated detection of clustered
microcalcifications on mammograms: Cad system application to mias database.
Physics in Medicine and Biology, 42(12):2577–2589, 1997.
[190] M. Heath, K. Bowyer, and D. et al Kopans.
The digital database for
screening mammography.
In M. J. Yaffe, editor, IWDM, pages 212–
218, http://marathon.csee.usf.edu/ Mammography/Database.html, 2001. Medical
Physics Publishing.
[191] Ayman A AbuBaker, R S Qahwaji, Musbah J Aqel, Hussam Al-Osta, and Mohmmad H Saleh. Efficient pre-processing of usf and mias mammogram images.
Journal of Computer Science, 3(2):67–75, 2007.
[192] J.E.E. de Oliveira, A.M.C. Machado, G.C. Chavez, A.P.B. Lopes, T.M. Deserno, and
A.d.A. Arajo. Mammosys: A content-based image retrieval system using breast
density patterns. Comput Methods Programs Biomed, 2010.
[193] Soo-chang Pei and Chao-nan Lin. Image normalization for pattern recognition.
Image and Vision Computing, 13(10):711–723, 1995.
[194] I Reljin, B Reljin, I Pavlovic, and I Rakocevic. Multifractal analysis of gray-scale
images. 2000 10th Mediterranean Electrotechnical Conference Information Technology
and Electrotechnology for the Mediterranean Countries Proceedings MeleCon 2000 Cat
No00CH37099, 2:490–493, 2000.
[195] I Daubechies. Ten Lectures on Wavelets, volume 61. Society for Industrial and
Applied Mathematics, 1992.
[196] Anil K. Jain, Robert P. W. Duin, and Jianchang Mao. Statistical pattern recognition:
A review. IEEE Trans. Pattern Anal. Mach. Intell., 22:4–37, January 2000.
[197] X Tang. Texture information in run-length matrices. IEEE Transactions on Image
Processing, 7(11):1602–1609, 1998.
[198] Olivier Chapelle, Patrick Haffner, and Vladimir Vapnik. Svms for histogram-based
image classification. Learning, 10(3):1–11, 1999.
[199] V N Vapnik. An overview of statistical learning theory. Neural Networks IEEE
Transactions on, 10(5):988–999, 1999.
[200] E R DeLong, D M DeLong, and D L Clarke-Pearson. Comparing the areas under
two or more correlated receiver operating characteristic curves: a nonparametric
approach. Biometrics, 44(3):837–845, 1988.
[201] Marcus A. Maloof, Sergey V. Beiden, and Robert F. Wagner. Analysis of competing
classifiers using components of variance of roc accuracy measures. CS, 1, 2002.
[202] Van Emden and F Helmut. Statistics for terrified biologists, volume 36. Blackwell,
2008.
[203] Xiubo Geng, Tie-Yan Liu, Tao Qin, and Hang Li. Feature Selection for Ranking, pages
407–414. Number 49. ACM Press, 2007.
[204] MATLAB. version 7.10.0 (R2010a). The MathWorks Inc., Natick, Massachusetts,
2010.
[205] Blot L. and Zwiggelaar R. Background texture extraction for the classification of
mammographic parenchymal patterns. In MIUA, 2001.
[206] Oliver A., Freixenet J., Bosch A., Raba D., and Zwigge laar R. Automatic classification of breas tissue. In IbPRIA, 2005.
[207] G. Torres-Meja, B. De Stavola, D.S. Allen, J.J. Prez-Gaviln, J.M. Ferreira, I.S. Fentiman, and I. Dos Santos Silva. Mammographic features and subsequent risk
of breast cancer: a comparison of qualitative and quantitative evaluations in the
guernsey prospective studies. Cancer Epidemiol Biomarkers Prev, 14(5):1052–9, 2005.
[208] G.A. Greendale, B.A. Reboussin, S. Slone, C. Wasilauskas, M.C. Pike, and G. Ursin.
Postmenopausal hormone therapy and change in mammographic density. J Natl
Cancer Inst, 95(1):30–7, 2003.
[209] G. A. Greendale, B. A. Reboussin, S. Slone, C. Wasilauskas, M. C. Pike, and
G. Ursin. Postmenopausal hormone therapy and change in mammographic density. Journal of the National Cancer Institute, January 2003.
[210] A. Sue, R. Dorothy, Pathak, A. Mettler Fred, R. Key Charles, and C. Pike Malcolm.
Breast mammographic pattern: A concatenation of confounding and breast cancer
risk factors. Am. J. Epidemiol, 142(8):813–819, 1995.
[211] J. R. Porter Gareth, J. Evans Andrew, J. Cornford Eleanor, C. Burrell Helen, J. James
Jonathan, H. S. Lee Andrew, and Chakrabarti Jayeta. Influence of mammographic
parenchymal pattern in screening-detected and interval invasive breast cancers
on pathologic features, mammographic features, and patient survival. AJR Am J
Roentgenol, 3:676–83, 2007.
[212] J W Byng, N F Boyd, E Fishell, R A Jong, and M J Yaffe. Automated analysis of
mammographic densities. Physics in Medicine and Biology, 41:909–923, 1996.
