Development of an Image Registration Procedure Marco Ribolla

Development of an Image Registration Procedure Marco Ribolla

Development of an Image Registration Procedure

Matching of Brain MRI Data Sets

Marco Ribolla

Thesis submitted in partial fulfilment of the requirements for the degree of

Bachelor of Science in Life Science Technologies FHNW

Institute for Medical and Analytical Technologies (IMA), School of Life Sciences,

University of Applied Sciences and Arts of Northwestern Switzerland, Switzerland a

Department of Biomedical Engineering (IMT), Linköping University, Sweden b

Supervisor: Karin Wårdell, Prof., Ph.D.

b

Elin Diczfalusy, MSc.

b

Examiner: Karin Wårdell, Prof., Ph.D.

b

Expert:

Simone Hemm-Ode, Ph.D.

a

Alex Ringenbach, Prof., Ph.D.

a

Linköping, April - July 2012

Acknowledgement

I would like to thank Prof. Dr. Karin Wårdell and Dr. Simone Hemm-Ode for the opportunity, to write my thesis here in Linköping, Sweden. It was a great experience, which I surely never will forget. I also would like to thank Elin Diczfalusy and Mats Andersson who supported me, when there was a need to.

Development of an Image Registration Procedure 19.07.12 I

Declaration of Authencity

I hereby affirm that the bachelor thesis at hand is my own written work and that I have used no other sources and aids other than those indicated.

All passages, which are quoted from publications or paraphrased from these sources, are indicated as such.

This thesis was not submitted in the same or in a substantially similar version, not even partially, to another examination board and was not published elsewhere.

Place, Date Signature

Development of an Image Registration Procedure 19.07.12 II

Abstract

Background: Registration is a key process in comparing different image sets. The registered images are used by surgeons for reasons of evaluation and surveillance (e.g. post-operative position control and particular health state evaluation). To compare images at an appropriate level of quality, it requires an understanding of how the images are related to each other and which registration basis and transformation should be chosen, to achieve the best possible registration result. The intention of this thesis is, to develop and evaluate a registration method for comparing the amount of cerebrospinal fluid, in order to apply it as a basis for the deep brain stimulation. Since the cerebrospinal fluid has an influence on the electrical current within the brain it is important, to know how much cerebrospinal fluid exists.

Material and Methods: This thesis presents a straightforward approach, to register magnetic resonance (MR) image sets by subtracting the normalized intensities and by calculating the particular rigid transformations. Two T2 weighted image sets and two spoiled gradient recalled echo (SPGR) image sets were used for the registration process. Furthermore the T2 images were used for the validation of the whole registration method.

Results: Both image set modalities, the T2 as well as the SPGR were successfully registered using the developed registration method. Therefore a translation correction of 54 pixels in x-direction, respectively 65 pixels in y-direction (T2) and 7 pixels in x-direction, respectively 6 pixels in y-direction (SPGR) was necessary. The detected rotation of 1.5 ° in the T2 matching set was adjusted too. The SPGR matching set showed no rotation.

The median sum of squares of intensity differences resulted in a value of 6438 (T2) and

25.86 (SPGR). The validation procedure constitutes an indication that the developed registration process is reliable and stable.

Conclusion: The implemented registration procedure constitutes a straightforward, time consuming approach, which is useful to gain results within the same image modality. If there is any need for an inter-modality registration, the approach must be changed.

Development of an Image Registration Procedure 19.07.12 III

Abstract

Hintergrund: Die Registrierung ist ein Schlüsselprozess in der Wertschöpfungskette zum Vergleich von Bild-Datensätzen. Dabei werden die registrierten Bilder von Ärzten aus Gründen der Evaluierung und Überwachung, wie beispielsweise die postoperative

Positionskontrolle (Elektrodenposition im Gehirn) oder die Evaluierung des gesundheitlichen Zustandes eines Patienten über einen bestimmten Zeitraum, eingesetzt. Dabei muss ein gewisser Qualitätsstandard gewahrt bleiben, welcher durch das Verständnis der herrschenden Relationen zwischen den Datensätzen, der Wahl der Registrierungsbasis sowie der Wahl der geeigneten Transformation sichergestellt wird. Somit wird das bestmögliche Resultat gewährleistet. Die Absicht dieser Thesis ist, die registrierten Datensätze als Grundlage für eine nachfolgende Segmentierung und Flächenvergleich

(zwischen den Datensätzen) der cerebrospinalen Flüssigkeit zu nutzen. Da sie den

Strom während einer Tiefenhirnstimulation schneller leitet (löst Seiteneffekte aus) als das umliegende Gewebe, ist es zentral zu wissen, wie viel davon im Hirn vorhanden ist.

Material und Methodik: In dieser Thesis wird ein Ansatz präsentiert, um Datensätze zu registrieren. Dabei werden T2 und spoiled gradient recalled echo (SPGR) Datensätze als Materialien eingesetzt. Die Registrierung wird durch die Anwendung einer Subtraktion der normalisierten Intensitäten und das Berechnen der dazugehörigen rigiden Transformation erreicht. Des Weiteren wurden die T2-Datensätze zur Validierung der implementierten Methoden verwendet.

Resultat: Beide Datensätze, sowohl der T2 als auch der SPGR Datensatz wurden registriert. Die vorhandene Translation wurde mit 54 Pixeln in x-Richtung und 65 Pixeln in y-Richtung (T2) sowie 7 Pixeln in x-Richtung und 65 Pixeln in y-Richtung (SPGR) eliminiert. Im Matching-Datensatz (T2) wurde die vorhandene Rotation von 1.5 ° korrigiert. Im

SPGR-Datensatz war keine Rotation vorhanden. Die Werte der quadrierten Summe der

Intensitätsdifferenzen betragen für den T2-Datensatz 6438 und für den SPGR-

Datensatz 25.86. Die Validierung zeigt auf, dass es sich um einen verlässlichen und stabilen Registrierungsalgorithmus handelt.

Schlussfolgerung: Die implementierten Funktionen erlauben eine direkte, aber zeitintensive Registrierung der Bilder innerhalb der gleichen Bildmodalität. Für den Fall das man eine intermodale Registrierung benötigt muss ein anderer Ansatz gewählt werden.

Development of an Image Registration Procedure 19.07.12 IV

Table of Contents

Acknowledgement ........................................................................................................... I

Declaration of Authencity ................................................................................................ II

Abstract ......................................................................................................................... III

Abstract ......................................................................................................................... IV

Table of Contents ........................................................................................................... V

List of Figures .............................................................................................................. VIII

List of Tables .................................................................................................................. X

Abbreviations ................................................................................................................. XI

1 Introduction ............................................................................................................ 1

2 Theoretical Background ......................................................................................... 2

2.1

Brain ............................................................................................................. 2

2.1.1

Grey and White Matter ...................................................................... 2

2.1.2

Cerebrospinal Fluid ........................................................................... 3

2.1.3

Basal Ganglia and its Structures ....................................................... 3

2.2

Deep Brain Stimulation ................................................................................. 4

2.3

Electric properties of tissue ........................................................................... 5

2.4

MR Imaging Physics ..................................................................................... 6

2.4.1

Proton Behaviour in a Magnetic Field ............................................... 6

2.4.2

Relaxation Processes ....................................................................... 8

2.5

Registration .................................................................................................. 9

2.5.1

Landmark Based............................................................................. 10

2.5.2

Intensity Based ............................................................................... 11

2.5.3

Mutual Information .......................................................................... 11

2.5.4

Sum of Squares of Intensity Differences ......................................... 12

2.6

Segmentation ............................................................................................. 13

2.6.1

Pixel Based ..................................................................................... 14

2.6.2

Region Based ................................................................................. 14

2.6.3

Edge Based .................................................................................... 15

3 Material and Methods .......................................................................................... 16

3.1

Software ..................................................................................................... 16

3.1.1

Tool ................................................................................................ 16

3.1.2

Functions ........................................................................................ 16

3.2

Raw Data.................................................................................................... 16

3.2.1

Format ............................................................................................ 16

3.2.2

T2 Image Sets ................................................................................ 16

Development of an Image Registration Procedure 19.07.12 V

3.2.3

SPGR Image Sets .......................................................................... 17

3.3

Registration ................................................................................................ 17

3.3.1

Choice of the Registration Method .................................................. 17

3.3.2

Task Overview ................................................................................ 17

3.3.3

Alignment in z-Direction .................................................................. 18

3.3.4

Rotation Determination and Elimination .......................................... 19

3.3.5

Interpolation in z-Direction .............................................................. 20

3.3.6

Offset Determination in z-Direction ................................................. 20

3.3.7

Interpolation in x- and y-Direction ................................................... 21

3.3.8

Translation in x- and y-Direction ..................................................... 22

3.4

Validation.................................................................................................... 23

3.4.1

Z-Interpolation and its Error ............................................................ 23

3.4.2

XY-Interpolation and its Error .......................................................... 23

3.4.3

Rotation .......................................................................................... 23

3.4.4

Translation ...................................................................................... 24

3.4.5

Visual .............................................................................................. 24

3.4.6

Evaluation of the Registration Result by Pixel Categorization ......... 25

3.4.7

Evaluation of the Registration Result by Histogram Analysis .......... 25

3.4.8

Influence of the Sequential Arrangement on Translation Values ..... 25

3.4.9

Robustness ..................................................................................... 26

4 Results ................................................................................................................ 27

4.1

Registration ................................................................................................ 27

4.1.1

Alignment in z-Direction .................................................................. 27

4.1.2

Rotation Determination and Elimination .......................................... 29

4.1.3

Interpolation in z-Direction .............................................................. 29

4.1.4

Offset Determination in z-Direction ................................................. 30

4.1.5

Interpolation in x- and y-Direction ................................................... 30

4.1.6

Translation Determination in x- and y-Direction .............................. 30

4.2

Validation.................................................................................................... 32

4.2.1

Z-Interpolation and its Error ............................................................ 32

4.2.2

XY-Interpolation and its Error .......................................................... 32

4.2.3

Rotation .......................................................................................... 33

4.2.4

Translation ...................................................................................... 34

4.2.5

Visual .............................................................................................. 34

4.2.6

Evaluation of the Registration Result by Pixel Categorization ......... 36

4.2.7

Evaluation of the Registration Result by Histogram Analysis .......... 36

4.2.8

Influence of the Sequential Arrangement on Translation Values ..... 37

Development of an Image Registration Procedure 19.07.12 VI

4.2.9

Robustness ..................................................................................... 37

5 Discussion ........................................................................................................... 39

5.1

Registration ................................................................................................ 39

5.1.1

Alignment in z-Direction .................................................................. 39

