comprehensive survey
1
Image Change Detection Algorithms:
A Systematic Survey
Richard J. Radke∗ , Srinivas Andra, Omar Al-Kofahi, and Badrinath Roysam,
Department of Electrical, Computer, and Systems Engineering
Rensselaer Polytechnic Institute
110 8th Street, Troy, NY, 12180 USA
[email protected],{andras,alkofo}@rpi.edu,[email protected]
EDICS categories: 2-MODL, 2-ANAL, 2-SEQP
∗
Please address correspondence to Richard Radke. This research was supported in part by CenSSIS, the NSF Center for
Subsurface Sensing and Imaging Systems, under the Engineering Research Centers program of the National Science Foundation
(Award Number EEC-9986821) and by Rensselaer Polytechnic Institute.
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Abstract
Detecting regions of change in multiple images of the same scene taken at different times is of
widespread interest due to a large number of applications in diverse disciplines, including remote sensing,
surveillance, medical diagnosis and treatment, civil infrastructure, and underwater sensing. This paper
presents a systematic survey of the common processing steps and core decision rules in modern change
detection algorithms, including significance and hypothesis testing, predictive models, the shading model,
and background modeling. We also discuss important preprocessing methods, approaches to enforcing the
consistency of the change mask, and principles for evaluating and comparing the performance of change
detection algorithms. It is hoped that our classification of algorithms into a relatively small number of
categories will provide useful guidance to the algorithm designer.
Index Terms
Change detection, change mask, hypothesis testing, significance testing, predictive models, illumination invariance, shading model, background modeling, mixture models.
I. I NTRODUCTION
Detecting regions of change in images of the same scene taken at different times is of widespread
interest due to a large number of applications in diverse disciplines. Important applications of change
detection include video surveillance [1], [2], [3], remote sensing [4], [5], [6], medical diagnosis and
treatment [7], [8], [9], [10], [11], civil infrastructure [12], [13], underwater sensing [14], [15], [16] and
driver assistance systems [17], [18]. Despite the diversity of applications, change detection researchers
employ many common processing steps and core algorithms. The goal of this paper is to present a
systematic survey of these steps and algorithms. Previous surveys of change detection were written by
Singh in 1989 [19] and Coppin and Bauer in 1996 [20]. These articles discussed only remote sensing
methodologies. Here, we focus on more recent work from the broader (English-speaking) image analysis
community that reflects the richer set of tools that have since been brought to bear on the topic.
The core problem discussed in this paper is as follows. We are given a set of images of the same scene
taken at several different times. The goal is to identify the set of pixels that are “significantly different”
between the last image of the sequence and the previous images; these pixels comprise the change
mask. The change mask may result from a combination of underlying factors, including appearance or
disappearance of objects, motion of objects relative to the background, or shape changes of objects. In
addition, stationary objects can undergo changes in brightness or color. A key issue is that the change
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mask should not contain “unimportant” or “nuisance” forms of change, such as those induced by camera
motion, sensor noise, illumination variation, non-uniform attenuation, or atmospheric absorption. The
notions of “significantly different” and “unimportant” vary by application, which sometimes makes it
difficult to directly compare algorithms.
Estimating the change mask is often a first step towards the more ambitious goal of change understanding: segmenting and classifying changes by semantic type, which usually requires tools tailored to a
particular application. The present survey emphasizes the detection problem, which is largely applicationindependent. We do not discuss algorithms that are specialized to application-specific object classes,
such as parts of human bodies in surveillance imagery [3] or buildings in overhead imagery [6], [21].
Furthermore, our interest here is only in methods that detect changes between raw images, as opposed
to those that detect changes between hand-labeled region classes. In remote sensing, the latter approach
is called “post-classification comparison” or “delta classification”.1 Finally, we do not address two other
problems from different fields that are sometimes called “change detection”: first, the estimation theory
problem of determining the point at which signal samples are drawn from a new probability distribution
(see, e.g., [24]), and second, the video processing problem of determining the frame at which an image
sequence switches between scenes (see, e.g., [25], [26]).
We begin in Section II by formally defining the change detection problem and illustrating different
mechanisms that can produce apparent image change. The remainder of the survey is organized by the
main computational steps involved in change detection. Section III describes common types of geometric
and radiometric image pre-processing operations. Section IV describes the simplest class of algorithms
for making the change decision based on image differencing. The subsequent Sections (V -VII) survey
more sophisticated approaches to making the change decision, including significance and hypothesis
tests, predictive models, and the shading model. With a few exceptions, the default assumption in these
sections is that only two images are available to make the change decision. However, in some scenarios,
a sequence of many images is available, and in Section VIII we discuss background modeling techniques
that exploit this information for change detection. Section IX focuses on steps taken during or following
change mask estimation that attempt to enforce spatial or temporal smoothness in the masks. Section
X discusses principles and methods for evaluating and comparing the performance of change detection
1
Such methods were shown to have generally poor performance [19], [20]. We note that Deer and Eklund [22] described an
improved variant where the class labels were allowed to be fuzzy, and that Bruzzone and Serpico [23] described a supervised
learning algorithm for estimating the prior, transition, and posterior class probabilities using labeled training data and an adaptive
neural network.
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algorithms. We conclude in the final section by mentioning recent trends and directions for future work.
II. M OTIVATION AND P ROBLEM S TATEMENT
To make the change detection problem more precise, let {I1 , I2 , . . . , IM } be an image sequence in
which each image maps a pixel coordinate x ∈ Rl to an intensity or color I(x) ∈ Rk . Typically, k = 1
(e.g., gray-scale images) or k = 3 (e.g., RGB color images), but other values are possible. For instance,
multispectral images have values of k in the tens, while hyperspectral images have values in the hundreds.
Typically, l = 2 (e.g., satellite or surveillance imagery) or l = 3 (e.g., volumetric medical or biological
microscopy data). Much of the work surveyed assumes either that M = 2, as is the case where satellite
views of a region are acquired several months apart, or that M is very large, as is the case when images
are captured several times a second from a surveillance camera.
A basic change detection algorithm takes the image sequence as input and generates a binary image
B : Rl → [0, 1] called a change mask that identifies changed regions in the last image according to the
following generic rule:

 1 if there is a significant change at pixel x of I ,
M
B(x) =
 0 otherwise.