[213] N F Boyd, J W Byng, R A Jong, E K Fishell, L E Little, A B Miller, G A Lockwood,
D L Trichler, and M J Yaffe. Quantitative classification of mammographic densities
and breast cancer risk: Results from the canadian national breast screening study.
Academic Radiology, 87(9):670–675, 1995.
[214] R. Gupta and P.E. Undrill. The use of texture analysis to delineate suspicious
masses in mammography. Phys Med Biol, 40(5):835–55, 1995.
[215] Nan-Chyuan Tsai, Hong-Wei Chen, and Sheng-Liang Hsu. Computer-aided diagnosis for early-stage breast cancer by using wavelet transform. Computerized
medical imaging and graphics the official journal of the Computerized Medical Imaging
Society, 35(1):1–8, 2011.
[216] R.J. Ferrari, R.M. Rangayyan, J.E. Desautels, and A.F. Frre. Analysis of asymmetry
in mammograms via directional filtering with gabor wavelets. IEEE Trans Med
Imaging, 20(9):953–64, 2001.
[217] ME Mavroforakis, HV Georgiou, N Dimitropoulos, D Cavouras, and S. Theodoridis. Mammographic masses characterization based on localized texture and
dataset fractal analysis using linear, neural and support vector machine classifiers. Artif Intell Med., 37:145–62, 2006.
[218] C.E. Priebe, J.L. Solka, R.A. Lorey, G.W. Rogers, W.L. Poston, M. Kallergi, W. Qian,
L.P. Clarke, and R.A. Clark. The application of fractal analysis to mammographic
tissue classification. Cancer Lett, 77(2-3):183–9, 1994.
[219] Karahaliou A, Skiadopoulos S, Boniatis I, Sakellaropoulos P, LikakiE, Panayiotakis
G, and Costaridou L. Texture analysis of tissue surrounding microcalcifications
on mammograms for breast cancer diagnosis. Br J Radiol., 80:648–56, 2007.
[220] J.D.M. Otten, N. Karssemeijer, J.H.C.L. Hendriks, J.H. Groenewoud, J. Fracheboud,
A.L.M. Verbeek, H.J. de Koning, and R. Holland. Effect of recall rate on earlier
screen detection of breast cancers based on the dutch performance indicators. J
Natl Cancer Inst, 97(10):748–54, 2005.
[221] G. Karemore, I. Arganda-Carreras, and M. Nielsen. Automatic and consistent
registration framework for temporal pairs of mammograms in application to breast
cancer risk assessment due to hormone replacement therapy (hrt). Int J CARS,
4(Supplement 1):S356, June 2009. Poster Session: 11th International Workshop on
Computer-Aided Diagnosis.
[222] Michael F Barnsley. Fractals Everywhere. Academic Press, 1988.
[223] James R Carr and William B Benzer. On the practice of estimating fractal dimension. Mathematical Geology, 23(7):945–958, 1991.
[224] J M Escs, C L Alados, and J M Emlen. Fractal structures and fractal functions as
disease indicators. Oikos, 74(2):310–314, 1995.
[225] Shyang Chang, Shiun-Jeng Li, Meng-Ju Chiang, Shih-Jen Hu, and Ming-Chun
Hsyu. Fractal dimension estimation via spectral distribution function and its
application to physiological signals. IEEE Transactions on Biomedical Engineering,
54(10):1895–1898, 2007.
[226] S Peleg, J Naor, R Hartley, and D Avnir. Multiple resolution texture analysis
and classification. IEEE Transactions on Pattern Analysis and Machine Intelligence,
6(4):518–523, 1984.
[227] Fraclac F O R Imagej. Flaclac for imagej. Imaging, 2004.
[228] Roy E Plotnick, Robert H Gardner, and Robert V O’Neill. Lacunarity indices as
measures of landscape texture. Landscape Ecology, 8(3):201–211, 1993.
[229] T J Collins. Imagej for microscopy. Biotechniques, 43(1 Suppl):25–30, 2007.
[230] J. Raundahl, M. Loog, P. Pettersen, L.B. Tanko, and M. Nielsen. Automated effectspecific mammographic pattern measures. IEEE Trans Med Imaging, 27(8):1054–60,
2008.
[231] J. Raundahl, M. Loog, and M. Nielsen. Understanding hessian-based density
scoring. In Proc. 8th International Workshop on Digital Mammography, volume 4046
of Lecture Notes in Computer Science, pages 447–452, Manchester, UK, June 2006.
[232] J. Raundahl, M. Loog, P. Pettersen, L.B. Tanko, and M. Nielsen. Automated effectspecific mammographic pattern measures. IEEE Transactions on Medical Imaging,
27(8):1054–1060, August 2008.
[233] C J Wild and George A F Seber. The wilcoxon rank-sum test. Behaviour, 2:1–10,
1988.
[234] J Ferlay, P Autier, M Boniol, M Heanue, M Colombet, and P Boyle. Estimates of
the cancer incidence and mortality in europe in 2006. Annals of oncology official
journal of the European Society for Medical Oncology ESMO, 18(3):581–592, 2007.