5.1.2

Rotation Determination and Elimination .......................................... 39

5.1.3

Interpolation in z-Direction .............................................................. 40

5.1.4

Offset Determination in z-Direction ................................................. 40

5.1.5

Interpolation in x- and y-Direction ................................................... 40

5.1.6

Offset Determination in x- and y-Direction ...................................... 40

5.2

Validation.................................................................................................... 41

5.2.1

Z-Interpolation and its Error ............................................................ 41

5.2.2

XY-Interpolation and its Error .......................................................... 42

5.2.3

Rotation .......................................................................................... 42

5.2.4

Translation ...................................................................................... 42

5.2.5

Visual .............................................................................................. 42

5.2.6

Evaluation of the Registration Result by Pixel Categorization ......... 43

5.2.7

Evaluation of the Registration Result by Histogram Analysis .......... 43

5.2.8

Influence of the Sequential Arrangement on Translation Values ..... 43

5.2.9

Robustness ..................................................................................... 43

5.3

Future Tasks .............................................................................................. 44

5.3.1

Cropping of Invalid Image Regions ................................................. 44

5.3.2

Mutual Information .......................................................................... 44

5.3.3

Segmentation ................................................................................. 44

6 Conclusion ........................................................................................................... 45

References ................................................................................................................... 46

Development of an Image Registration Procedure 19.07.12 VII

List of Figures

Fig. 2-1: Anatomical overview of the brain [1, modified by M.R.] ................................. 2

Fig. 2-2: Basal ganglia divisions [4, modified by M.R.] ................................................ 3

Fig. 2-3: Basal ganglia [5, modified by M.R.]............................................................... 4

Fig. 2-4: Brain overview [5, modified by M.R.] ............................................................. 4

Fig. 2-5: Circuit diagram. The bold dark lines constitute the electrodes, which guarantee a current flow. [8, modified by M.R.] ............................................................... 6

Fig. 2-6: Stimulation of spins [14, modified by M.R.] ................................................... 7

Fig. 2-7: Turn down of spins [14, modified by M.R.] .................................................... 7

Fig. 2-8: The recovery process of the z-magnetization [14, modified by M.R.] ............ 8

Fig. 2-9: Loss of phase information [14, modified by M.R.] ......................................... 9

Fig. 2-10: Registration overview [16, modified by M.R.] ................................................ 9

Fig. 2-11: Segmentation method overview [17, modified by M.R.] .............................. 13

Fig. 2-12: Region Growing [17, modified by M.R.] ...................................................... 15

Fig. 2-13: Pixel neighbourhood [18, modified by M.R.] ................................................ 15

Fig. 3-1: Overview registration tasks ......................................................................... 18

Fig. 3-2: Z-Alignment T2 [created by M.R.] ............................................................... 18

Fig. 3-3: Rotation axes [created by M.R.] .................................................................. 19

Fig. 3-4: Z-Interpolation T2 [created by M.R.] ........................................................... 20

Fig. 3-5: Offset in z-direction [created by M.R.] ......................................................... 21

Fig. 3-6: Interpolation in x- and y-direction [created by M.R.] .................................... 22

Fig. 3-7: Translation in x- and y-direction [created by M.R.] ...................................... 22

Fig. 3-8: Validation of translation task. The dummy matching image (green) is shifted within the SSD-mask until the image object (white) of the matching image fits the image object of the reference image........................................................................................ 24

Fig. 4-1: T2 matching set slice 14 (left) and reference set slice 91 (right). Eyes are visible in reference image but invisible in matching image. In both images the ventricles, the ACPC-line and the CSF-vessels are well recognizable. .......................................... 28

Fig. 4-2: SPGR matching set slice 64 (left) and reference set slice 51 (right).

Reference image presents the positions of the electrodes, constituted by the two small, dark dots beside the upper part of the ventricles. .......................................................... 28

Fig. 4-3: Rotated T2 matching set slice 14 (left) and unrotated reference set slice 91

(right). Eyes are visible now in both images. ................................................................. 29

Fig. 4-4: XY-Offset determination (T2). The images (left to right) show the iterative process of the translation elimination. The last image on the right presents the translation elimination with the SSD window coordinates. ............................................. 31

Development of an Image Registration Procedure 19.07.12 VIII

Fig. 4-5: XY-Offset determination (SPGR). The images (left to right) show the iterative process of the translation elimination. The last image on the right presents the translation elimination with the SSD window coordinates. ............................................. 31

Fig. 4-6: Subtracted images no. 1, 11 and 21 (left to right) ....................................... 35

Fig. 4-7: Subtracted images no. 31, 41 and 51 (left to right) ..................................... 35

Fig. 4-8: Subtracted images no. 61, 71 and 81 (left to right) ..................................... 35

Fig. 4-9: Subtracted images no. 91 and 101 (left to right) ......................................... 35

Fig. 4-10: Validation of Pixel Categorization. Figure shows the subtracted image from the chosen image pair and the corresponding histogram (first row), as well as the mean image of the subtracted images and the corresponding histogram (second row). The peak around the grey value of 0.5 marks the amount pixels, which are matched as its best. ...................................................................................................... 37

Fig. 5-1: Invalid image regions. The original image stack (black quadrangle) is rotated by a certain amount of degrees around the rotation axis or rotation centre (red dot with blue boarder). The rotated image stack (orange quadrangle) is located in some regions in a space, where no image information exist (red region). The valid volume (left), respectively the valid image area (right) is presented in green. ..................................... 41

Development of an Image Registration Procedure 19.07.12 IX

List of Tables

Table 2-1:

Table 2-2:

Table 3-1:

Table 3-2:

Table 3-3:

Table 3-4:

Table 4-1:

Table 4-2:

Table 4-3:

Table 4-4:

Table 4-5:

Table 4-6:

Table 4-7:

Table 4-8:

Table 4-9:

Table 4-10:

Table 4-11:

Table 4-12:

Table 4-13:

Table 4-14:

Electric conductivity for ex-vivo biological tissue at 37 °C ................. 6

Categorization of registration methods ............................................ 10

T2 meta data .................................................................................. 17

SPGR meta data............................................................................. 17

Categorization of the codomain of grey value ................................. 25

Scenarios of the sequential arrangement ........................................ 26

Group of interest (T2) ..................................................................... 27

Group of interest (SPGR) ................................................................ 27

Offset between matching and reference set (T2) ............................ 27

Offset between matching and reference set (SPGR) ...................... 28

Z-Interpolation results ..................................................................... 30

Offset values ................................................................................... 30

Resolution values ........................................................................... 30

SSD results (T2) ............................................................................. 31

SSD results (SPGR) ....................................................................... 32

Correlation values of the z-interpolation and their errors ................. 32

Statistical analysis of the z-Interpolation errors ............................... 32

T2 xy-interpolation error values ....................................................... 33

Rotation validation results ............................................................... 34

Statistic results of rotation validation ............................................... 34

Table 4-15:

Table 4-16:

Validation results of translation ....................................................... 34

Mean frequencies of pixel values .................................................... 36

Table 4-17: SSD values of influence scenarios. The SSD values are to multiply with 1000 to get the precise result. ............................................................................... 37

Table 4-18: Validation results of robustness task. The SSD values are to multiply with 1000 for the precise result. .................................................................................... 38

Development of an Image Registration Procedure 19.07.12 X

Abbreviations

GOI

IMT

MHz

MI

MRI

PD

PDF

Pw

2D

3D

ACPC-Line

CNS

DBS

DICOM

FHNW

GMM

RF

ROI

SNc

SNr

SPGR

SSD

STN

T

T

1 w

T

2 w

Two dimensional

Three dimensional

Anterior-commissure to posterior-commissure line

Central nervous system

Deep brain stimulation

Digital Imaging and Communications in Medicine

University of Applied Sciences Northwestern Switzerland

Gauss mixture model

Group of interest

Department of Biomedical Engineering

Mega Hertz

Mutual information

Magnetic resonance imaging

Parkinson’s disease

Probability distribution function

Proton weighted

Radiofrequency

Region of interest

Substantia nigra pars compacta

Substantia nigra pars reticulate

Spoiled gradient recalled echo

Sum of square of intensity differences

Subthalamic nucleus

Tesla

T1 weighted

T2 weighted

Development of an Image Registration Procedure 19.07.12 XI

1 Introduction

In the age of information, knowledge tends to become more and more important. This development is also observed in the field of medicine and biomedical engineering. Surgeons need to gain as much information about a patient as possible. Therefore the most modern equipment and technologies are developed (e.g. high resolution image processes). Knowing that a combination of these new imaging modalities leads to higher level of knowledge, the engineers and surgeons are working together to develop such stable combinations. Before the combined image sets can be used to give a scientifically established medical statement, they have to be registered.

This project deals with the registration of MR image sets of the brain, which differ in magnetic field strengths, instant of time of image acquisition and / or several other important parameters, which should be considered in the registration. Therefore a literature research about MR imaging, brain anatomy and different segmentation methods is executed, to accomplish prior to a practical programming and image processing part.

The programming part includes a straightforward approach for relating MR image sets to each other, by registration tasks such as image resampling, cropping, translation and rotation. The goal is, to match these image sets to the highest possible degree for classification of tissue for deep brain stimulation (DBS). Therefore usually a stereotactic frame is placed on the patient’s head prior to imaging. However in one of the available T2 image sets no frame is applied. So the markers from the stereotactic frame are useless and another process is needed. In the both SPGR image sets markers are available, which means that they can be used, to validate the registration procedure. The mentioned classification considers a segmentation of the cerebrospinal fluid, in the matching set as well as in the reference set. Furthermore the segmented area of both image sets is compared.

Due to the current level of knowledge it will be a huge challenge, to get these image sets matched as good as possible.

Development of an Image Registration Procedure 19.07.12 1

2 Theoretical Background

2.1 Brain

Fig. 2-1: Anatomical overview of the brain [1, modified by M.R.]

The brain, also called encephalon, is the second major division in the central nervous system (CNS) beside the spinal cord. As shown in Fig. 2-1, it can be divided in three parts, the cerebrum (forebrain), the cerebellum and the brain stem. At a hierarchical step deeper, the forebrain, which is responsible for complex functions such as cognition, consists of telencephalon and diencephalon. The cerebral cortex, the subcortical white matter, the commissures and the basal ganglia complete the telencephalon such as the thalamus, the hypothalamus, the epithalamus and the subthalamus complete the diencephalon. The cerebellum can be divided into the segments cerebellar cortex and cerebellar nuclei. The brain stem consists of the midbrain (mesencephalon), the pons and the medulla oblongata [2].