M
S
S
A
A
Fig. 1. Apparent image changes have many underlying causes. This simple example includes changes due to different camera
and light source positions, and well as changes due to nonrigid object motion (labeled “M”), specular reflections (labeled “S”),
and object appearance variations (labeled “A”). Deciding and detecting which changes are considered significant and which are
considered unimportant are difficult problems and vary by application.
Figure 1 is a toy example that illustrates the complexity of a real change detection problem, containing
two images of a stapler and a banana taken several minutes apart. The apparent intensity change at
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V
I
A
Fig. 2. A biomedical change detection example involving a pair of images of the same human retina taken 6 months apart.
This example contains several changes involving the vasculature (labeled “V”) and numerous other important changes in the
surrounding retinal tissue (labeled “A”). It also contains many illumination artifacts at the periphery (labeled “I”). It is of interest
to detect the significant changes while rejecting registration and illumination artifacts.
each pixel is due to a variety of factors. The camera has moved slightly. The direct and ambient light
sources have changed position and intensity. The objects have been moved independently of the camera.
In addition, the stapler arm has moved independently of the base, and the banana has deformed nonrigidly.
Specular reflections on the stapler have changed, and the banana has changed color over time.
Figure 2 is a real biomedical example showing a pair of images of the human retina taken 6 months
apart. The images need to be registered, and contain several local illumination artifacts at the borders of
the images. The gray spots in the right image indicate atrophy of the retinal tissue. Changes involving
the vasculature are also present, especially a vessel marked “V” that has been cut off from the blood
supply.
In both cases, it is difficult to say what the gold-standard or ground-truth change mask should be; this
concept is generally application-specific. For example, in video surveillance, it is generally undesirable to
detect the “background” revealed as a consequence of camera and object motion as change, whereas in
remote sensing, this change might be considered significant (e.g. different terrain is revealed as a forest
recedes). In the survey below, we try to be concrete about what the authors consider to be significant
change and how they go about detecting it.
The change detection problem is intimately involved with several other classical computer vision
problems that have a substantial literature of their own, including image registration, optical flow, object
segmentation, tracking, and background modeling. Where appropriate, we have provided recent references
where the reader can learn more about the state of the art in these fields.
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III. P RE - PROCESSING M ETHODS
The goal of a change detection algorithm is to detect “significant” changes while rejecting “unimportant” ones. Sophisticated methods for making this distinction require detailed modeling of all the expected
types of changes (important and unimportant) for a given application, and integration of these models
into an effective algorithm. The following subsections describe pre-processing steps used to suppress or
filter out common types of “unimportant” changes before making the change detection decision. These
steps generally involve geometric and radiometric (i.e., intensity) adjustments.
A. Geometric Adjustments
Apparent intensity changes at a pixel resulting from camera motion alone are virtually never desired to
be detected as real changes. Hence, a necessary pre-processing step for all change detection algorithms
is accurate image registration, the alignment of several images into the same coordinate frame.
When the scenes of interest are mostly rigid in nature and the camera motion is small, registration can
often be performed using low-dimensional spatial transformations such as similarity, affine, or projective
transformations. This estimation problem has been well-studied, and several excellent surveys [27], [28],
[29], [30], and software implementations (e.g., the Insight toolkit [31]) are available, so we do not detail
registration algorithms here. Rather, we note some of the issues that are important from a change detection
standpoint.
Choosing an appropriate spatial transformation is critical for good change detection. An excellent
example is registration of curved human retinal images [32], for which an affine transformation is
inadequate but a 12-parameter quadratic model suffices. Several modern registration algorithms are
capable of switching automatically to higher-order transformations after being initialized with a loworder similarity transformation [33]. In some scenarios (e.g. when the cameras that produced the images
have widely-spaced optical centers, or when the scene consists of deformable/articulated objects) a nonglobal transformation may need to be estimated to determine corresponding points between two images,
e.g. via optical flow [34], tracking [35], object recognition and pose estimation [36], [37], or structurefrom-motion [38], [39] algorithms.2
Another practical issue regarding registration is the selection of feature-based, intensity-based or hybrid
registration algorithms. In particular, when feature-based algorithms are used, the accuracy of the features
themselves must be considered in addition to the accuracy of the registration algorithm. One must
2
We note that these non-global processes are ordinarily not referred to as “registration” in the literature.
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consider the possibility of localized registration errors that can result in false change detection, even
when average/global error measures appear to be modest.
Several researchers have studied the effects of registration errors on change detection, especially in the
context of remote sensing [40], [41]. Dai and Khorram [42] progressively translated one multispectral
image against itself and analyzed the sensitivity of a difference-based change detection algorithm (see
Section IV). They concluded that highly accurate registration was required to obtain good change detection
results (e.g. one-fifth-pixel registration accuracy to obtain change detection error of less than 10%).
Bruzzone and Cossu [43] did a similar experiment on two-channel images, and obtained a nonparametric
density estimate of registration noise over the space of change vectors. They then developed a changedetection strategy that incorporated this a priori probability that change at a pixel was due to registration
noise.
B. Radiometric/Intensity Adjustments
In several change detection scenarios (e.g. surveillance), intensity variations in images caused by
changes in the strength or position of light sources in the scene are considered unimportant. Even in cases
where there are no actual light sources involved, there may be physical effects with similar consequences
on the image (e.g. calibration errors and variations in imaging system components in magnetic resonance
and computed tomography imagery). In this section, we describe several techniques that attempt to precompensate for illumination variations between images. Alternately, some change detection algorithms
are designed to cope with illumination variation without explicit pre-processing; see Section VII.
1) Intensity Normalization: Some of the earliest attempts at illumination-invariant change detection
used intensity normalization [44], [45], and it is still used [42]. The pixel intensity values in one image
are normalized to have the same mean and variance as those in another, i.e.,
σ1
{I2 (x) − µ2 } + µ1 ,
I˜2 (x) =
σ2
(1)
where I˜2 is the normalized second image and µi , σi are the mean and standard deviation of the intensity
values of Ii , respectively. Alternatively, both images can be normalized to have zero mean and unit
variance. This allows the use of decision thresholds that are independent of the original intensity values
of the images.
Instead of applying the normalization (1) to each pixel using the global statistics µi , σi , the images
can be divided into corresponding disjoint blocks, and the normalization independently performed using
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the local statistics of each block. This can achieve better local performance at the expense of introducing
blocking artifacts.