[235] L. Tabar, M. Yen, B. Vitak, H.T. Chen, R.A. Smith, and S.W. Duffy. Mammography
service screening and mortality in breast cancer patients: 20-year follow-up before
and after introduction of screening. Lancet, 361(9367):1405–10, 2003.
[236] M. H. Gail, L. A. Brinton, D. P. Byar, D. K. Corle, S. B. Green, C. Schairer, and
J. J. Mulvihill. Projecting individualized probabilities of developing breast cancer
for white females who are being examined annually. Journal of the National Cancer
Institute, 81(24):1879–86, December 1989.
[237] Wolfe JN. Risk for breast cancer development determined by mammographic
parenchymal pattern. Cancer, 37:2486–92, 1976.
[238] R.T. Chlebowski, L.H. Kuller, R.L. Prentice, M.L. Stefanick, J.E. Manson, M. Gass,
A.K. Aragaki, J.K. Ockene, D.S. Lane, G.E. Sarto, A. Rajkovic, R. Schenken, S.L.
Hendrix, P.M. Ravdin, T.E. Rohan, S. Yasmeen, and G. Anderson. Breast cancer
after use of estrogen plus progestin in postmenopausal women. N Engl J Med,
360(6):573–87, 2009.
[239] C.M. Vachon, V.S. Pankratz, C.G. Scott, S.D. Maloney, K. Ghosh, K.R. Brandt,
T. Milanese, M.J. Carston, and T.A. Sellers. Longitudinal trends in mammographic
percent density and breast cancer risk. Cancer Epidemiol Biomarkers Prev, 16(5):921–
8, 2007.
[240] N.F. Boyd, L.J. Martin, Q. Li, L. Sun, A.M. Chiarelli, G. Hislop, M.J. Yaffe, and
S. Minkin. Mammographic density as a surrogate marker for the effects of hormone
therapy on risk of breast cancer. Cancer Epidemiol Biomarkers Prev, 15(5):961–6, 2006.
[241] J. Couzin. Breast cancer. dissecting a hidden breast cancer risk.
309(5741):1664–6, 2005.
Science,
[242] N. Karssemeijer. Automated classification of parenchymal patterns in mammograms. Physics in Medicine and Biology, 43:365–378, 1998.
[243] J Raundahl, M Nielsen, OF Olsen, and YZ Bagger. Effect of projective viewpoint
in detecting temporal density changes. In 5370, editor, Proc SPIE, page 8592, 2004.
[244] P.C. Pettersen, J. Raundahl, M. Loog, M. Nielsen, L.B. Tank, and C. Christiansen.
Parallel assessment of the impact of different hormone replacement therapies on
breast density by radiologist- and computer-based analyses of mammograms.
Climacteric, 11(2):135–43, 2008.
[245] B.M. ter Haar Romeny. Front-End Vision and Multi-Scale Image Analysis. Kluwer
Academic Publisher, 2003.
[246] A. Whitney. A direct method of nonparametric measurement selection. In IEEE
Trans. Comput., volume 20, pages 1100–1103, 1971.
[247] Sunil Arya, David M. Mount, Nathan S. Netanyahu, Ruth Silverman, and Angela Y. Wu. An optimal algorithm for approximate nearest neighbor searching
fixed dimensions. J. ACM, 45:891–923, November 1998.
[248] Marleen De Bruijne. A pattern classification approach to aorta calcium scoring in
radiographs. Lecture Notes in Computer Science, 3765:170–177, 2005.
[249] E.R. DeLong, D.M. DeLong, and D.L. Clarke-Pearson. Comparing the areas under
two or more correlated receiver operating characteristic curves: a nonparametric
approach. Biometrics, 44(3):837–45, 1988.
[250] W.E. Barlow, E. White, R. Ballard-Barbash, P.M. Vacek, L. Titus-Ernstoff, P.A. Carney, J.A. Tice, D.S.M. Buist, B.M. Geller, R. Rosenberg, B.C. Yankaskas, and K. Kerlikowske. Prospective breast cancer risk prediction model for women undergoing
screening mammography. J Natl Cancer Inst, 98(17):1204–14, 2006.
[251] J.A. Tice, S.R. Cummings, E. Ziv, and K. Kerlikowske. Mammographic breast density and the gail model for breast cancer risk prediction in a screening population.
Breast Cancer Res Treat, 94(2):115–22, 2005.
[252] G. Maskarinec and L. Meng. A case-control study of mammographic densities in
hawaii. Breast Cancer Res Treat, 63(2):153–61, 2000.
[253] N.F. Boyd, H. Guo, L.J. Martin, L. Sun, J. Stone, E. Fishell, R.A. Jong, G. Hislop,
A. Chiarelli, S. Minkin, and M.J. Yaffe. Mammographic density and the risk and
detection of breast cancer. N Engl J Med, 356(3):227–236, 2007.
[254] K. Kerlikowske, L. Ichikawa, D.L. Miglioretti, D.S.M. Buist, P.M. Vacek, R. SmithBindman, B. Yankaskas, P.A. Carney, and R. Ballard-Barbash. Longitudinal measurement of clinical mammographic breast density to improve estimation of breast
cancer risk. J Natl Cancer Inst, 99(5):386–95, 2007.