2.1.1 Grey and White Matter

The cerebral white matter is one of three basic regions in the cerebral hemisphere and is surrounded by the grey matter. Both of them are related to the communication within the brain. The white matter, which consists of large amounts of myelinated fibre tracts, is responsible for the communications between cerebral areas, cerebral cortex and lower centres of the (CNS). The myelinated fibres are distinguishable between association fibres, which are responsible for the connection with the cortical lobes and the projection fibres, which receive the information flux of the cerebral cortex and the motor output.

The cortical grey matter adopts the function of interpretation and localization of sensory

Development of an Image Registration Procedure 19.07.12 2

inputs, voluntary controls, skilled skeletal muscle activity and functions in intellectual and emotional processing [3].

2.1.2 Cerebrospinal Fluid

The cerebrospinal fluid (CSF), also called liquor, is a clear and colourless body fluid, which formation is provided by a combination of two components. These components together form the choroid plexus. On the one side specialized ependymal cells adopt the part of secretion of CSF in the ventricles, as well as they clean the CSF from waste products and on the other side permeable capillaries are involved in the formation.

The CSF surrounds the exposed surfaces of the CNS. Due to this embedding it cushions tenuous and neural structures. Another important function is the support of the brain by a weight reduction due to its addiction to the different densities of CSF and air.

The impact in percentage is given by: ℎ : 1400 ℎ : 50

= 100 % −

50 ∙ 100 %

1400

= 96.429 %

( 2.1 )

The last important function of CSF is the transport of nutrients, chemical messengers and waste products (ependymal cells). This transport, respective the exchange of aforementioned components executes between the CSF and the interstitial fluid, which surrounds the neurons and neuroglia of the CNS [2].

2.1.3 Basal Ganglia and its Structures

Fig. 2-2: Basal ganglia divisions [4, modified by M.R.]

Development of an Image Registration Procedure 19.07.12 3

The basal ganglia illustrate a larger, functional group of the basal nuclei, which demonstrate for their part masses of grey matter. These nuclei are situated at the base of the forebrain, deep to the floor of the lateral ventricle. Under the term of basal ganglia the basal nuclei of the cerebrum and the associated motor nuclei in the diencephalon and midbrain are included. The structure of the basal ganglia as shown in Fig. 2-2, Fig. 2-3 and Fig. 2-4 can be divided in the striatum (caudate nucleus and putamen), the internal and external segment of the globus pallidus, the reticular and compact part of the substantia nigra (SNr and SNc) and the subthalamic nucleus. In summary the involvement with the subconscious control of skeletal muscle tone and the coordination of learned movement patterns, the supply of the general pattern and rhythm (movement of the trunk and proximal limb muscles) are important functions as well as the caudate nucleus and putamen are responsible for the information receiving from sensory, motor and integrative areas of the cerebral cortex. The converting of this information occurs in the basal nuclei. If there is a need to decrease the activity of the basal nuclei, the substantia nigra of the midbrain dumps the neurotransmitter dopamine. Therefore, a defect or damaged substantia nigra leads to a higher level of activation such as an increased muscle tone [2].

Fig. 2-3: Basal ganglia [5, modified by

M.R.]

Fig. 2-4: Brain overview [5, modified by M.R.]

2.2 Deep Brain Stimulation

DBS is a medical approach, which serves to stimulate the deep structures of the brain for the purpose of treatment of movement disorders such as tremor as a symptom for the Parkinson’s disease (PD) and rigor as a symptom for dystonia. The reason of PD is based on the damage of dopaminergic neurons and a degeneration of over 70 % of the dopaminergic neurons, which are situated in the SNc. On the contrary dystonia denominates a disease, which lasting and repeating contractions of muscle lead to a malposi-

Development of an Image Registration Procedure 19.07.12 4

tion. Furthermore there is a continuous feed stream of new operation areas. Nowadays the chance for patients of cluster headache, epilepsy, obsessive and compulsive disorders and Tourette’s syndrome to reach an advancement to depreciate the annoying and sore symptoms, is rising [6, 9].

Two electrodes, one extension cable and the stimulator represent all technical components of a DBS system. One electrode consists of four platinum-irridium rings, which are fixed on a polymer cable. The extension cable connects the two electrodes to the stimulator, which can be programmed over a special programming device. Therefore the principle of telemetry is used. The stimulator consists of titanium and his sealings are made out of silicone rubber [6, 9].

During the implantation it is necessary to fix the cranium of the patient to ensure the right position of the electrodes. Therefore the patient is fixed within a stereotactic frame.

This frame serves as base of reference for the calculation of the stereotactic coordinates. A surgery in these dimensions needs a careful planning. This planning is supported by software, in which the surgeon can choose the target point and the associated trajectories. The position of the electrodes is screened during the operation using radiography. Postoperative there is executed some magnetic resonance (MR) and computer tomography (CT) images, which serve in a fusion of both to gain more quality control. If everything is, as it should technically and medically be, the stimulator is implanted below the clavicle and is ready to be programmed [6, 9].

2.3 Electric properties of tissue

This chapter comprises the most important electric parameters, which affect DBS in a fundamental way. An understanding of how these properties affect the electrical field and its pathways during electric stimulation, leads to a higher level of control, which goes hand in hand with a higher level of stimulation effectiveness as much as the patient’s quality of life due to reduced side effects.

One electric property of interest is the electric impedance of the brain tissues white and grey matter, as well as the electric impedance of the CSF. Another property, which constitutes the inverse of the electric impedance, is the electric conductivity. The white and grey matter differ in this property, due to the fact, that grey matter possesses a typically higher electric conductivity than white matter. The reason has its origin in the chemical components of the white matter. White matter consists of large amounts of lipid. These lipids act like an electrical insulator, which decreases the electric conductivity. The CSF has a higher electric conductivity due to its electrolyte and the fact, that it does not represent a cell. Therefore it does not possess a capacity (cell membrane, shown in Fig. 2-

Development of an Image Registration Procedure 19.07.12 5

5). The comparison between the grey and white matter, as well as the CSF shows that the significant difference occurs during “stimulation” with current of low frequency. As seen in Tab. 2-1, a high frequency reduces the effect of the capacitor. This is due to the fact, that the cell membrane (capacitor) does not have the time to charge itself [6, 7, 8].

Fig. 2-5: Circuit diagram. The bold dark lines constitute the electrodes, which guarantee a current flow. [8, modified by M.R.]

Tissue

σ

10 Hz

(S/m)

σ

100 Hz

(S/m)

σ

500 kHz

(S/m)

CSF

Grey matter

2.0

0.03

2.0

0.09

2.0

0.15

White matter 0.03 0.06 0.09

Table 2-1: Electric conductivity for ex-vivo biological tissue at 37 °C

σ

900 MHz

(S/m)

2.4

0.94

0.59

2.4 MR Imaging Physics

MR imaging describes an imaging process, which delivers an exceptional soft-tissue contrast, which allows, showing organs very well without any use of contrast medium. In this chapter all important physical and mathematical laws are treated, to show on what the image information of the MR imaging process relies.

2.4.1 Proton Behaviour in a Magnetic Field

The derivation of the whole MR imaging process is located in the hydrogen

1

H nuclei bound the tissue water (H

2

O) and fat (general long carbon hydride chains, e.g. paraffin).

For the sake of completeness it is to say, that there are other isotopes of significant interest like carbon

13

C, phosphorous

31

P, sodium

23

Na and fluorine

19

F. The hydrogen atom consists of an electron with a negative electric charge, which travels in a certain orbit around the nucleus. This nucleus consists of the elementary particle called proton, which distributes the positive electric charge, so the hydrogen atom is electrically neutral. The proton disposes, like every elementary particle does, a spin. A spin is a physical property, which stays equal even if the acceleration changes. As a rotating mass the

Development of an Image Registration Procedure 19.07.12 6

proton constitutes an angular momentum (P), which, due its electrical charge, acts as a magnetic moment

$

. The magnitude of the magnetic moment is proportional to the magnitude of the angular momentum, where

%

refers to a constant called the gyromagnetic ratio [10, 11, 12, 13, 14, 15].

|$'| = %()*'(

( 2.2 )

The superconducting magnet of MR imaging system causes an external magnetic field, which tries to align the spins. The spins react due to this disturbance with a precession of characteristic frequency of rotation called Larmor frequency

+

,

. This frequency features a proportional behaviour to the strength of the magnetic field

-

,

.

+

,

= %-

,

( 2.3 )

Due to its energy loss the spins gradually align in parallel. For the sake of completeness it is to say, that the spins align antiparallel as well. But the parallel alignment is energetically more favourable. The alignment results due its accumulation of the magnetic vectors of each spin in a magnetisation M

Z

in the z direction. If the spins are initiated, as shown in Fig. 2-7, by electromagnetic waves in radio frequency (RF), which corresponds to the Larmor frequency, a condition of resonance is reached and the spins are turned down into the x-y-layer. The magnetisation in z direction changes to a transversal magnetisation M

XY

. According to the right demand and endurance a maximum deflection of

90 degrees, as shown in Fig. 2-8, can be reached. This movement in the x-y-layer acts like a generator and induces an alternating current, the MR imaging signal, to a receiver coil [10, 11, 12, 13, 14, 15].

Fig. 2-6: Stimulation of spins [14, modified by M.R.]

Fig. 2-7: Turn down of spins [14, modified by M.R.]

Development of an Image Registration Procedure 19.07.12 7

2.4.2 Relaxation Processes

Two independent events affect a decreasing transversal magnetisation and due to this a reduction of the MR imaging signal – the relaxation time T

1

(spin-lattice relaxation) and the relaxation time T

2

(spin-spin relaxation). The longitudinal relaxation T

1

describes a process of recovery of the magnetisation in z direction, shown in Fig. 2-9, which goes hand in hand with a decreasing amount of M

XY

and an energy loss to the environment

(the lattice) [10, 11, 12, 13, 14, 15]. The recovery is given by

.

/

= .

,

01 −

1

2

34

5 + .

/

(0)

1

2

34

,

( 2.4 ) where

9

:

constitutes the T

1

-relaxation time value for the corresponding tissue. The transversal relaxation T

2

describes a process of energy loss due to the loss of the phase information of the spins. In contrast to the longitudinal relaxation T

1

the energy is not lost to the environment but shared with the other spins. This exchange can be divided in two components, the exchange of energy between the spins by fast switching, local changes in the magnetic field and time invariant inhomogeneity of the external magnetic field

(mainly at tissue interfaces). The inhomogeneity occurs an additional loss of the phase information as shown in Fig. 2-10. The rate at which the MR imaging signal decays after it has been created is given by

.

;<

( ) = .