2) Homomorphic Filtering: For images of scenes containing Lambertian surfaces, the observed image
intensity at a pixel x can be modeled as the product of two components: the illumination Il (x) from the
light source(s) in the scene and the reflectance Io (x) of the object surface to which x belongs:
I(x) = Il (x)Io (x).
(2)
This is called the shading model [46]. Only the reflectance component Io (x) contains information about
the objects in the scene. A type of illumination-invariant change detection can hence be performed by
first filtering out the illumination component from the image. If the illumination due to the light sources
Il (x) has lower spatial frequency content than the reflectance component Io (x), a homomorphic filter
can be used to separate the two components of the intensity signal. That is, logarithms are taken on both
sides of (2) to obtain
ln I(x) = ln Il (x) + ln Io (x).
Since the lower frequency component ln Il (x) is now additive, it can be separated using a high pass
filter. The reflectance component can thus be estimated as
I˜o (x) = exp{F (ln I(x))},
where F (·) is a high pass filter. The reflectance component can be provided as input to the decision rule
step of a change detection process (see, e.g. [47], [48]).
3) Illumination Modeling: Modeling and compensating for local radiometric variation that deviates
from the Lambertian assumption is necessary in several applications (e.g. underwater imagery [49]). For
example, Can and Singh [50] modeled the illumination component as a piecewise polynomial function.
Negahdaripour [51] proposed a generic linear model for radiometric variation between images of the
same scene:
I2 (x, y) = M (x, y)I1 (x, y) + A(x, y),
where M (x, y) and A(x, y) are piecewise smooth functions with discontinuities near region boundaries.
Hager and Belhumeur [52] used principal component analysis (PCA) to extract a set of basis images
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Bk (x, y) that represent the views of a scene under all possible lighting conditions, so that after registration,
I2 (x, y) = I1 (x, y) +
K
X
αk Bk (x, y).
k=1
In our experience, these sophisticated models of illumination compensation are not commonly used in the
context of change detection. However, Bromiley et al. [53] proposed several ways that the scattergram,
or joint histogram of image intensities, could be used to estimate and remove a global non-parametric
illumination model from an image pair prior to simple differencing. The idea is related to mutual
information measures used for image registration [54].
4) Linear Transformations of Intensity: In the remote sensing community, it is common to transform
a multispectral image into a different intensity space before proceeding to change detection. For example,
Jensen [55] and Niemeyer et al. [56] discussed applying PCA to the set of all bands from two multispectral
images. The principal component images corresponding to large eigenvalues are assumed to reflect the
unchanged part of the images, and those corresponding to smaller eigenvalues to changed parts of the
images. The difficulty with this approach is determining which of the principal components represent
change without visual inspection. Alternately, one can apply PCA to difference images as in Gong [57],
in which case the first one or two principal component images are assumed to represent changed regions.
Another linear transformation for change detection in remote sensing applications using Landsat data
is the Kauth-Thomas or “Tasseled Cap” transform [58]. The transformed intensity axes are linear combinations of the original Landsat bands and have semantic descriptions including “soil brightness”, “green
vegetation”, and “yellow stuff”. Collins and Woodcock [5] compared different linear transformations of
multispectral intensities for mapping forest changes using Landsat data. Morisette and Khorram [59]
discussed how both an optimal combination of multispectral bands and corresponding decision threshold
to discriminate change could be estimated using a neural network from training data regions labeled as
change/no-change.
G
B
In surveillance applications, Elgammal et al. [60] observed that the coordinates ( R+G+B
, R+G+B
, R+
G + B) are more effective than RGB coordinates for suppressing unwanted changes due to shadows of
objects.
5) Sudden Changes in Illumination: Xie et al. [61] observed that under the Phong shading model with
slowly spatially varying illumination, the sign of the difference between corresponding pixel measurements
is invariant to sudden changes in illumination. They used this result to create a change detection algorithm
that is able to discriminate between “uninteresting” changes caused by a sudden change in illumination
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(e.g. turning on a light switch) and “interesting” changes caused by object motion. See also the background
modeling techniques discussed in Section VIII.
Watanabe et al. [21] discussed an interesting radiometric pre-processing step specifically for change
detection applied to overhead imagery of buildings. Using the known position of the sun and a method
for fitting building models to images, they were able to remove strong shadows of buildings due to direct
light from the sun, prior to applying a change detection algorithm.
6) Speckle Noise: Speckle is an important type of noise-like artifact found in coherent imagery such as
synthetic aperture radar and ultrasound. There is a sizable body of research (too large to summarize here)
on modeling and suppression of speckle (for example, see [62], [63], [64] and the survey by Touzi [65]).
Common approaches to suppressing false changes due to speckle include frame averaging (assuming
speckle is uncorrelated between successive images), local spatial averaging (albeit at the expense of
spatial resolution), thresholding, and statistical model-based and/or multi-scale filtering.
IV. S IMPLE D IFFERENCING
Early change detection methods were based on the signed difference image D(x) = I2 (x)−I1 (x), and
such approaches are still widespread. The most obvious algorithm is to simply threshold the difference
image. That is, the change mask B(x) is generated according to the following decision rule:

 1 if |D(x)| > τ
B(x) =
 0 otherwise,
We denote this algorithm as “simple differencing”. Often the threshold τ is chosen empirically. Rosin [66],
[67] surveyed and reported experiments on many different criteria for choosing τ . Smits and Annoni [68]
discussed how the threshold can be chosen to achieve application-specific requirements for false alarms
and misses (i.e. the choice of point on a receiver-operating-characteristics curve [69]; see Section X).
There are several methods that are closely related to simple differencing. For example, in change vector
analysis (CVA) [4], [70], [71], [72], often used for multispectral images, a feature vector is generated for
each pixel in the image, considering several spectral channels. The modulus of the difference between the
two feature vectors at each pixel gives the values of the “difference image”.3 Image ratioing is another
related technique that uses the ratio, instead of the difference, between the pixel intensities of the two
images [19]. DiStefano et al. [73] performed simple differencing on subsampled gradient images. Tests
3
In some cases, the direction of this vector can also be used to discriminate between different types of changes [43].
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that have similar functional forms but are more well-defended from a theoretical perspective are discussed
further in Sections VI and VII below.
However the threshold is chosen, simple differencing with a global threshold is unlikely to outperform
the more advanced algorithms discussed below in any real-world application. This technique is sensitive
to noise and variations in illumination, and does not consider local consistency properties of the change
mask.