[255] J. Stone, L.C. Gurrin, G.B. Byrnes, C.J. Schroen, S.A. Treloar, E.J.D. Padilla, G.S.
Dite, M.C. Southey, V.M. Hayes, and J.L. Hopper. Mammographic density and
candidate gene variants: a twins and sisters study. Cancer Epidemiol Biomarkers
Prev, 16(7):1479–84, 2007.
[256] C.M. Vachon, T.A. Sellers, E.E. Carlson, J.M. Cunningham, C.A. Hilker, R.L. Smalley, D.J. Schaid, L.E. Kelemen, F.J. Couch, and V.S. Pankratz. Strong evidence of
a genetic determinant for mammographic density, a major risk factor for breast
cancer. Cancer Res, 67(17):8412–8, 2007.
[257] N. F. Boyd, J. M. Rommens, K. Vogt, V. Lee, J. L. Hopper, M. J. Yaffe, and A. D.
Paterson. Mammographic breast density as an intermediate phenotype for breast
cancer. The Lancet Oncology, 5:798–808, 2005.
[258] S. Alowami, S. Troup, S. Al-Haddad, I. Kirkpatrick, and P.H. Watson. Mammographic density is related to stroma and stromal proteoglycan expression. Breast
Cancer Res, 5(5):R129–35, 2003.
[259] T. Li, L. Sun, N. Miller, T. Nicklee, J. Woo, L. Hulse-Smith, M. Tsao, R. Khokha,
L. Martin, and N. Boyd. The association of measured breast tissue characteristics
with mammographic density and other risk factors for breast cancer. Cancer
Epidemiol Biomarkers Prev, 14(2):343–9, 2005.
[260] M.A. Karsdal, L. Larsen, M.T. Engsig, H. Lou, M. Ferreras, A. Lochter, J. Delaiss,
and N.T. Foged. Matrix metalloproteinase-dependent activation of latent transforming growth factor-beta controls the conversion of osteoblasts into osteocytes
by blocking osteoblast apoptosis. J Biol Chem, 277(46):44061–7, 2002.
[261] H. Liu, D.C. Radisky, and M.J. Bissell. Proliferation and polarity in breast cancer:
untying the gordian knot. Cell Cycle, 4(5):646–9, 2005.
[262] D.J. Leeming, G. Delling, M. Koizumi, K. Henriksen, M.A. Karsdal, B. Li, P. Qvist,
L.B. Tank, and I. Byrjalsen. Alpha ctx as a biomarker of skeletal invasion of breast
cancer: Immunolocalization and the load dependency of urinary excretion. Cancer
Epidemiol Biomarkers Prev, 15(7):1392–5, 2006.
[263] J. N.Wolfe. Risk for breast cancer development determined by mammographic
parenchymal pattern. Cancer, 37(5):2486–2498, 1976.
[264] C. H. van Gils, J. H. C. L. Hendriks, R. Holland, N. Karssemeijer, J. D. M. Otten,
H. Straatman, and A. L. M. Verbeek. Changes in mammographic breast density and
concomitant changes in breast cancer risk. European Journal of Cancer Prevention,
8:509–515, 1999.
[265] J. Koenderink and A. van Doorn. Representation of local geometry in the visual
system. Biological Cybernetics, 55(6):367–375, 1987.
[266] Y. Guo, R. Sivaramakrishna, C.-C. Lu, J.S. Suri, and S. Laxminarayan. Breast image
registration techniques: A survey. Med Biol Eng Comput, 44:15–26, 2006.
[267] N Karssemeijer. Automated classification of parenchymal patterns in mammograms. Physics in Medicine and Biology, 43(2):365–378, February 1998.
[268] S.M. Kwok, R. Chandrasekhar, Y. Attikiouzel, and M.T. Rickard. Automatic pectoral muscle segmentation on mediolateral oblique view mammograms. IEEE
transactions on medical imaging, 23(9):1129–1140, 2004.
[269] S.K. Kinoshita, P.M. Azevedo-Marques, R.R. Pereira, J.A.H. Rodrigues, and R.M.
Rangayyan. Radon-Domain Detection of the Nipple and the Pectoral Muscle in
Mammograms. Journal of Digital Imaging, 21(1):37–49, 2008.
[270] F.F. Yin, M.L. Giger, K. Doi, C.J. Vyborny, and R.A. Schmidt. Computerized
detection of masses in digital mammograms: Automated alignment of breast
images and its effect on bilateral-subtraction technique. Medical Physics, 21:445,
1994.
[271] A.J. Méndez, P.G. Tahoces, M.J. Lado, M. Souto, J.L. Correa, and J.J. Vidal. Automatic detection of breast border and nipple in digital mammograms. Computer
methods and programs in biomedicine, 49(3):253–262, 1996.
[272] R. Chandrasekhar and Y. Attikiouzel. A simple method for automatically locating
the nipple on mammograms. IEEE transactions on medical imaging, 16(5):483–494,
1997.