;<

(0)

1

2

3=

,

( 2.5 ) where

9

>

constitutes the T

2

-relaxation time value for the corresponding tissue. The image contrast is affected by another parameter than the transversal and longitudinal relaxation. Similar to the recently explained parameters, the proton density also affects the contrast of the image. It describes the maximum of signal, which can be emitted off the tissue. As it is hidden in the term density, the proton density corresponds to the amount of excitable protons per volume. If there is a need for the proton density to be weighted, the transversal and longitudinal relaxations are to decrease [10, 11, 12, 13, 14, 15].

Fig. 2-8: The recovery process of the z-magnetization [14, modified by M.R.]

Development of an Image Registration Procedure 19.07.12 8

Fig. 2-9: Loss of phase information [14, modified by M.R.]

2.5 Registration

Fig. 2-10: Registration overview [16, modified by M.R.]

In clinical practice it is a common procedure, to compare different image sets, to evaluate the progression of a patient’s health or to gain additional information from one image set, which does not appear in the other. Due to the fact that these image sets could differ in the instant of time of image acquisition or tomographic modality, the possibility of data difference exists, which makes a registration irremissible (e.g. the registration of

MR and CT images for the post-operative surveillance of the implanted electrode and its position). Therefore one image set is treated as reference set and the other is treated as template. A registration means that points, pixels or voxels are geometrically trans-

Development of an Image Registration Procedure 19.07.12 9

formed from one view to another. It constitutes a mathematical mapping from points, which correspond to their counterpart in the reference set if the registration process was successful [16].

The registration methods can be categorized in eight categories, which are represented in Tab. 2-2.:

Image dimensionality

Registration basis

Geometrical transformation

Degree of interaction

Optimization procedure

Modalities

Subject

Number of geometrical dimensions of the image spaces involved

- Usually 3-dim

Aspect of the matching and reference view

- Points (stereotactic markers)

- Planes

- Intensity

Mathematical form of the geometrical mapping

Amount of interaction generated by a human operator

- Optimal degree if interaction is zero

- Full automatization

Continual quality estimation function during the registration process, which is minimized or maximized by some degree of interaction

Acquisition type

- Intra-, monomodal (MR-MR)

- Inter-, multimodal (MR-CT)

Patient involvement

- Intrapatient

- Interpatient

- Atlas

Object

Anatomical region of interest (ROI)

- Brain, liver, heart

Table 2-2: Categorization of registration methods

2.5.1 Landmark Based

A registration, which is based on the calculation of landmarks, uses intrinsic attributes in the given image. The setting of the anatomical landmarks can occur by an interactive form, in which the user can determine the start values, by a semi-automatic form, in which the user initialize the registration and has an opportunity for corrections or by an full automation. If there are corresponding landmarks in the images, the preferred transformation is given by a rigid transformation, represented by a simple translation and rotation [16]. Their formulas are given by

9(?) = ? +

( 2.6 )

Development of an Image Registration Procedure 19.07.12 10

sin D cos D G ∙ @

H

IG

, ( 2.7 ) where

9(?)

constitutes the transformation matrix, x the image, R the rotation matrix with theta as rotation angle and X, Y as pixel coordinates. Appropriate landmarks are distinct and are visible even if the resolution changes. For the case that they should be extracted automatically, for each pixel the gradient I x

and I y

is to be calculated. Out of the gradients an inertia matrix is to determine. A landmark is chosen if the smaller eigenvalue of C(x,y) is a local maximum [16].

(?, K) = 0

L

L

;

<

L

;

L

;

L

;

L

<

L

<

L

<

5

( 2.8 )

A typical landmark in the brain is the line from the anterior commissure to the posterior commissure, also called ACPC-Line. If a non-automatic algorithm is used for the landmark-based registration this line should be included as registration reference [16].

2.5.2 Intensity Based

An intensity-based registration uses the pixel or voxel values for the transformation calculation. Therefore the similarity is measured by several approaches. Due to the large amount of data it is recommended to use just a subset of the image, which means the image has to be cropped. A filtering by a median filter should eliminate the noise in the image and also prevent the subsampled image from an aliasing. Due to the fact that the demand for intramodal registrations of images is growing, a corresponding growth of intensity based approaches such as image subtraction techniques is recognized. These techniques are used to detect changes in images that are too subtle to be reliably detected or quantified by simple visual inspection [16].

2.5.3 Mutual Information

The third and last approach, which is treated in this project, is the approach of mutual information (MI). The MI uses three algorithms, which accomplish different tasks. The first algorithm constitutes the calculation of a joint probability distribution function (PDF) out of a joint histogram HIST [j,k]. It is given by:

)M NO, P =

QL 9NO, P

∑ QL 9NO, P

( 2.9 )

The second algorithm calculates the joint entropy and minimizes it. Therefore it uses the

Shannon entropy, which is used for measuring of information [16]. The Shannon entropy is given by:

Development of an Image Registration Procedure 19.07.12 11

Q = − U V(W) ∙ V(W)

X

( 2.10 )

If all pixels or voxels have equal probability p(s), then the entropy will be at maximum. If one pixel or voxel has a probability of one and the other pixels or voxels have a probability of zero, the entropy will be at minimum. Tight clusters, which are surrounded by large, dark regions, are a hint for a correct alignment of the images. So misregistration leads to an increased joint entropy. For a correct registration the joint entropy is, as mentioned above, to be minimized [16]. The calculation of joint entropy is given by:

Q = − U )M NO, P ∙ )M NO, P

S,T

( 2.11 )

To minimize the joint entropy, the appropriate transformation function is to find. For maximizing the MI first the PDF, second the joint entropy, third the marginal entropies given have to be calculated [16]. The calculation of the marginal entropies is given by:

Q(Y) = U ZU )M NO, P ∙ log U )M NO, P ^

S T ]

( 2.12 )

Q(-

_

) = U `U )M N , P ∙ log U )M NO, P b

T a S

Finally the MI is to calculate by:

.L(Y, -

_

) = Q(Y) + Q(-

_

) − Q(Y, -

_

)

( 2.13 )

The mutual information is a stable algorithm. Nevertheless it can fail, when the clinical images contain a lot of air. This can be solved by the normalization of the MI, which constitutes a heuristic possibility [16]. It is given by: c.L(Y, -

_

) =

Q(Y) + Q(-

_

Q(Y, _ )

)

( 2.14 )

2.5.4 Sum of Squares of Intensity Differences

The simplest approach for measuring the similarity in an image is to subtract the normalized image intensities and to monitor if there is a visible translation (constituted by brighter and darker areas) in the resulting image or not. A second approach, which is quite similar to the previous one, involves the sum of squares of intensity differences

(SSD). If the SSD is zero, the registration was successful and images are correctly

Development of an Image Registration Procedure 19.07.12 12

aligned. Due to this fact, the SSD increases with each misregistration error [16]. The

SSD formula is given by,

M =

1 d c U|Y( ) − -

_

( )|

>

∀ ∈ Y ∩ -

_

( 2.15 ) where A constitutes the matching image set, B the reference image set, i the index and

N the amount pixels.

2.6 Segmentation

Fig. 2-11: Segmentation method overview [17, modified by M.R.]

The term of segmentation (S) is based on the fact that a segmentation of an image domain leads inevitably to a certain amount of segments. These segments can be, in dependence of the given criteria, disjoint or cohesive. The segmented image illustrates a new image from the image source (

), which allocates every pixel (

? ∈

) in the image a certain Label (

λ

) with a value (

λ ∈ i1, 2, 3, … , l

). This value is a fundamental, characteristic property of a single segment (

Ω n

) [17]. The coherence explained above is given by:

: ? ∈ o → q(?)ri1, 2, 3, … , l

( 2.16 )

The segmentation process is important within the image processing pipeline, because just through the definition of segments it is possible to obtain geometric attributes [17].

As shown in Fig. 2-12 the segmentation can be divided in two possible segmentation paths. The data based segmentation approach does not need any precognition about a form, it just uses the given data. According to requirements, it uses local or global criteria to gain the requested segmentation result. On the contrary the model based approach needs a precognition to draw conclusions, which is the appropriate way to seg-

Development of an Image Registration Procedure 19.07.12 13

ment an image. There are two ways, to gain information of the conclusions through a form model or through a coherence analysis [17].

The local criteria are divisible in the pixel based, the region based and the edge based approach. The term “local” means that the focus lies on the pixel and its environment or as well just on the pixel itself. As the term “pixel based” indicates, the grey value of one single pixel defines whether it counts to the label of interest or not [17].

2.6.1 Pixel Based

The first segmentation method, which constitutes a straight forward approach, is called thresholding. The threshold value (grey value) defines a certain border. This border can be set, in dependence due to its need, more or less strict. All grey values that possess higher values than the threshold value are set accordingly to the data type to 1 or to

255. The values under the border are set to 0. It seems to be clear that in dependence on the property of the threshold you will get different results. The advantage of this approach is the simple, straight forward design, which is really good expendable to the third dimension. But it usually needs a post-processing and it is very prone to fluctuations of the image signal. Further examples for pixel based approaches, which are quite similar to thresholding, are the Otsu approach (automatic threshold optimization), the

Gauss mixture model (GMM, minimal failure classification), local thresholding (inhomogeneous illumination of an image) and many more [17].

2.6.2 Region Based

Due to the mentioned need of more stable approaches, the region based approach, shown in Fig. 2.12, delivers a segmentation method, which is based on the criterion of homogeneity. The starting pixel or voxel is called seed point and it represents the centre from which the growth starts. For the segmentation the neighbourhood, shown in Fig. 2-

13, is to define, which influences the growth, especially the growth direction, very strongly [17].

The neighboured pixels have to fulfil the mentioned criterion, in order to be added. If no more pixels are added, the region growing is aborted. The advantage of this approach is that it constitutes connected segments and it is, similarly to the pixel based approach well expendable to the third dimension. The disadvantage comes from the difficulty to find the right tolerance criterion why there exists a certain danger of “over-boarding”.

This means that in dependence of the chosen neighbourhood it consists the possibility that the region grows too far. To prevent this it is necessary, as mentioned before, to define a proper tolerance criterion. For the sake of completeness there are more ap-

Development of an Image Registration Procedure 19.07.12 14

proaches than just region growing, such as split and merge approaches (e.g. Quadtree)

[17].

Fig. 2-12: Region Growing [17, modified by M.R.]

Fig. 2-13: Pixel neighbourhood [18, modified by M.R.]

2.6.3 Edge Based

The last local approach focuses on the edges (boundaries) between different image regions. There are a huge variety of edge operators (e.g. LoG, Sobel, Prewitt and Canny).

One possibility is to track the edge through the calculation of the gradient of each pixel.