V. S IGNIFICANCE AND H YPOTHESIS T ESTS
The decision rule in many change detection algorithms is cast as a statistical hypothesis test. The
decision as to whether or not a change has occurred at a given pixel x corresponds to choosing one of
two competing hypotheses: the null hypothesis H0 or the alternative hypothesis H1 , corresponding to
no-change and change decisions, respectively.
The image pair (I1 (x), I2 (x)) is viewed as a random vector. Knowledge of the conditional joint
probability density functions (pdfs) p(I1 (x), I2 (x)|H0 ) and p(I1 (x), I2 (x)|H1 ) allows us to choose the
hypothesis that best describes the intensity change at x using the classical framework of hypothesis testing
[69], [74].
Since interesting changes are often associated with localized groups of pixels, it is common for the
change decision at a given pixel x to be based on a small block of pixels in the neighborhood of x in
each of the two images (such approaches are also called “geo-pixel” methods). Alternately, decisions can
be made independently at each pixel and then processed to enforce smooth regions in the change mask;
see Section IX.
We denote a block of pixels centered at x by Ωx . The pixel values in the block are denoted:
ˆ
I(x)
= {I(y)|y ∈ Ωx }.
ˆ
Note that I(x)
is an ordered set to ensure that corresponding pixels in the image pair are matched
correctly. We assume that the block contains N pixels. There are two methods for dealing with blocks,
as illustrated in Figure 3. One option is to apply the decision reached at x to all the pixels in the block
Ωx (Figure 3a), in which case the blocks do not overlap, the change mask is coarse, and block artifacts
are likely. The other option is to apply the decision only to pixel x (Figure 3b), in which case the blocks
can overlap and there are fewer artifacts; however, this option is computationally more expensive.
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Ω1
Ω2
x1
x2
Ω1
x1
x2
(a)
Ω2
(b)
Fig. 3. The two block-based approaches: (a) The decision is applied to the entire block of pixels Ωx , (b) The decision is
applied only to the center pixel x. In case (a), the blocks Ωx do not overlap, but in case (b) they do. Approach (b) is generally
preferred.
A. Significance Tests
Characterizing the null hypothesis H0 is usually straightforward, since in the absence of any change,
the difference between image intensities can be assumed to be due to noise alone. A significance test on
the difference image can be performed to assess how well the null hypothesis describes the observations,
and this hypothesis is correspondingly accepted or rejected. The test is carried out as below:
H0
S(x) = p(D(x))|H0 ) ≷ τ.
H1
The threshold τ can be computed to produce a desired false alarm rate α.
Aach et al. [75], [76] modeled the observation D(x) under the null hypothesis as a Gaussian random
variable with zero mean and variance σ02 . The unknown parameter σ02 can be estimated offline from the
imaging system, or recursively from unchanged regions in an image sequence [77]. In the Gaussian case,
this results in the conditional pdf
D2 (x)
exp −
.
p(D(x)|H0 ) = p
2σ02
2πσ02
1
(3)
They also considered a Laplacian noise model that is similar.
The extension to a block-based formulation is straightforward. Though there are obvious statistical
dependencies within a block, the observations for each pixel in a block are typically assumed to be
independent and identically distributed (iid). For example, the block-based version of the significance
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test (3) uses the test statistic
p(D̂(x)|H0 ) =
2πσ02
!N
1
p
2πσ02
( P
exp −
p
=
Here G(x) =
!N
1
2
y∈Ωx D (y)
)
2σ02
G(x)
.
exp −
2
P
2 (y) /σ 2 , which has a χ2 pdf with N degrees of freedom. Tables for the
D
0
y∈Ωx
χ2 distribution can be used to compute the decision threshold for a desired false alarm rate. A similar
computation can be performed when each observation is modelled as an independent Laplacian random
variable.
B. Likelihood Ratio Tests
Characterizing the alternative (change) hypothesis H1 is more challenging, since the observations
consist of change components that are not known a priori or cannot easily be described by parametric
distributions. When both conditional pdfs are known, a likelihood ratio can be formed as:
L(x) =
p(D(x)|H1 )
.
p(D(x)|H0 )
This ratio is compared to a threshold τ defined as:
τ=
P (H0 )(C10 − C00 )
,
P (H1 )(C01 − C11 )
where P (Hi ) is the a priori probability of hypothesis Hi , and Cij is the cost associated with making a
decision in favor of hypothesis Hi when Hj is true. In particular, C10 is the cost associated with “false
alarms” and C01 is the cost associated with “misses”. If the likelihood ratio at x exceeds τ , a decision is
made in favor of hypothesis H1 ; otherwise, a decision is made in favor of hypothesis H0 . This procedure
yields the minimum Bayes risk by choosing the hypothesis that has the maximum a posteriori probability
of having occurred given the observations (I1 (x), I2 (x)).
Aach et al. [75], [76] characterized both hypotheses by modelling the observations comprising D̂(x)
under Hi as iid zero-mean Gaussian random variables with variance σi2 . In this case, the block-based
likelihood ratio is given by:
p(D̂(x)|H1 )
p(D̂(x)|H0 )
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σ0N
σ1N



 X
1
1
exp −
D2 (y)
− 2
.
2

2σ1
2σ0 
y∈Ωx
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The parameters σ02 and σ12 were estimated from unchanged (i.e. very small D(x)) and changed (i.e.
very large D(x)) regions of the difference image respectively. As before, they also considered a similar
Laplacian noise model. Rignot and van Zyl [78] described hypothesis tests on the difference and ratio
images from SAR data assuming the true and observed intensities were related by a gamma distribution.
Bruzzone and Prieto [70] noted that while the variances estimated as above may serve as good initial
guesses, using them in a decision rule may result in a false alarm rate different from the desired value.
They proposed an automatic change detection technique that estimates the parameters of the mixture
distribution p(D) consisting of all pixels in the difference image. The mixture distribution p(D) can be
written as:
p(D(x)) = p(D(x)|H0 )P (H0 ) + p(D(x)|H1 )P (H1 ).