[273] C. Zhou, H.P. Chan, C. Paramagul, M.A. Roubidoux, B. Sahiner, L.M. Hadjiiski,
and N. Petrick. Computerized nipple identification for multiple image analysis in
computer-aided diagnosis. Medical Physics, 31:2871, 2004.
[274] M. Karnan and K. Thangavel. Automatic detection of the breast border and
nipple position on digital mammograms using genetic algorithm for asymmetry approach to detection of microcalcifications. Comput. Methods Prog. Biomed.,
87(1):12–20, 2007.
[275] U. Bick, M.L. Giger, R.A. Schmidt, R.M. Nishikawa, D.E. Wolverton, and K. Doi.
Automated segmentation of digitized mammograms. Academic Radiology, 2(1):1–9,
1995.
[276] T. Ojala, J. Näppi, and O. Nevalainen. Accurate segmentation of the breast region
from digitized mammograms. Computerized Medical Imaging and Graphics, 25(1):47–
59, 2001.
[277] F. Georgsson. Anatomical coordinate system for bilateral registration of mammograms. In Proc. Scandinavian Conference on Image Analysis (SCIA), volume 2749 of
LNCS, pages 335–342, 2003.
[278] Y. Kita, E Tohno, R.P. Highnam, and M. Brady. A CAD system for the 3d location
of lesions in mammograms. Medical Image Analysis, 6:267–273, 2002.
[279] M. Yam, M. Brady, R. Highnam, C. Behrenbruch, R. English, and Y. Kita.
Three-dimensional reconstruction of microcalcification clusters from two mammographic views. IEEE Transactions on Medical Imaging, 20(6):479–489, 2001.
[280] S.-C. Yang, H.-H. Hsu, G.-C. Hsu, P.-C. Chung, S.M. Guo, C.-S. Lo, C.-W. Yang,
S.-K. Lee, and C.-I. Chang. 3d localization of clustered microcalcifications using
cardio-caudal and medio-lateral oblique views. Computerized Medical Imaging and
Graphics, 29:521–532, 2005.
[281] Lise Warming, Pernille Ravn, Danile Spielman, Pierre Delmas, and Claus Christiansen. Trimegestone in a low-dose, continuous-combined hormone therapy
regimen prevents bone loss in osteopenic postmenopausal women. Menopause,
11(3):337–342, May/June 2004.
[282] Ignacio Arganda-Carreras, Carlos O. S. Sorzano, Roberto Marabini, Jose M.
Carazo, Carlos Ortiz de Solorzano, and Jan Kybic. Consistent and elastic registration of histological sections using vector-spline regularization. In Proc. Computer
Vision Approaches to Medical Image Analysis (CVAMIA), volume 4241 of Lecture Notes
in Computer Science, pages 85–95, 2006.
[283] Saskia van Engeland, Peter Snoeren, Jan Hendriks, and Nico Karssemeijer. A
comparison of methods for mammogram registration. IEEE Transactions of Medical
Imaging, 22(11), 2003.
[284] Rafael C. Gonzalez and Richard E. Woods. Digital Image Processing. AddisonWesley Longman Publishing Co., Inc., Boston, MA, USA, 2nd edition, 2001.
[285] D. Mattes, D. R. Haynor, H. Vesselle, and T. K. Lewellenand W. Eubank. Petct image registration in the chest using free-form deformations. IEEE Trans. on
Medical Imaging, 22(1):120–128, January 2003.
[286] Lewis D Griffin and Martin Lillhom. Image features and the 1-D, 2nd order
Gaussian derivative jet. In Scale Space and PDE Methods in Computer Vision: 5th
International Conference Scale Space 2005, pages 26–27. Springer, 2005.
[287] Nico Karssemeijer, Johan T.M. Frieling, and Jan H.C.L. Hendrinks. Spatial resolution in digital mammography. Investigative Radiology, 28(5):395–472, May 1993.
[288] S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Wu. An optimal algorithm for approximate nearest neighbor searching. Journal of the ACM,
45(6):891–923, 1998.
[289] Dimitrios Ververidis and Constantine Kotropoulos. Fast and accurate sequential floating forward feature selection with the bayes classifier applied to speech
emotion recognition. Signal Processing, 88(12):2956–2970, 2008.
[290] J.A. Hanley and B.J. McNeil. meaning and use of the area under a receiver operating characteristic (roc) curve. Radiology, 143:29–36, 1982.
[291] L. Tabar, M. Yen, B. Vitak, H.T. Chen, R.A. Smith, and S.W. Duffy. Mammography
service screening and mortality in breast cancer patients: 20-year follow-up before
and after introduction of screening. Lancet, 361(9367):1405–10, 2003.
[292] Warner E. Clinical practice. breast-cancer screening. N Engl J Med, 365:1025–32,
2011.
[293] AP Dhawan, Y Chitre, and C. Kaiser-Bonasso. Analysis of mammographic microcalcifications using gray-level image structure features. IEEE Trans Med Imaging,
15:246–59, 1996.
[294] Zhang M, Giger M L, Vyborny C J, and K Doi. Mammographic texture analysis for
the detection of spiculated lesions, page 347. Elsevier Science Ltd, 1996.