Therefore it is to choose a start point, which possesses a high gradient. Step by step the neighboured pixel, which has the highest gradient and which lies orthogonal to the previous gradient, will be chosen. This approach represents a stable method to delimit a segment. The disadvantages are the need of a post-processing and the fact, that it does not deliver closed curves a priori. [16, 17].

Development of an Image Registration Procedure 19.07.12 15

3 Material and Methods

3.1 Software

3.1.1 Tool

The registration, validation and segmentation are performed with the included Image

Processing Toolbox

TM

(version 7.0, R2010a) in MATLAB, version 7.10.0.499 (R2010a,

64-bit) from MathWorks, Inc. (Natick, MA; United States) on Microsoft Windows 7 (version 6.1, build 7600).

3.1.2 Functions

Three functions, provided by IMT and developed by Elin Diczfalusy, are used for acquiring, extracting and presenting the data, the image-data as well as the meta-data. A fourth function provided by Matlab Central and developed by Robert Bemis on 21. January 2005 (updated 02. February 2010), is used to segment an image by setting a soft threshold.

3.2 Raw Data

3.2.1 Format

The Digital Imaging and Communications in Medicine (DICOM) format is a standard, which handles the storage, the slice coherence and the communications between the imaging hardware systems [10].

3.2.2 T2 Image Sets

In this project two T2 weighted, DICOM data sets of different magnetic flux density constitute the base of information extraction. Although these data sets are from the same patient, they differ in several important parameters, which are registered in Tab. 3-1. For the sake of completeness it is to say, that only a defined part of the brain is represented by the two different image sets. Due to the more detailed structures available in the images of the 3.0 T data set, this data set will be treated as reference and the 1.5 T data set as matching set.

Height x Width (in pixel)

Amount of images

Slice thickness (in mm)

1.5 Tesla Data Set

512x512

26

2

3.0 Tesla Data Set

384x384

256

0.5000

Development of an Image Registration Procedure 19.07.12 16

Pixel spacing (y- and x-direction in mm)

Table 3-1: T2 meta data

0.4883 0.5208

3.2.3 SPGR Image Sets

Spoiled gradient recalled echoes (SPGR) constitute sequences, which allow a fast 3D imaging procedure during apnoea of 10 to 20 seconds [19]. The given data sets possess fiducial markers of a stereotactic frame. These markers are used in the validation task to confirm the correctness of the accomplished registration, which means that they must not be considered for the registration process. Due to the given meta-data the postoperative data set is treated as reference set, while the pre-operative data set constitutes the matching set.

Pre-operative Data Set Post-operative Data Set

Height x Width(in pixel)

256x256

Amount of images

124

Slice thickness (in mm)

2

Pixel spacing (y- and x-direction in mm) 0.9766

Table 3-2: SPGR meta data

256x256

124

1.5

0.9375

3.3 Registration

3.3.1 Choice of the Registration Method

As shown in Tab. 2-2 the given data, the T2 as well as the SPGR data sets, can be categorized in 3D, intramodal data sets. Within the same image type the subject (patient) stays the same. In both image type cases the object is constituted by the brain. Due to the consultation of literature, as described in chapter 2.5.2, the intensity based approach is chosen. The premise of intensity based registration methods such as intensity subtraction is straightforward [16].

3.3.2 Task Overview

As shown in Tab. 3-1 and Tab. 3-2 both image sets differ in several parameters, so that an image registration is a key factor, to increase the accuracy of the subsequent segmentation process and its following comparison of the segmented area of CSF. Therefore the matching process is divided in several matching tasks, to provide a plain step by step adjustment. The process’s aim is providing two corresponding image sets. The se-

Development of an Image Registration Procedure 19.07.12 17

quential arrangement, shown in Fig. 3-1, is chosen because of reasons of simplicity and effectiveness during the image matching process.

Fig. 3-1: Overview registration tasks

3.3.3 Alignment in z-Direction

The data volume and as such the corresponding brain volume, differ between the T2 image sets. On the other side they also differ in the particular z-coordinate of the starting and ending slice. Due to reasons of comparability it is necessary, to find the corresponding slices in each image set. The whole comparison process is done visually by comparing each slice of the 1.5 T and the 3.0 T image set, to find the corresponding starting images. Subsequently the slices, which possess the highest possibility of correspondence, are merged together in a group of interest (GOI). From this group the slice with the highest correspondence is chosen after an afresh comparison within the GOI. Due to the fact that the slice thickness in the 1.5 T image set is four times bigger than the one in the 3.0 T image set, just every fourth image is chosen from the starting image in the 3.0

T image set. The final choice of the images is confirmed by a neurological surgeon.

The SPGR image sets represent quite similar brain volumes. The difference of the represented brain volume is just given by the difference of slice thickness, due to the fact that the amount of slices is equal. Similar to the T2 image sets they differ in the particular z-coordinate of the starting and ending slice. Therefore the alignment process is executed in the same way as it will be for the T2 image sets.

Fig. 3-2: Z-Alignment T2 [created by M.R.]

Development of an Image Registration Procedure 19.07.12 18

3.3.4 Rotation Determination and Elimination

To determinate and eliminate the rotation between the two image sets of both modalities, two approaches are chosen. One of them involves the visual examination of the matching set. Slice by slice the matching image is compared to the reference image, to monitor if the same information appears in both images (e.g. eyes, ACPC-line). The determined amount of rotation is confirmed by a neurological surgeon. To eliminate the rotation, it is requisite to know around which axis the rotation is taking place.

Fig. 3-3: Rotation axes [created by M.R.]

Due to the reason that the axes will change in dependence of the anatomical plane, it has to be considered before doing the rotation. Therefore the Z vector is the key vector.

It constitutes a fixed vector, because it is, independent of the particular anatomical plane, the vector which comes out of the plane. Hence it establishes two possibilities to execute the rotation. The first possibility is to transform the images from one anatomical plane to another prior to the rotation. Therefore the rotation matrix will stay the same for each anatomical plane and the rotation matrix can be used as shown in equation 2.8.

The second possibility is to rotate out of one anatomical plane. This means that one anatomical plane is treated as reference plane, with reference axes, which results in a change in the rotation axes.

The second approach uses landmarks, set by the user. By choosing the corresponding landmarks in the matching and reference image, the user gets a vector out of two landmarks. Between the vectors a and b the angle of rotation

λ

is given by: q = cos

1:

Z

' ∙ *'

| '| ∙ (*'(

^

( 3.1 )

Development of an Image Registration Procedure 19.07.12 19

3.3.5 Interpolation in z-Direction

As the image sets are aligned, on each slice of the 1.5 T image set come four slices of the 3.0 T image set. Because of a difference in the particular slice thickness it is necessary, to interpolate between the slices of 1.5 T image set, to gain the missing information. As shown in Fig. 3-4 the function fZInterpolation is displayed by the red arrows and it interpolates three slices between two source slices, so that the slice thickness shrinks from 2 mm to 0.5 mm. The grey values in each position of the intensity matrix

(slice) are interpolated as a whole, respectively as a slice due to reasons of effectiveness.

A similar approach is used to interpolate the SPGR image sets. Due to the fact that the slice thickness of the pre-operative set is not a multiple of the slice thickness of the postoperative set, it is not possible to keep the reference set untouched. If it would be kept untouched, a mathematical problem is created because there is more than one possibility to use information for the interpolation. Therefore the slice thickness of both data sets is to shrink to 0.5 mm, the biggest possible, common quotient.

Fig. 3-4: Z-Interpolation T2 [created by M.R.]

3.3.6 Offset Determination in z-Direction

The interpolation influences the amount of slices and it creates an offset in the data set, which would decrease the accuracy of the subsequent segmentation process, due to the fact that the particular slices would not correspond. The determination of the offset value occurs visually similar to the alignment in z-direction. The elimination of the offset can be contemplated as realignment in the z-direction. After the interpolation, the position of the slice in the new image stack can be calculated by following equation:

V W stu

= V W v]w

+ (V W

W = V W v]w

− 1) ∙ x stu

− V W v]w asytz{v]|ytw}]a~tX

( 3.2 )

Development of an Image Registration Procedure 19.07.12 20

The final choice of the images is confirmed again by neurological surgeon. After the authentication in both image sets the images of interest are assigned and they are aligned in the z-direction, so they are ready for the next step of the matching process.

Fig. 3-5: Offset in z-direction [created by M.R.]

3.3.7 Interpolation in x- and y-Direction

Due to the fact, that the matching and the reference set, the T2 as well as the SPGR, possess different pixel spacings and pixel sizes, it is necessary to equalize them in both dimensions – in the x-dimension as well as in the y-dimension. The approach is to resample the pixel size, illustrated in Fig. 3-6, of the matching sets because the information loss would be less (just in case of the T2 image sets). To execute the interpolation, the function fXYInterpolation is written. In this function two mesh grids are created.

One is used to store the data of every single image of the old image set with the old parameters such as pixel size and pixel spacing. The second mesh grid size is set through the definition of the new pixel size / pixel spacing. Both mesh grids are centred by the following calculation:

? = ? − x (?);

K = K − x (K);

( 3.3 )

Every single image of the old image set is interpolated with the new mesh grid by the function interp2. Due to the fact that the size of the image in mm should stay the same, the amount of pixels will be reduced. The proof if the reduction corresponds with a minimal error to the right amount of pixels can be done by following equation: x =

€ V ? W • ∗ € x

V ? W • ∗ x

V ? W

V ? W

( 3.4 )

Development of an Image Registration Procedure 19.07.12 21

Fig. 3-6: Interpolation in x- and y-direction [created by M.R.]

3.3.8 Translation in x- and y-Direction

The approach is to calculate the SSD-values as shown in equation 2.10. It searches for the smallest sum of intensity differences in the images. Due to the fact that the reference image possesses the smaller dimension (just in case of the T2 image sets) a window with the dimensions of the reference image is created. Within this image the sum of squares of intensity differences is calculated. Then the window, which is placed in the left upper corner of the matching image, is shifted one pixel to the right. The procedure is repeated until the border of the reference image is reached. Then the window is shifted one pixel down. During this process a current comparison between the SSD values occurs. If the particular SSD value is smaller than the previous one it will be stored by raising the previous value. The translation is retrieved by storing the particular shift of the window in dependence of the SSD value. If a SSD value is stored, the dedicated x- and y-position of the window will also be stored. The particular x- and y-position values constitute the left upper start point for the cropping of the matching image. Starting from this point the image is cropped to the dimension of the reference image.

Fig. 3-7: Translation in x- and y-direction [created by M.R.]