The means and variances of the class conditional distributions p(D(x)|Hi ) are estimated using an
expectation-maximization (EM) algorithm [79] initialized in a similar way to the algorithm of Aach
et al. In [4], Bruzzone and Prieto proposed a more general algorithm where the difference image is
initially modelled as a mixture of two nonparametric distributions obtained by the reduced Parzen estimate
procedure [80]. These nonparametric estimates are iteratively improved using an EM algorithm. We
note that these methods can be viewed as a precursor to the more sophisticated background modeling
approaches described in Section VIII.
C. Probabilistic Mixture Models
This category is best illustrated by Black et al. [81], who described an innovative approach to estimating
changes. Instead of classifying the pixels as change/no-change as above, or as object/background as in
Section VIII, they are softly classified into mixture components corresponding to different generative
models of change. These models included (1) parametric object or camera motion, (2) illumination
phenomena, (3) specular reflections and (4) “iconic/pictorial changes” in objects such as an eye blinking
or a nonrigid object deforming (using a generative model learned from training data). A fifth outlier
class collects pixels poorly explained by any of the four generative models. The algorithm operates on
the optical flow field between an image pair, and uses the EM algorithm to perform a soft assignment
of each vector in the flow field to the various classes. The approach is notable in that image registration
and illumination variation parameters are estimated in-line with the changes, instead of beforehand. This
approach is quite powerful, capturing multiple object motions, shadows, specularities, and deformable
models in a single framework.
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D. Minimum Description Length
To conclude this section, we note that Leclerc et al. [82] proposed a change detection algorithm based
on a concept called “self-consistency” between viewpoints of a scene. The algorithm involves both raw
images and three-dimensional terrain models, so it is not directly comparable to the methods surveyed
above; the main goal of the work is to provide a framework for measuring the performance of stereo
algorithms. However, a notable feature of this approach is its use of the minimum description length
(MDL) model selection principle [83] to classify unchanged and changed regions, as opposed to the
Bayesian approaches discussed earlier. The MDL principle selects the hypothesis Hi that more concisely
describes (i.e. using a smaller number of bits) the observed pair of images. We believe MDL-based
model selection approaches have great potential for “standard” image change-detection problems, and
are worthy of further study.
VI. P REDICTIVE M ODELS
More sophisticated change detection algorithms result from exploiting the close relationships between
nearby pixels both in space and time (when an image sequence is available).
A. Spatial Models
A classical approach to change detection is to fit the intensity values of each block to a polynomial
function of the pixel coordinates x. In two dimensions, this corresponds to
Iˆk (x, y) =
p X
p−i
X
k i j
βij
xy ,
(4)
i=0 j=0
where p is the order of the polynomial model. Hsu et al. [84] discussed generalized likelihood ratio
tests using a constant, linear, or quadratic model for image blocks. The null hypothesis in the test is that
0 , whereas the
corresponding blocks in the two images are best fit by the same polynomial coefficients βij
alternative hypothesis is that the corresponding blocks are best fit by different polynomial coefficients
1 , β 2 ). In each case, the various model parameters β k are obtained by a least-squares fit to the intensity
(βij
ij
ij
values in one or both corresponding image blocks. The likelihood ratio is obtained based on derivations
by Yakimovsky [85] and is expressed as:
F (x) =
σ02N
,
σ1N σ2N
where N is the number of pixels in the block, σ12 is the variance of the residuals from the polynomial fit
to the block in I1 , σ22 is the variance of the residuals from the polynomial fit to the block in I2 , and σ02
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is the variance of the residuals from the polynomial fit to both blocks simultaneously. The threshold in
the generalized likelihood ratio test can be obtained using the t-test (for a constant model) or the F -test
(for linear and quadratic models). Hsu et al. used these three models to detect changes between a pair of
surveillance images and concluded that the quadratic model outperformed the other two models, yielding
similar change detection results but with higher confidence.
Skifstad and Jain [86] suggested an extension of Hsu’s intensity modelling technique to make it
illumination-invariant. The authors suggested a test statistic that involved spatial partial derivatives of
Hsu’s quadratic model, given by:
T (x) =
X
y∈Ωx
!
∂ Iˆ1
∂ Iˆ2
∂ Iˆ1
∂ Iˆ2
(y) −
(y) +
(y) −
(y) .
∂x
∂x
∂y
∂y
(5)
Here, the intensity values Iˆj (x) are modelled as quadratic functions of the pixel coordinates (i.e. (4) with
p = 2). The test statistic is compared to an empirical threshold to classify pixels as changed or unchanged.
Since the test statistic only involves partial derivatives, it is independent of linear variations in intensity.
As with homomorphic filtering, the implicit assumption is that illumination variations occur at lower
spatial frequencies than changes in the objects. It is also assumed that true changes in image objects will
be reflected by different coefficients in the quadratic terms that are preserved by the derivative.
B. Temporal Models
When the change detection problem occurs in the context of an image sequence, it is natural to exploit
the temporal consistency of pixels in the same location at different times.
Many authors have modeled pixel intensities over time as an autoregressive (AR) process. An early
reference is Elfishawy et al. [87]. More recently, Jain and Chau [88] assumed each pixel was identically
and independently distributed according to the same (time-varying) Gaussian distribution related to the
past by the same (time-varying) AR(1) coefficient. Under these assumptions, they derived maximum
likelihood estimates of the mean, variance, and correlation coefficient at each point in time, and used
these in likelihood ratio tests where the null (no-change) hypothesis is that the image intensities are
dependent, and the alternate (change) hypothesis is that the image intensities are independent. (This is
similar to Yakimovsky’s hypothesis test above.)
Similarly, Toyama et al. [89] described an algorithm called Wallflower that used a Wiener filter to
predict a pixel’s current value from a linear combination of its k previous values. Pixels whose prediction
error is several times worse than the expected error are classified as changed pixels. The predictive
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coefficients are adpatively updated at each frame. This can also be thought of as a background estimation
algorithm; see Section VIII. The Wallflower algorithm also tries to correctly classify the interiors of
homogeneously colored, moving objects by determining the histogram of connected components of change
pixels and adding pixels to the change mask based on distance and color similarity. Morisette and
Khorram’s work [59], discussed in Section III-B.4, can be viewed as a supervised method to determine
an optimal linear predictor.
Carlotto [90] claimed that linear models perform poorly, and suggested a nonlinear dependence to model
the relationship between two images in a sequence Ii (x) and Ij (x) under the no-change hypothesis. The
optimal nonlinear function is simply fij , the conditional expected value of the intensity Ii (x) given Ij (x).