[295] A Oliver, J Freixenet, R Mart, J Pont, E Prez, ER Denton, and R. Zwiggelaar.
A novel breast tissue density classification methodology. IEEE Trans Inf Technol
Biomed, 12:55–65, 2008.
[296] Tahoces PG, Correa J, Souto M, Gmez L, and Vidal JJ. Computer-assisted diagnosis:
the classification of mammographic breast parenchymal patterns. Phys Med Biol.,
40:103–17, 1995.
[297] N R Mudigonda, R M Rangayyan, and J E Desautels. Gradient and texture
analysis for the classification of mammographic masses. IEEE Transactions on
Medical Imaging, 19(10):1032–1043, 2000.
[298] H P Chan, D Wei, M A Helvie, B Sahiner, D D Adler, M M Goodsitt, and N Petrick.
Computer-aided classification of mammographic masses and normal tissue: linear
discriminant analysis in texture feature space. Physics in Medicine and Biology,
40(5):857–876, 1995.
[299] H Li, ML Giger, OI Olopade, and L. Lan. Fractal analysis of mammographic
parenchymal patterns in breast cancer risk assessment. Acad Radiol., 14:513–21,
2007.
[300] JW Byng, MJ Yaffe, GA Lockwood, LE Little, DL Tritchler, and NF. Boyd. Automated analysis of mammographic densities and breast carcinoma risk. Cancer,
80:66–74, 1997.
[301] E Couto, D Harrison, and S et-al Duffy. Estimation of disease progression parameters from case-control data: application to mammographic patterns and breast
cancer natural history. J Epidemiol Biostat, 6:235–42, 2001.
[302] M. Brown, C. Eccles, and M.G. Wallis. Geographical distribution of breast cancers
on the mammogram: an interval cancer database. Br J Radiol, 74(880):317–22, 2001.
[303] S. Meeson, K.C. Young, M.G. Wallis, J. Cooke, A. Cummin, and M.L. Ramsdale.
Image features of true positive and false negative cancers in screening mammograms. Br J Radiol, 76(901):13–21, 2003.
[304] S. Timp and N. Karssemeijer. Interval change analysis to improve computer aided
detection in mammography. Medical Image Analysis, 10:82–95, 2006.
[305] Brandi T Nicholson, Jennifer A Harvey, and Michael A Cohen. Nipple-areolar
complex: normal anatomy and benign and malignant processes. Radiographics a
review publication of the Radiological Society of North America Inc, 29(2):509–523, 2009.
[306] P.R. Snoeren and N. Karssemeijer. Thickness correction of mammographic images
by means of a global parameter model of the compressed breast. IEEE Trans Med
Imaging, 23(7):799–806, 2004.
[307] MATLAB. version 7.10.0 (R2010a). The MathWorks Inc., Natick, Massachusetts,
2010.
[308] Frederick Mosteller. A k-sample slippage test for an extreme population. The
Annals of Mathematical Statistics, 19(1):58–65, 1948.
[309] J F Osborn. Minimising errors in clinical studies by proper selection of sample
size. Annals Of The Academy Of Medicine Singapore, 20(1):95–100, 1991.
[310] R.O. Duda, P.E. Hart, and D.G. Stork. Pattern classification, new york: John wiley
& sons, 2001, pp. xx + 654, isbn: 0-471-05669-3. J. Classif., 24:305–307, September
2007.
[311] Peter W Glynn and Donald L Iglehart. Importance sampling for stochastic simulations. Management Science, 35(11):1367–1392, 1989.
[312] Chi-Rong Li, Chen-Tuo Liao, and Jen-Pei Liu. On the exact interval estimation
for the difference in paired areas under the roc curves. Statistics in Medicine,
27(2):224–242, 2008.
[313] H P Schneider. hrt and cancer risk: separating fact from fiction. Maturitas, 33
Suppl 1:S65–S72, 1999.
[314] John J Heine and Robert P Velthuizen. Spectral analysis of full field digital mammography data. Medical Physics, 29(5):647–661, 2002.
[315] Hanley J.A and McNeil B.J. The meaning and use of the area under a receiver
operating characteristic (roc) curve. Radiology, 143:29–36, 1982.
[316] R Baker, K D Rogers, N Shepherd, and N Stone. New relationships between breast
microcalcifications and cancer. British Journal of Cancer, 103(7):1034–1039, 2010.
[317] Istvn Plka, Katalin Ormndi, Szilvia Gal, Krisztina Boda, and Zsuzsanna Kahn.
Casting-type calcifications on the mammogram suggest a higher probability of
early relapse and death among high-risk breast cancer patients. Acta oncologica
Stockholm Sweden, 46(8):1178–1183, 2007.
[318] Samuel Shapiro, Richard D T Farmer, Helen Seaman, John C Stevenson, and
Alfred O Mueck. Does hormone replacement therapy cause breast cancer? an
application of causal principles to three studies: Part 1. the collaborative reanalysis.
The journal of family planning and reproductive health care Faculty of Family Planning
Reproductive Health Care Royal College of Obstetricians Gynaecologists, 37(2):103–109,
2011.