Development of an Image Registration Procedure 19.07.12 22

3.4 Validation

3.4.1 Z-Interpolation and its Error

In order to determinate the produced error through interpolation function (interp1) the correlation between the original slices and the corresponding interpolated slices can be calculated. The correlation is calculated by the 2D correlation function corr2, which delivers values between 0 (minimum) and 1 (maximum). Fig. 3-8 presents the procedure how the calculation is executed. For the comparison of the correlation values a new image stack is created. This image stack involves the first and the third slice of the matching set as initialization. Between these slices a new slice, which should correspond to the second slice of the original matching set, is interpolated. The correlation between the interpolated slice and the second slice of the original matching can be calculated. Subsequently the slices within the created image stack are incremented and the procedure is repeated until the boarder of the original matching stack is reached. The mean correlation error for this registration task is given by

ƒt|s

=

1 d c U 1 − „

~vzzt]|yavs

( 3.5 )

3.4.2 XY-Interpolation and its Error

Within this validation task the objective is to determinate the produced error of the 2D interpolation function (interp2). Therefore a similar approach as in chapter 3.4.1 is used.

To calculate the error of the interpolation, the correlation value of each image of the matching set is calculated before and after the correlation. This procedure is repeated in a logarithmic manner to predict the error growth due to its number of interpolation steps.

The error values, calculated by equation 3.4, constitute the base for statistical analysis through the calculation of the mean values, median values, minimum and maximum values, as well as the calculation of the standard deviation.

3.4.3 Rotation

To evaluate the accuracy of the rotation method the matching set is manipulated by an external person. The amount of rotation is unknown. The goal is to match the manipulated data set as good as possible and to determine the amount rotation. The external person is called in the end of the procedure to verify the result. After the publication of the real manipulation values through the external person, the deviation of the calculated rotation is calculated.

Development of an Image Registration Procedure 19.07.12 23

3.4.4 Translation

To evaluate the accuracy of the translation detection method, a similar approach is used as for the accuracy evaluation of the rotation method. The external person translates a dummy data image in different scenarios. The dummy data constitutes a MxN vector filled with zeros (black) and an image object, which is represented by the MxN vector filled with ones (white). To determine the x-translation and y-translation values, the SSDmethod is used. Post treatment the external person is called to verify the result.

Fig. 3-8: Validation of translation task. The dummy matching image (green) is shifted within the SSD-mask until the image object (white) of the matching image fits the image object of the reference image.

3.4.5 Visual

To determinate a translation in the x- and y-direction a visual examination of the images is executed. Therefore the images are normalized and subtracted by each other. The term normalization in this case means, that the grey values are set between 0 and 1.

W Lx = † ∙ (x ℎ Lx − Lx ) + ‡

( 3.6 )

Equation 3.6 shows the two weighting factors alpha and beta. If they are initialized with

†, ‡ = 0.5

it guarantees, that the values in the subtraction image are between zero and one. Therefore well matched objects will appear with a grey value of 0.5. Brighter and darker objects are an indication of a translation.

Development of an Image Registration Procedure 19.07.12 24

3.4.6 Evaluation of the Registration Result by Pixel Categorization

To control the accuracy of this registration task, an investigation of the grey values of the subtracted image pair (slice 14 of matching set and slice 91 reference set) is executed.

This investigation constitutes a check if a grey value in the subtracted image pair refers to pre-defined grey category. Therefore the grey values from 0 to 1 are categorized in ten categories, as shown in Tab. 3-3.

Category 1

0.0 – 0.1

Category 6

0.5 – 0.6

Category 2

0.1 – 0.2

Category 7

0.6 – 0.7

Category 3

0.2 – 0.3

Category 8

0.7 – 0.8

Category 4

0.3 – 0.4

Category 9

0.8 – 0.9

Table 3-3: Categorization of the codomain of grey value

Category 5

0.4 – 0.5

Category 10

0.9 – 1.0

If a grey value refers to a certain category, a reference value in this particular category is incremented. At the end of the procedure, if all pixels are categorized, the result constitutes a first overview of the precision (the width of the peak around 0.5 in the histogram), which is represented by a histogram of grey value frequencies.

3.4.7 Evaluation of the Registration Result by Histogram Analysis

The evaluation of the registration result by histogram analysis is a second approach to verify the received result. It describes the summation of the grey values of the pixels with the corresponding position through the whole data set. After the summation the mean value for each pixel is calculated. Hence a mean image is created. This mean image is treated with approach number one (evaluation of the registration result by pixel categorization), which means that the mean pixel values are categorized. In a second step the histogram of the chosen image pair is created, to compare the quality of registration between the chosen image pair and the whole data set.

3.4.8 Influence of the Sequential Arrangement on Translation Values

Within this validation task the influence of the particular registration task on the translation values in dependence of its position in the value chain of the whole registration process, is determined. Within five additional scenarios (the original scenarios, which constitutes the fifth scenario is not mentioned here), which are presented in Tab. 3-4, the particular registration tasks are switched. At the end of the value chain the translation values are calculated and compared to each other in a qualitative manner.

Development of an Image Registration Procedure 19.07.12 25

Scenario 1

Task 1

Z-Alignment

Scenario 2

Z-Alignment

Scenario 3

Z-Alignment

Scenario 4

Z-Alignment

Scenario 5

Z-Alignment

Task 2

Z-Interpolation Z-Interpolation XY-

Task 3

Z-Offset

Task 4

Rotation

Z-Offset

XY-

Interpolation

Interpolation

Rotation

XY-

Interpolation

Rotation

Z-Interpolation XY-

Interpolation

Z-Interpolation Z-Offset Z-Interpolation

Task 5

XY-

Interpolation

Rotation Z-Offset Rotation Z-Offset

Task 6

XY-Offset XY-Offset XY-Offset

Table 3-4: Scenarios of the sequential arrangement

XY-Offset XY-Offset

3.4.9 Robustness

To define the robustness of the intensity based registration process, a logarithmic approach is used. The goal is to simulate the noise of the type “salt and pepper”, but with adjustable grey values. Within this logarithmic approach, the grey values of the test image are grouped from 0 to the maximum grey value in steps of 10 % of the maximum value. The amount of pixels, which should be changed are defined by the resolution of the image. They are grouped in a logarithmic manner. An iterative approach involves the setting of the particular amount of pixels for each category of grey values. This procedure is repeated until for every category of grey values the corresponding image with the manipulated pixels exists. For the validation of this task the whole registration process is executed. The results of each particular registration task are compared to the original result.

Development of an Image Registration Procedure 19.07.12 26

4 Results

4.1 Registration

4.1.1 Alignment in z-Direction

As shown in Tab. 4-1 and Tab. 4-2 the alignment for the T2 and SPGR image sets results in a GOI of three image pairs, which were determined and confirmed by a neurological surgeon. An image pair represents the two images, which constitute the highest correlation, respectively the most similar, significant structures. The offset between the matching and reference set is presented in Tab. 4-3 and Tab. 4-4. From the given GOI the first image pair, which is shown in Fig. 4-1 and Fig. 4-2, is selected for the subsequent registration process.

Image Pair Matching Set (Slice No. | No total

)

1 14 | 26

2 23 | 26

3 26 | 26

Table 4-1: Group of interest (T2)

Reference Set (Slice No. | No total

)

91 | 256

128 | 256

141 | 256

Image Pair Matching Set (Slice No. | No total

)

1 64 | 124

2 68 | 124

3 70 | 124

Table 4-2: Group of interest (SPGR)

Reference Set (Slice No. | No total

)

51 | 124

57 | 124

60 | 124

Image Pair Matching Set (Slice No. | No total

) Reference Set (Slice No. | No total

) Offset

1 1 | 26 39 | 256 38 slices

2

3

1 | 26

1 | 26

40 | 256

41 | 256

Table 4-3: Offset between matching and reference set (T2)

39 slices

40 slices

Image Pair Matching Set (Slice No. | No total

) Reference Set (Slice No. | No total

) Offset

1 14 | 124 1 | 124 13 slices

2 12 | 124 1 | 124 11 slices

Development of an Image Registration Procedure 19.07.12 27

3 11 | 124 1 | 124

Table 4-4: Offset between matching and reference set (SPGR)

10 slices

Fig. 4-1: T2 matching set slice 14 (left) and reference set slice 91 (right). Eyes are visible in reference image but invisible in matching image. In both images the ventricles, the ACPC-line and the CSF-vessels are well recognizable.

Fig. 4-2: SPGR matching set slice 64 (left) and reference set slice 51 (right). Reference image presents the positions of the electrodes, constituted by the two small, dark dots beside the upper part of the ventricles.

Development of an Image Registration Procedure 19.07.12 28

4.1.2 Rotation Determination and Elimination

For both modalities, the T2 as well as the SPGR the first approach was used to determine and eliminate any rotation. The visual examination of the T2 sets results in the decision that in the matching set a rotation around the x-axis (axial view) or around the zaxis (sagittal view) occurred. An indication for this conclusion is that the eyes in the upper half of the matching image (slice 14) are missing. Due to the fact that the whole data set is tilted, the grey values in the lower half of the matching image (slice 14) represent certain information from the upper slices. After an iterative approach it was considered that the amount of rotation is 1.5 degrees. The corrected matching set is presented in

Fig. 4-3.

The visual examination of the SPGR sets has not shown any rotation around an axis.

Therefore no correction procedure was applied.

Fig. 4-3: Rotated T2 matching set slice 14 (left) and unrotated reference set slice 91

(right). Eyes are visible now in both images.

4.1.3 Interpolation in z-Direction

The growth values of the interpolated image stacks are presented in Tab. 4-5. The T2 reference set was not interpolated. As explained in chapter 3.3.5 – interpolation in zdirection, it was necessary to interpolate a different amount of slices in the SPGR matching and reference set.

T2-Matching

Set

Original

Stack Size

26

Gap

Amount

25

Slice Amount (interpolated)

3

Stack Size (interpolated)

101

Development of an Image Registration Procedure 19.07.12 29

T2-Reference

Set

SPGR-Matching

Set

256

124

255

123

SPGR-

Reference Set

124 123

Table 4-5: Z-Interpolation results

-

3

2

-

493

370

4.1.4 Offset Determination in z-Direction

The offset values are presented in Tab. 4-6.

T2-Matching Set

Old Slice Position

14

T2-Reference Set

91

SPGR-Matching Set

64

SPGR-Reference Set

51

Table 4-6: Offset values

New Slice Position

53

91

253

151

Offset

39

0

189

100

4.1.5 Interpolation in x- and y-Direction

The resolution values are presented in Tab. 4-7.