For an N -image sequence, there are N (N − 1)/2 total residual error images:
ij (x, y) = [Ii (x, y) − fij (Ij (x))] − [Ij (x, y) − fji (Ii (x))].
These images are then thresholded to produce binary change masks. Carlotto went on to detect specific
temporal patterns of change by matching the string of N binary change decisions at a pixel with a desired
input pattern.
Clifton [91] used an adaptive neural network to identify small-scale changes from a sequence of
overhead multispectral imagery. This can be viewed as an unsupervised method for learning the parameters
of a nonlinear predictor. Pixels for which the predictor performs poorly are classified as changed. The
goal is to distinguish “unusual” changes from “expected” changes, but this terminology is somewhat
vague does not seem to correspond directly to the notions of “foreground” and “background” in Section
VIII.
VII. T HE S HADING M ODEL
Several change detection techniques are based on the shading model for the intensity at a pixel as
described in Section III-B.2 to produce an algorithm that is said to be illumination-invariant. Such
algorithms generally compare the ratio of image intensities
R(x) =
I2 (x)
.
I1 (x)
to a threshold determined empirically. We now show the rationale for this approach.
Assuming shading models for the intensities I1 (x) and I2 (x), we can write I1 (x) = Il1 (x)Io1 (x) and
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I2 (x) = Il2 (x)Io2 (x), which implies
I2 (x)
Il2 (x)Io2 (x)
=
.
I1 (x)
Il1 (x)Io1 (x)
(6)
Since the reflectance component Ioi (x) depends only on the intrinsic properties of the object surface
imaged at x, Io1 (x) = Io2 (x) in the absence of a change. This observation simplifies (6) to:
I2 (x)
Il2 (x)
=
.
I1 (x)
Il1 (x)
Hence, if the illuminations Il1 and Il2 in each image are approximated as constant within a block Ωx ,
the ratio of intensities I2 (x)/I1 (x) remains constant under the null hypothesis H0 . This justifies a null
hypothesis that assumes linear dependence between vectors of corresponding pixel intensities, giving rise
to the test statistic R(x).
Skifstad and Jain [86] suggested the following method to assess the linear dependence between two
blocks of pixel values Iˆ1 (x) and Iˆ2 (x): construct
η(x) =
1 X
(R(x) − µx )2 ,
N
(7)
y∈Ωx
where µx is given by:
µx =
1 X
R(x).
N
y∈Ωx
When η(x) exceeds a threshold, a decision is made in favor of a change. The linear dependence
detector (LDD) proposed by Durucan and Ebrahimi [92], [93] is closely related to the shading model in
both theory and implementation, mainly differing in the form of the linear dependence test (e.g. using
determinants of Wronskian or Grammian matrices [94]).
Mester, Aach and others [48], [95] criticized the test criterion (7) as ad hoc, and expressed the
linear dependence model using a different hypothesis test. Under the null hypothesis H0 , each image is
assumed to be a function of a noise-free underlying image I(x). The vectors of image intensities from
corresponding N -pixel blocks centered at x under the null hypothesis H0 are expressed as:
ˆ
Iˆ1 (x) = I(x)
+ δ1 ;
ˆ
Iˆ2 (x) = k I(x)
+ δ2 .
Here, k is an unknown scaling constant representing the illumination, and δ1 , δ2 are two realizations of a
noise block in which each element is iid N (0, σn2 ). The projection of Iˆ2 (x) onto the subspace orthogonal
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to Iˆ1 (x) is given by:
Ô(x) = Iˆ2 (x) −
Iˆ1 (x)T Iˆ2 (x)
kIˆ1 (x)k2
!
Iˆ1 (x).
This is zero if and only if Iˆ1 (x) and Iˆ2 (x) are linearly dependent. The authors showed that in an
appropriate basis, the joint pdf of the projection Ô(x) under the null hypothesis H0 is approximately a
χ2 distribution with N − 1 degrees of freedom, and used this result both for significance and likelihood
ratio tests.
Li and Leung [96] also proposed a change detection algorithm involving the shading model, using a
weighted combination of the intensity difference and a texture difference measure involving the intensity
ratio. The texture information is assumed to be less sensitive to illumination variations than the raw
intensity difference. However, in homogeneous regions, the texture information becomes less valid and
more weight is given to the intensity difference.
Liu et al. [97] suggested another change detection scheme that uses a significance test based on the
shading model. The authors compared circular shift moments to detect changes instead of intensity ratios.
These moments are designed to represent the reflectance component of the image intensity, regardless
of illumination. The authors claimed that circular shift moments capture image object details better than
the second-order statistics used in (7), and derived a set of iterative formulas to calculate the moments
efficiently.
VIII. BACKGROUND M ODELING
In the context of surveillance applications, change detection is closely related to the well-studied
problem of background modeling. The goal is to determine which pixels belong to the background,
often prior to classifying the remaining foreground pixels (i.e. changed pixels) into different object
classes.4 Here, the change detection problem is qualitatively much different than in typical remote sensing
applications. A large amount of frame-rate video data is available, and the images between which it is
desired to detect changes are spaced apart by seconds rather than months. The entire image sequence is
used as the basis for making decisions about change, as opposed to a single image pair. Furthermore,
there is frequently an important semantic interpretation to the change that can be exploited (e.g. a person
enters a room, a delivery truck drives down a street).
4
It is sometimes difficult to rigorously define what is meant by these terms. For example, a person may walk into a room and
fall asleep in a chair. At what point does the motionless person transition from foreground to background?
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Several approaches to background modeling and subtraction were recently collected in a special issue
of IEEE PAMI on video surveillance [1]. The reader is also referred to the results from the DARPA
VSAM (Visual Surveillance and Monitoring) project at Carnegie Mellon University [98] and elsewhere.
Most background modeling approaches assume the camera is fixed, meaning the images are already
registered (though see the last paragraph in this section). Toyama et al. [89] gave a good overview of
several background maintenance algorithms and provided a comparative example.
Many approaches fall into the mixture-of-Gaussians category: the probability of observing the intensity
It (x, y) at location (x, y) and time t is the weighted sum of K Gaussian distributions:
pIt (x,y) (C) =
K
X
wti (x, y)
i=1
k/2
· (2π)
|Σit (x, y)|−1/2 exp
1
−1
i
T i
i
− (C − µt (x, y)) Σt (x, y) (C − µt (x, y)) .