[319] N. Colacurci, F. Fornaro, P. De Franciscis, M. Palermo, and W. del Vecchio. Effects
of different types of hormone replacement therapy on mammographic density.
Maturitas, 40, November 2001.
[320] Wyeth Trial Manager. Phase 4:tudy evaluating estradiol/trimegestone in vasomotor symptoms (vms) in post-menopausal women. 2005.
[321] Clause Christiansen. Nordic-bioscience a/s, copenhagen, denmark. 2008.
[322] J W Byng, N F Boyd, L Little, G Lockwood, E Fishell, R A Jong, and M J Yaffe.
Symmetry of projection in the quantitative analysis of mammographic images. European journal of cancer prevention the official journal of the European Cancer Prevention
Organisation ECP, 5(5):319–327, 1996.
[323] Ivan Laptev and Tony Lindeberg. Local descriptors for spatio-temporal recognition. Science, 3667:91103, 2006.
[324] Joachim Weickert. Coherence-enhancing diffusion filtering. Int. J. Comput. Vision,
31:111–127, April 1999.
[325] Michael Barnathan, Jingjing Zhang, Despina Kontos, Predrag R. Bakic, Andrew
D. A. Maidment, and Vasileios Megalooikonomou. Analyzing tree-like structures
in biomedical images based on texture and branching: An application to breast
imaging. In Digital Mammography / IWDM’08, pages 25–32, 2008.
[326] Rein van den Boomgaard. Algorithms for non-linear diffusion. Technical report,
Intelligent Sensory Information Systems, University of Amsterdam, Kruislaan 403,
1098 SJ Amsterdam,The Netherlands.
[327] C Evans, K Yates, and M Brady. Statistical characterization of normal curvilinear
structures in mammograms. Digital Mammography Proceedings, pages 285–291 596,
2003.
[328] N Cerneaz and M Brady. Finding curvilinear structures in mammograms. 1995.
[329] A R Yezzi. Modified curvature motion for image smoothing and enhancement.
IEEE Transactions on Image Processing, 7(3):345–352, 1998.
[330] G Boccignone and A Picariello. Anisotropic enhancement of mammographic
images. Proceedings of 13th International Conference on Pattern Recognition, pages
408–412, 1996.
[331] P Mayo, F Rodenas, D Ginestar, G Verd, and R Mir. Diffusion equations with
negentropy applied to denoise mammographic images. Conference Proceedings
of the International Conference of IEEE Engineering in Medicine and Biology Society,
1(X):4751–4754, 2006.
[332] E. Shelley Hwang, Terri Chew, Stephen Shiboski, Georgianna Farren, Christopher C. Benz, and Margaret Wrensch. Risk factors for estrogen receptorpositive
breast cancer. ARCH SURG, 140:58–62, 2005.
[333] Boyd NF, Melnichouk O, Martin LJ, Hislop G, Chiarelli AM, Yaffe MJ, and Minkin
S. Mammographic density, response to hormones, and breast cancer risk. J Clin
Oncol, 29:2985–92, 2011.
[334] Savage L. Researchers wonder why high-risk women are not taking chemoprevention drugs. J Natl Cancer Inst, 99:913–4, 2007.
[335] Elad Ziv, Jeffrey Tice, Rebecca Smith-Bindman, John Shepherd, Steven Cummings,
and Karla Kerlikowske. Mammographic density and estrogen receptor status of
breast cancer. Cancer epidemiology biomarkers prevention a publication of the American Association for Cancer Research cosponsored by the American Society of Preventive
Oncology, 13(12):2090–2095, 2004.
[336] Young RA. The gaussian derivative model for spatial vision: I. retinal mechanisms.
Spat Vis, 2(4):273–93, 1987.
[337] Belgium MedCalc Software, Mariakerke. Medcalc for windows, version 9.5.0.0.
[338] W.Y. Chen, S.E. Hankinson, S.J. Schnitt, B.A. Rosner, M.D. Holmes, and G.A.
Colditz. Association of hormone replacement therapy to estrogen and progesterone receptor status in invasive breast carcinoma. Cancer, 101(7):1490–500, 2004.
[339] L.J. Hofseth, A.M. Raafat, J.R. Osuch, D.R. Pathak, C.A. Slomski, and S.Z. Haslam.
Hormone replacement therapy with estrogen or estrogen plus medroxyprogesterone acetate is associated with increased epithelial proliferation in the normal
postmenopausal breast. J Clin Endocrinol Metab, 84(12):4559–65, 1999.
[340] MA Roubidoux, JE Bailey, LA Wray, and MA Helvie. Invasive cancers detected
after breast cancer screening yielded a negative result: relationship of mammographic density to tumor prognostic factors. Radiology, 230:42–8, 2004.
[341] Diane Li, Sara Gavenonis, Emily Conant, and Despina Kontos. Comparison of
breast percent density estimation from raw versus processed digital mammograms. In Bram van Ginneken Ronald M. Summers, editor, Medical Imaging 2011:
Computer-Aided Diagnosis. Proc. SPIE 7963, 79631X, 2011.