T2-Matching Set

Old Resolution

512x512

SPGR-Reference Set

256x256

Table 4-7: Resolution values

New Resolution

480x480

246x246

4.1.6 Translation Determination in x- and y-Direction

The first two images of Fig. 4-4 and Fig. 4-5 show the iterative process of translation correction. The last image presents the subtracted image after the correction of x- and ytranslation through the calculation of the SSD value and the corresponding coordinates of the SSD window, which are shown in Tab. 4-8 and Tab. 4-9. For the correction in the last image the median translation values are used.

Development of an Image Registration Procedure 19.07.12 30

Fig. 4-4: XY-Offset determination (T2). The images (left to right) show the iterative process of the translation elimination. The last image on the right presents the translation elimination with the SSD window coordinates.

Fig. 4-5: XY-Offset determination (SPGR). The images (left to right) show the iterative process of the translation elimination. The last image on the right presents the translation elimination with the SSD window coordinates.

X-Translation [Pixel]

Y-Translation [Pixel]

SSD-Value

Minimum Maximum Mean Median Standard Deviation

-56 -37 -54 -54 2.498

-138

4876

Table 4-8: SSD results (T2)

40

7987

-60

6372

-65

6438

25.39

699

Minimum Maximum Mean Median Standard Deviation

X-Translation [in Pixel]

-7 -7 -7 -7 0

Y-Translation [in Pixel]

-6

SSD-Value

22.55

-6

29.66

-6

25.74

-6

25.86

0

2.00

Development of an Image Registration Procedure 19.07.12 31

Table 4-9: SSD results (SPGR)

4.2 Validation

4.2.1 Z-Interpolation and its Error

The calculation of the error, occurring during the z-interpolation of the T2 matching set results in a vector with 24 values (starts from slice 2 and ends with slice 25), which are presented in Tab. 4-10. From these values the mean error, the median error and the standard deviation is calculated, which are for their part shown in Tab. 4-11.

Slice No.

Correlation Value

Error Value [%]

Slice No.

Correlation Value

Error Value [%]

Slice No.

Correlation Value

Error Value [%]

Slice No.

Correlation Value

2

0.9517

4.83

8

0.9436

5.64

14

0.9637

3.63

20

0.9729

3

0.9552

4.48

9

0.9421

5.79

15

0.9658

3.42

21

0.9729

4

0.9551

4.49

10

0.9412

5.88

16

0.9668

3.32

22

0.9740

5

0.9542

4.58

11

0.9460

5.40

17

0.9665

3.35

23

0.9735

Error Value [%]

2.71 2.72 2.60 2.65

Table 4-10: Correlation values of the z-interpolation and their errors

2.54

6

0.9508

4.92

12

0.9529

4.71

18

0.9700

3.00

24

0.9746

7

0.9478

5.22

13

0.9603

3.97

19

0.9705

2.95

25

0.9704

2.96

T2 Matching Set

3.99

Mean Value [%]

Median Value [%]

3.80

Standard Deviation [%]

1.13

Table 4-11: Statistical analysis of the z-Interpolation errors

4.2.2 XY-Interpolation and its Error

The original T2 matching set was interpolated 500 times forwards and backwards. The mean error, median error and the standard deviation were calculated for each iteration

Development of an Image Registration Procedure 19.07.12 32

step and through the whole data set. Additionally the particular errors for each slice in data set were added. All results are presented in Tab. 4-12.

Interpolation

1 Iteration

10 Iterations

20 Iterations

30 Iterations

40 Iterations

50 Iterations

Error in Data Set

[%]

5.008

68.08

104.79

129.02

147.14

161.42

100 Iterations

201.01

150 Iterations

210.36

200 Iterations

211.36

250 Iterations

211.46

300 Iterations

211.47

350 Iterations

211.47

400 Iterations

211.47

450 Iterations

211.47

500 Iterations

211.47 8.133

Table 4-12: T2 xy-interpolation error values

7.731

8.091

8.129

8.133

8.134

8.133

8.133

8.133

Mean Error

[%]

0.1926

2.618

4.031

4.962

5.659

6.209

7.855

8.244

8.300

8.304

8.304

8.304

8.304

8.304

8.304

Median Error

[%]

0.1953

2.621

4.063

5.011

5.732

6.258

0.0059

0.0068

0.0069

0.0069

0.0069

0.0069

0.0069

0.0069

0.0069

Standard Deviation

0.0002

0.0019

0.0024

0.0028

0.0032

00038

4.2.3 Rotation

The external person has manipulated the T2 matching set in three different scenarios.

The sequential arrangement of rotations for each particular scenario is presented in Tab.

4-13. The rotations in the images (axial, sagittal and frontal) were well visible. Therefore it was easy to set adequate landmarks for calculation the angle between the vectors

(two landmarks). The results of the calculations are also presented in Tab. 4-13. Within each scenario the error was calculated. The error of each scenario was used to calculate the mean error, median error and the standard deviation. The results are presented in Tab. 4-14.

Rotation 1

Rotation 2

Z

X

Rota-

Y

Scenario 1

Axis Control

Calculation

14.0 ° 14.2 ° X

0.9 °

1.2 °

0.9 °

1.3 °

Scenario 2

Axis Control

Z

Y

0.5 °

20.0 °

1.3 °

Calculation

0.6 °

20.1 °

1.2 °

Y

Z

X

Scenario 3

Axis Control

1.9 °

10.2 °

0.9 °

Calculation

1.8 °

10.2 °

0.9 °

Development of an Image Registration Procedure 19.07.12 33

tion 3

Table 4-13: Rotation validation results

Error Value [%]

Scenario 1

9.76

Scenario 2

28.2

Mean Error [%]

Median Error [%]

Standard Deviation

Table 4-14: Statistic results of rotation validation

Scenario 3

5.23

14.4

9.76

12.2

4.2.4 Translation

The external person has defined three translation scenarios with different translation values. The result is presented in Tab. 4-11. It shows that the translation detection procedure works. In every single scenario the right translation value was found without any deviation. The SSD values all represent 0, which means that no differences in intensities exist.

Control

Calculation

Scenario 1

X Y

0 0

0 0

Scenario 2

SSD X Y

0

0

10

10

Table 4-15: Validation results of translation

4

4

0

0

Scenario 3

SSD X Y

8

8

2

2

SSD

0

0

4.2.5 Visual

The image stack of the subtracted images is represented, as shown in Fig. 4-6, Fig. 4-7,

Fig. 4-8 and Fig. 4-9, by eleven images from the first image to the ending image in steps of ten images. Image 1 and 11 show a well visible darker area in the upper half of itself.

This area disappears with each incrementation in the image stack. The image 101 shows a similar, darker area but this time it appears in the lower half of the image. Every single image constitutes a large amount of grey values around 0.5.

Development of an Image Registration Procedure 19.07.12 34

Fig. 4-6: Subtracted images no. 1, 11 and 21 (left to right)

Fig. 4-7: Subtracted images no. 31, 41 and 51 (left to right)

Fig. 4-8: Subtracted images no. 61, 71 and 81 (left to right)

Fig. 4-9: Subtracted images no. 91 and 101 (left to right)

Development of an Image Registration Procedure 19.07.12 35

4.2.6 Evaluation of the Registration Result by Pixel Categorization

The amount per category of the categorized pixels of the chosen image pair and mean image is presented in Tab. 4-16. Category 5 and 6 composes 93 % of the total possible amount of pixels. The subtracted image pair possesses more pixels that are farther away from categories 5 and 6 than the mean image.

Category 1 [0.0 – 0.1]

Category 2 [0.1 – 0.2]

Category 3 [0.2 – 0.3]

Category 4 [0.3 – 0.4]

Category 5 [0.4 – 0.5]

Category 6 [0.5 – 0.6]

Category 7 [0.6 – 0.7]

Category 8 [0.7 – 0.8]

Category 9 [0.8 – 0.9]

Subtracted Image Pair

0

119

1645

4628

37900

99723

3134

295

7

Category 10 [0.9 – 1.0]

5

Table 4-16: Mean frequencies of pixel values

0

0

Mean Image

0

502

52143

94528

258

18

6

1

4.2.7 Evaluation of the Registration Result by Histogram Analysis

The subtraction image of the chosen image pair shows a large area of grey values around 0.5. This fact is also represented in the histogram. It shows a narrow peak with a slightly widened base. The mean image possesses an even larger area of grey values around 0.5. Like before it is represented in the histogram. The received images and histograms correspond with the calculated amount of pixels in Tab. 4-16.

Development of an Image Registration Procedure 19.07.12 36

Fig. 4-10: Validation of Pixel Categorization. Figure shows the subtracted image from the chosen image pair and the corresponding histogram (first row), as well as the mean image of the subtracted images and the corresponding histogram (second row). The peak around the grey value of 0.5 marks the amount pixels, which are matched as its best.

4.2.8 Influence of the Sequential Arrangement on Translation Values

The results, shown in Tab. 4-17, present almost consistent values, except the scenario

2. Within scenario 2 the SSD-value is not calculable. The x- and y-translation values differ too much from the other values, which is an indication of a problem case.

Scenario 1

Scenario 2

Scenario 3

Scenario 4

X-Translation Value

-54

143

-54

-54

Y-Translation Value

-64

143

-64

-64

SSD Value

6.6617

NaN

6.1634

6.6507

Scenario 5

-54 .54 6.2029

Table 4-17: SSD values of influence scenarios. The SSD values are to multiply with

1000 to get the precise result.

4.2.9 Robustness

The SSD-value is stable until the amount of pixel reaches the boarder of 2’600. In case this amount is raised, the SSD-algorithm starts becoming unstable and the x- and ycoordinates are varying randomly. The SSD coordinates show a different behaviour. The y-coordinate seems to be more prone to noise than the x-coordinate.

Development of an Image Registration Procedure 19.07.12 37

Pixel

Amount

Intensity Group 1

[0]

3

X Y SSD

Intensity Group 2

[344]

X Y SSD

Intensity Group 3

[688]

X Y

Intensity Group 4

[1032]

SSD X Y SSD

-53 -68 5.892 -54 -68 6.251 -54 -68 7.242 -55 -134 8.818

26

262

2621

26214

-54

-54

-55

-51

-65

-63

-63

22

5.521

5.428

6.309

6.475

-54

-54

-55

-47

-65

-64

-62

11

5.877

5.725

6.643

6.742

-54

-54

-54

-47

-66

-64

-60

11

6.898 -54

6.682 -54

7.652 -54

7.648 -47

-67

-64

-60

11

8.581

8.299

9.332

9.198

262144

-52 38 6.393 -53 31 6.610 -53 32 7.413 -53 32 8.808

Table 4-18: Validation results of robustness task. The SSD values are to multiply with

1000 for the precise result.

Development of an Image Registration Procedure 19.07.12 38

5 Discussion

5.1 Registration

5.1.1 Alignment in z-Direction

This registration task possesses high amount of user interaction coupled with a large amount of evaluation time, which is necessary to select a proper image pair. This subjective evaluation constitutes a highly error-prone approach, which should be replaced by a more reliable automatic approach. To minimize the risk of a wrong image pair, which is chosen by an iterative manually based decision, it was necessary to take medical advice. It would have been even more accurate if a second, professional advice could have been taken. Due to fact that the originally chosen image pair was confirmed by the neurosurgeon, it constitutes a proper basis for the subsequent registration process. Nevertheless it is a very sensitive task and due to the fact that it constitutes the starting point of the whole registration process it should be taken enough time to make the right decision.

5.1.2 Rotation Determination and Elimination

The rotation task, done by visual examination, constitutes the same risk of a false interpretation as the alignment in z-direction. The subjective evaluation and the high amount of user interaction lead to a high error sensitivity. Therefore it was necessary to acquire several professional opinions, such as the one of the neurosurgeon. In order to reduce the amount of user interaction, an automatic approach might be more appropriate. The determination result has shown that no rotation occurred around the x- and y-axis of the axial plane. However, if there would have been any rotation, the rotation would have been executed after the transformation of the axial plane in the sagittal and frontal plane. The advantage of one single rotation matrix is definitely higher than the disadvantage of plane transformation. The risk to calculate the rotation with the wrong input parameters is not acceptable and the produced, additional planes can be used for additional evaluations.

The reason why the second approach was not used is that the determined rotation around the z-axis of the sagittal plane (x-axis axial plane) was not visible. Due to the small neurological background it was impossible, to set adequate landmarks.

Development of an Image Registration Procedure 19.07.12 39

5.1.3 Interpolation in z-Direction

For the T2 matching set the desired amount of slices was reached. The slice thickness was accordingly reduced to the fourth of its original size, which means that the z-size of voxels in the matching set correspond to the z-size of voxels in the reference set. It has to be considered that this registration task is almost user-interaction free. For the SPGR matching and reference set the desired amount of slices was also reached.

The gained results should be interpreted with caution, because it might be sensitive to the kind of interpolation that has been used.

5.1.4 Offset Determination in z-Direction

A difference between the chosen T2 offset and the calculated offset exists. It shows pretty well how easily an interpretation mistake can occur. That is why the user interaction should be reduced. However the visual intension was this time stronger than the rational calculated decision. In the SPGR image sets no difference occurred. The offset values for both image sets were adopted for the remaining registration parts.

5.1.5 Interpolation in x- and y-Direction

For the T2 matching set the desired resolution of 480 by 480 pixels was reached. The

SPGR reference set was resampled to 246 by 246 pixels. This constitutes a proof that the pixel spacing in both image sets was successfully corrected and the voxel geometries from the T2 matching and the SPGR reference set now correspond to their counterpart.

5.1.6 Offset Determination in x- and y-Direction

Due to the received results, it is recognizable that the T2 y-translation value tends to be more error-prone than the x-translation value. This is confirmed by the high y-standard deviation value. The y-minimum and y-maximum values are also an indication that the

SSD-algorithm reaches an invalid image region. The case is that due to the rotation around the x-axis (axial plane) invalid regions are created. Within these regions the image information is missing, which influences more the y-direction. MATLAB interprets the invalid pixels with the value not a number (NaN). For the visualization NaN’s are treated as zeros. However if the number of NaN’s crosses a certain boarder it is not treatable anymore. The whole procedure of NaN insertion is presented in Fig. 5.1. The advantage of this method is the automatic, reliable deliverance of x- and y-translation as well as SSD values. The user interaction is kept as small as possible. The disadvantage is the large amount of time consumption due to the choice of a big SSD-mask, which

Development of an Image Registration Procedure 19.07.12 40

makes it possible to calculate the highest amount of translation. For the SPGR image sets within the small group of 20 chosen images the same amount of x- and ytranslation values were calculated. This is because within such a small group the translations are almost constant. But the most important reason for this is that it concerns similar image sets. The time space between the image acquisition was extremely short and the stereotactic frame not allows any movement, which could lead to an additional translation. Also the problem with the invalid area was inexistent due to the fact that no rotation occurred.

Fig. 5-1: Invalid image regions. The original image stack (black quadrangle) is rotated by a certain amount of degrees around the rotation axis or rotation centre (red dot with blue boarder). The rotated image stack (orange quadrangle) is located in some regions in a space, where no image information exist (red region). The valid volume (left), respectively the valid image area

(right) is presented in green.

5.2 Validation

5.2.1 Z-Interpolation and its Error

The validation of the z-interpolation and the evaluation of its error had shown that the mean error, produced by the one dimensional interpolation function, in the data set constitutes 3.99 %. This means that in each particular image an error of approximately 4 % was produced. Although the error of 4 % is reasonably low, this registration step should be placed late in the process, because it may cause interpolation errors. Another important factor is that the z-interpolation is really position depending. The receiving interpolation value depends on the particular slice position in the head. The image stack of the T2 matching set is situated in the middle of the head, which means that no unexpected changes should occur. If the matching would be situated at the top or the bottom of the head the correlation values would dramatically decrease, which goes hand in hand with a rapidly increasing error value. The pretty high error in the matching set does

Development of an Image Registration Procedure 19.07.12 41

not come from the position in the head. It is a result of the high slice thickness and the chosen validation approach.

5.2.2 XY-Interpolation and its Error

In order to keep the error as small as possible an interpolation should be executed in the smallest, possible number of steps. If several interpolation steps should be necessary due to any reason (e.g. miscalculation) the interpolation values should be added. Post calculation the interpolation should be executed from the original data with the value, which is resulting from the sum of interpolation values. As determined the amount of error is also depending on the new pixel size. The higher the pixel size the bigger is the amount of error. After 200 iterations of forward and backward interpolation the image is blurred in a manner that it does not depend from what pixel the interpolation information comes.

5.2.3 Rotation

The challenge in this validation task is the user depending accuracy. The user’s choice of setting the landmarks directly influences the result of the rotation angle. Especially the sagittal and frontal planes, which just consist of 26 slices, constitute a tricky setting of a proper landmark. An execution of an interpolation is not possible, because the interpolation would have resampled the image. This resampling would distort the right amount of rotation, which is definitely not preferred. For the sake of completeness there is to say, that the smaller the amount of rotation the more error-prone is the setting of a landmark.

The result depends therefore on one side on the user’s choice and on the other side on the amount of rotation angle.

5.2.4 Translation

The validation task possesses the same advantage as the one discussed in chapter

5.1.6. The precision of 100 % argues for itself. The problem of time consumption was, due to small chosen test mask (reduced amount of iterations), irrelevant.

5.2.5 Visual

The large amount of black pixels provokes a false interpretation of the subtracted images. In a future version the head or even the brain should be segmented. In a subsequent step just the segmented region of interest should be used for registration.

Development of an Image Registration Procedure 19.07.12 42

The effect of NaN introduction is well visible. The invalid volume or the valid image area as presented in Fig. 5-1 should be cropped (as done with the invalid are at the bottom of the images). This requires a corresponding cropping in the reference set.

5.2.6 Evaluation of the Registration Result by Pixel Categorization

The pixel distribution in each category of the subtracted mean image is shifted to the middle categories due to its weighting through the mean value calculation. Therefore the pixel distribution of the chosen image pair is more realistic. Nevertheless the given pixel distribution constitutes a clear indication of the precision of the developed registration procedure.

5.2.7 Evaluation of the Registration Result by Histogram Analysis

The peak of the subtracted mean image looks narrower than the peak of the subtracted chosen image pair. The narrowness comes from the weighting of the outer pixel values by N (appearance of the same pixel position). The appearance of bright pixels in the outer image area is more seldom than in the inner area. The seldom pixels are deleted.

Therefore the histogram of the subtracted chosen image pair constitutes a more realistic distribution. Nevertheless both histograms present very narrow peaks, which is an indication of the high precision.

5.2.8 Influence of the Sequential Arrangement on Translation Values

Scenario 3 shows the smallest amount of intensity differences. Nevertheless the original scenario should not be exchanged with scenario 3. Scenario 5 is even more appropriate.

In comparison with scenario 3 does scenario 5 not provoke any warning messages of

MATLAB (NaN’s found after interpolation). It also possesses an almost equal SSD value. Scenario 2 constitutes the worst scenario. The z-interpolation increases the invalid volume, which is generated by the rotation. Also the sequence within the scenario is wrong. The rotation should occur at the beginning because the smaller the image stack the smaller are the invalid regions after the rotation.

5.2.9 Robustness

The increased amount of error proneness is based on the large amount of information, which goes lost during the rotation task. The amount of changed pixels (over 2621) is just too high that precise translation value can be calculated. The y-translation value of intensity group 4 and pixel amount 3 (-134) constitutes a stochastic outlier.

Development of an Image Registration Procedure 19.07.12 43

5.3 Future Tasks

5.3.1 Cropping of Invalid Image Regions

In a future project an effective algorithm should be developed. This algorithm should consist a part, which determines the invalid regions through finding NaN’s. In this task it is important that no stochastic NaN is detected. The algorithm should just treat clusters of NaN’s. The particular invalid regions per particular slice should be stored and transferred to the reference image. With an additional scissor-algorithm the invalid region in both image sets, the matching as well the reference image set should be cut away.

5.3.2 Mutual Information

In the chapter of theoretical background the mutual information approach was mentioned. It should be seen as a kind of forecast for a future thesis. This algorithm constitutes an alternative to the developed one, because the intensity based approach cannot be used for the intermodal registration.

5.3.3 Segmentation

It was mentioned in the beginning of this thesis that the CSF should be segmented in order to compare the particular areas. Due to the fact, that without any registration a comparison would be totally useless, the registration was developed prior to segmentation algorithm. So the project goal and description was changed. However in the end of the project there was no time left to develop a proper segmentation algorithm. Nevertheless this very important goal should be mentioned in a future project. Experiments have shown that an first area estimation can be made by setting a soft threshold value. The region based approach should due to its neighbour sensitivity not be used. In the literature a promising way of segmenting the different brain tissues, is explained. It should be considered in the future project.

Development of an Image Registration Procedure 19.07.12 44

6 Conclusion

It was a big challenge, to register the different source images. Nevertheless it was very exciting. The developed registration procedure constitutes a reliable, time-consuming algorithm which assumes precognition of the particular user. In every step it should be taken care before running the algorithm. The algorithm still possesses a particular large amount of user interaction, which should definitely be replaced with an automatic approach. If the intensity based algorithm does not provide any further possibility to replace the user-interactive approaches with automatic approaches, then the whole registration basis should be changed.

Development of an Image Registration Procedure 19.07.12 45

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