2
At each point in time, the probability that a pixel’s intensity is due to each of the mixtures is estimated,
and the most likely mixture defines the pixel’s class. The mean and covariance of each background pixel
are usually initialized by observing several seconds of video of an empty scene. We briefly review several
such techniques here.
Several researchers [99], [100], [101] have described adaptive background subtraction techniques in
which a single Gaussian density is used to model the background. Foreground pixels are determined as
those that lie some number of standard deviations from the mean background model, and are clustered
into objects. The mean and variance of the background are updated using simple adaptive filters to
accommodate changes in lighting or objects that become part of the background. Collins et al. [98]
augmented this approach with a second level of analysis to determine whether a pixel is due to a moving
object, a stationary object, or an ambient illumination change. Gibbins et al. [102] had a similar goal of
detecting suspicious changes in the background for video surveillance applications (e.g. a suitcase left in
a bus station).
Wren et al. [3] proposed a method for tracking people and interpreting their behavior called Pfinder that
included a background estimation module. This included not only a single Gaussian distribution for the
background model at each pixel, but also a variable number of Gaussian distributions corresponding to
different foreground object models. Pixels are classified as background or object by finding the model with
the least Mahalanobis distance. Dynamic “blob” models for a person’s head, hands, torso, etc. are then fit
to the foreground pixels for each object, and the statistics for each object are updated. Hötter et al. [103]
described a similar approach for generic objects. Paragios and Tziritas [104] proposed an approach for
finding moving objects in image sequences that further constrained the background/foreground map to
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be a Markov Random Field (see Section IX below).
Stauffer and Grimson [2] extended the multiple object model above to also allow the background model
to be a mixture of several Gaussians. The idea is to correctly classify dynamic background pixels, such
as the swaying branches of a tree or the ripples of water on a lake. Every pixel value is compared against
the existing set of models at that location to find a match. The parameters for the matched model are
updated based on a learning factor. If there is no match, the least-likely model is discarded and replaced
by a new Gaussian with statistics initialized by the current pixel value. The models that account for some
predefined fraction of the recent data are deemed “background” and the rest “foreground”. There are
additional steps to cluster and classify foreground pixels into semantic objects and track the objects over
time.
The Wallflower algorithm by Toyama et al. [89] described in Section VI also includes a frame-level
background maintenance algorithm. The intent is to cope with situations where the intensities of most
pixels change simultaneously, e.g. as the result of turning on a light. A “representative set” of background
models is learned via k-means clustering during a training phase. The best background model is chosen
on-line as the one that produces the lowest number of foreground pixels. Hidden Markov Models can be
used to further constrain the transitions between different models at each pixel [105], [106].
Haritaoglu et al. [107] described a background estimation algorithm as part of their W 4 tracking
system. Instead of modeling each pixel’s intensity by a Gaussian, they analyzed a video segment of the
empty background to determine the minimum (m) and maximum (M ) intensity values as well as the
largest interframe difference (δ ). If the observed pixel is more than δ levels away from either m or M ,
it is considered foreground.
Instead of using Gaussian densities, Elgammal et al. [60] used a non-parametric kernel density estimate
for the intensity of the background and each foreground object. That is,
pIt (x,y) (C) =
N
1 X
Kσ (C − It−i (x, y)),
N
i=1
where Kσ is a kernel function with bandwidth σ . Pixel intensities that are unlikely based on the instantaneous density estimate are classified as foreground. An additional step that allows for small deviations
in object position (i.e. by comparing It (x, y) against the learned densities in a small neighborhood of
(x, y)) is used to suppress false alarms.
Ivanov et al. [108] described a method for background subtraction using multiple fixed cameras. A
disparity map of the empty background is interactively built off-line. On-line, foreground objects are
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detected as regions where pixels put into correspondence by the learned disparity map have inconsistent
intensities. Latecki et al. [109] discussed a method for semantic change detection in video sequences
(e.g. detecting whether an object enters the frame) using a histogram-based approach that does not
identify which pixels in the image correspond to changes.
Ren et al. [110] extended a statistical background modeling technique to cope with a non-stationary
camera. The current image is registered to the estimated background image using an affine or projective
transformation. A mixture-of-Gaussians approach is then used to segment foreground objects from the
background. Collins et al. [98] also discussed a background subtraction routine for a panning and
tilting camera whereby the current image is registered using a projective transformation to one of many
background images collected off-line.
We stop at this point, though the discussion could range into many broad, widely studied computer
vision topics such as segmentation [111], [112], tracking [35], and layered motion estimation [113], [114].
IX. C HANGE M ASK C ONSISTENCY
The output of a change detection algorithm where decisions are made independently at each pixel will
generally be noisy, with isolated change pixels, holes in the middle of connected change components,
and jagged boundaries. Since changes in real image sequences often arise from the appearance or motion
of solid objects in a specific size range with continuous, differentiable boundaries, most change detection
algorithms try to conform the change mask to these expectations.
The simplest techniques simply postprocess the change mask with standard binary image processing
operations, such as median filters to remove small groups of pixels that differ from their neighbors’ labels
(salt and pepper noise) [115] or morphological operations [116] to smooth object boundaries.
Such approaches are less optimal than those that enforce spatial priors in the process of constructing
the change mask. For example, Yamamoto [117] described a method in which an image sequence
is collected into a three-dimensional stack, and regions of homogeneous intensity are unsupervisedly
clustered. Changes are detected at region boundaries perpendicular to the temporal axis.
Most attempts to enforce consistency in change regions apply concepts from Markov-Gibbs random
fields (MRFs), which are widely used in image segmentation. A standard technique is to apply a Bayesian
approach where the prior probability of a given change mask is
P (B) =
1
exp−E(B) ,
Z
where Z is a normalization constant and E(B) is an energy term that is low when the regions in B
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exhibit smooth boundaries and high otherwise. For example, Aach et al. chose E(B) to be proportional
to the number of label changes between 4- and 8-connected neighbors in B . They discussed both an
iterative method for a still image pair [75] and a non-iterative method for an image sequence [76] for
Bayesian change detection using such MRF priors. Bruzzone and Prieto [4], [70] used an MRF approach
with a similar energy function. They maximized the a posteriori probability of the change mask using
Besag’s iterated conditional modes algorithm [118].
Instead of using a prior that influences the final change mask to be close to an MRF, Kasetkasem
and Varshney [119] explicitly constrained the output change mask to be a valid MRF. They proposed
a simulated annealing algorithm [120] to search for the globally optimal change mask (i.e. the MAP
estimate). However, they assumed that the inputs themselves were MRFs, which may be a reasonable
assumption in terrain imagery, but less so for indoor surveillance imagery.
Finally, we note that some authors [103], [121] have taken an object-oriented approach to change
detection, in which pixels are unsupervisedly clustered into homogeneously-textured objects before applying change detection algorithms. More generally, as stated in the introduction, there is a wide range of
algorithms that use prior models for expected objects (e.g. buildings, cars, people) to constrain the form
of the objects in the detected change mask. Such scene understanding methods can be quite powerful,
but are more accurately characterized as model-based segmentation and tracking algorithms than change
detection.
X. P RINCIPLES FOR P ERFORMANCE E VALUATION AND C OMPARISON
The performance of a change detection algorithm can be evaluated visually and quantitatively based
on application needs. Components of change detection algorithms can also be evaluated individually. For
example, Toyama et al. [89] gave a good overview of several background maintenance algorithms and
provided a comparative example.
The most reliable approach for qualitative/visual evaluation is to display a flicker animation [122], a
short movie file containing a registered pair of images (I1 (x), I2 (x)) that are played in rapid succession at
intervals of about a second each. In the absence of change, one perceives a steady image. When changes
are present, the changed regions appear to flicker. The estimated change mask can also be superimposed
on either image (e.g. as a semitransparent overlay, with different colors for different types of change).
Quantitative evaluation is more challenging, primarily due to the difficulty of establishing a valid
“ground truth,” or “gold standard.” This is the process of establishing the “correct answer” for what exactly
the algorithm is expected to produce. A secondary challenge with quantitative validation is establishing
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the relative importance of different types of errors.
Arriving at the ground truth is an image analysis problem that is known to be difficult and timeconsuming [123]. Usually, the most appropriate source for ground truth data is an expert human observer.
For example, a radiologist would be an appropriate expert human observer for algorithms performing
change detection of X-ray images. As noted by Tan et al. [124], multiple expert human observers can
differ considerably even when they are provided with a common set of guidelines. The same human
observer can even generate different segmentations for the same data at two different times.
With the above-noted variability in mind, the algorithm designer may be faced with the need to establish
ground truth from multiple conflicting observers [125]. A conservative method is to compare the algorithm
against the set intersection of all human observers’ segmentations. In other words, a change detected by
the algorithm would be considered valid if every human observer considers it a change. A method that is
less susceptible to a single overly conservative observer is to use a majority rule. The least conservative
approach is to compare the algorithm against the set union of all human observers’ results. Finally, it
is often possible to bring the observers together after an initial blind markup to develop a consensus
markup.
Once a ground truth has been established, there are several standard methods for comparing the ground
truth to a candidate binary change mask. The following quantities are generally involved:
•
True positives (TP): the number of change pixels correctly detected;
•
False positives (FP): the number of no-change pixels incorrectly detected as change (also known as
false alarms);
•
True negatives (TN): the number of no-change pixels correctly detected; and
•
False negatives (FN): the number of change pixels incorrectly detected as no-change (also known
as misses).
Rosin [67] described three methods for quantifying a classifier’s performance:
T P +T N
T P +F P +T N +F N ;
•
The Percentage Correct Classification P CC =
•
The Jaccard coefficient JC = T P +FT PP +F N ; and
P
TN
The Yule coefficient Y C = T PT+F
+
−
1
.
P
T N +F N
•
For a classifier with tunable parameters, one can investigate the receiver-operating-characteristics (ROC)
curve that plots the detection probability versus the false alarm probablility to determine a desired level
of performance. However, since an ROC curve gives little understanding of the qualitative behavior of a
particular algorithm in different regions of the image pair, visual inspection of the change masks is still
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recommended.
Finally, we note that when there is an expected semantic interpretation of the changed pixels in a
given application (e.g. an intruder in surveillance imagery), the algorithm designer should incorporate
higher-level constraints that reflect the ability of a given algorithm to detect the “most important” changes,
instead of treating every pixel equally.
XI. C ONCLUSIONS AND D ISCUSSION
The two application domains that have seen the most activity in change detection algorithms are
remote sensing and video surveillance, and their approaches to the problem are often quite different. We
have attempted to survey the recent state of the art in image change detection without emphasizing a
particular application area. We hope that our classification of algorithms into a relatively small number
of categories will provide useful guidance to the algorithm designer. We note there are several software
packages that include some of the change detection algorithms discussed here (e.g. [126], [127]). In
particular, we have developed a companion website to this paper [128] that includes implementations,
results, and comparative analysis of several of the methods discussed above.
We have tried not to over-editorialize regarding the relative merits of the algorithms, leaving the reader
to decide which assumptions and constraints may be most relevant for his or her application. However,
our opinion is that two algorithms deserve special mention. Stauffer and Grimson’s background modeling
algorithm [2], covered in Section VIII, provides for multiple models of background appearance as well
as object appearance and motion. The algorithm by Black et al. [81], covered in Section V-C, provides
for multiple models of image change and requires no preprocessing to compensate for misregistration or
illumination variation. We expect that a combination of these approaches that uses soft assignment of
each pixel to an object class and one or more change models would produce a very general, powerful,
and theoretically well-justified change detection algorithm.
Despite the substantial amount of work in the field, change detection is still an active and interesting
area of research. We expect future algorithm developments to be fueled by increasingly more integrated
approaches combining elaborate models of change, implicit pre- and post-processing, robust statistics,
and global optimization methods. We also expect future developments to leverage progress in the related
areas of computer vision research (e.g. segmentation, tracking, motion estimation, structure-from-motion)
mentioned in the text. Finally, and perhaps most importantly, we expect a continued growth of societal
applications of change detection and interpretation in key areas such as biotechnology and geospatial
intelligence.
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XII. ACKNOWLEDGMENTS
Thanks to the anonymous reviewers and associate editors for their important comments that helped
improve the quality of this work. This work was supported in part by CenSSIS, the Center for Subsurface
Sensing and Imaging Systems, under the Engineering Research Centers Program of the National Science
Foundation (Award Number EEC-9986821). Thanks to Dr. A. Majerovics at the Center for Sight in
Albany, NY for the images in Figure 2.
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