[342] CH van Gils, JD Otten, AL Verbeek, JH Hendriks, and R. Holland. Effect of
mammographic breast density on breast cancer screening performance: a study
in nijmegen, the netherlands. J Epidemiol Community Health, 52:267–71, 1998.
[343] Leslie K. Diaz and Nour Sneige. Estrogen receptor analysis for breast cancer :
Current issues and keys to increasing testing accuracy. Adv Anat Pathol, 12:10–19,
2005.
[344] Styliani Petroudi and Michael Brady. Breast density segmentation using texture.
In Susan M. Astley, Michael Brady, Chris Rose, and Reyer Zwiggelaar, editors,
International Workshop on Digital Mammography, pages 609–615. Springer, 2006.
[345] RP Highnam, JM Brady, and BJ Shepstone. Estimation of compressed breast
thickness during mammography. British Journal of Radiology, 71(846):646, 1998.
[346] Carolyn J Crandall, Aaron K Aragaki, Jane A Cauley, Anne McTiernan, Joann E
Manson, Garnet L Anderson, Jean Wactawski-Wende, and Rowan T Chlebowski.
Breast tenderness after initiation of conjugated equine estrogens and mammographic density change. Breast Cancer Research and Treatment, 2011.
[347] R Highnam, X Pan, R Warren, M Jeffreys, G Davey Smith, and M Brady. Breast composition measurements using retrospective standard mammogram form (smf).
Physics in Medicine and Biology, 51(11):2695–2713, 2006.
[348] Zoe Aitken, Valerie A McCormack, Ralph P Highnam, Lisa Martin, Anoma Gunasekara, Olga Melnichouk, Gord Mawdsley, Chris Peressotti, Martin Yaffe, Norman F Boyd, and et al. Screen-film mammographic density and breast cancer risk:
a comparison of the volumetric standard mammogram form and the interactive
threshold measurement methods. Cancer epidemiology biomarkers prevention a publication of the American Association for Cancer Research cosponsored by the American
Society of Preventive Oncology, 19(2):418–428, 2010.
[349] Lilian C Wang, Wendy B DeMartini, Savannah C Partridge, Sue Peacock, and
Constance D Lehman. Mri-detected suspicious breast lesions: predictive values
of kinetic features measured by computer-aided evaluation. Ajr American Journal
Of Roentgenology, 193(3):826–831, 2009.
[350] Lama Alchab, Guillaume Dupuis, Corinne Balleyguier, Marie-Christine Mathieu,
Marie-Pierre Fontaine-Aupart, and Ren Farcy. Towards an optical biopsy for
the diagnosis of breast cancer in vivo by endogenous fluorescence spectroscopy.
Journal of biophotonics, 3(5-6):373–384, 2010.
[351] Gopal Karemore, Lavanya Rai, Keerthilatha M Pai, and V B Kartha. Serum protein
profile study of clinical samples using high performance liquid chromatographylaser induced fluorescence: case of cervical and oral cancers. Proceedings of SPIE,
7182:71820J–71820J–9, 2009.
[352] Gopal Karemore, Sujatha N Raja, Lavanya Rai, V B Kartha, and Santhosh Chidangil. Protein profile study of clinical samples using laser induced fluorescence as
the detection method: case of malignant and normal cervical tissues. Proceedings
of SPIE, 7169:71691I–71691I–8, 2009.
[353] P Klein, E Glaser, L Grogan, M Keane, S Lipkowitz, P Soballe, L Brooks, J Jenkins,
S M Steinberg, D M DeMarini, and et al. Biomarker assays in nipple aspirate fluid.
The breast journal, 7(6):378–387, 1958.
[354] Gopal Karemore and Mads Nielsen. Mammographic parenchymal texture techniques in application to breast cancer risk assessment: A review. Invited: Biomedical
Imaging and Intervention Journal, 2011.
[355] Mads Nielsen, Jakob Raundahl, Paola C Pettersen, Marco Loog, Gopal Karemore,
Morten A Karsdal, and Claus Christiansen. Low-dose transdermal estradiol induces breast density and heterogeneity changes comparable to those of raloxifene.
Menopause New York Ny, 16(4):785–791, 2009.
[356] Gopal Karemore, Sami Brandt, Nico Karssemeijer, and Mads Nielsen. A framework to determine mammographic regions that show early changes due to development of breast cancer: An application in risk assessment. To be submitted:
Physics in Medicine and Biology, 2011.
[357] Gopal Karemore, I Arganda-Carreras, and Mads Nielsen. Automatic consistent
registration framework for temporal pairs ofmamogram: In application to breast
cancer risk assessment due to hrt (hormone replacementtherapy). International
Journal of Computer Assisted Radiology and Surgery, 4(S1):356–357, 2009.
[358] Gopal Karemore, Brad Keller, Huen Oh, Julia Tchou, Mads Nielsen, Emily Conant, and Despina Kontos. Computer-aided parenchymal texture analysis in
digital mammograms: The potential for estrogen-receptor specific breast cancer
risk estimation. To be submitted: Medical Physics, 2011.
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement