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12: Teerasit Kasetkasem, Pramod K. Varshney
basis of a quantitative measure. Then, a change is labeled, if this measure exceeds a predefined threshold, and no change is labeled, otherwise. Most of the
comparison techniques described in Singh (1989) only consider information
contained within a pixel even though intensity values of neighboring pixels
of images are known to have significant correlation. Also, changes are more
likely to occur in connected regions than at disjoint points. By using these
facts, a more accurate change detection algorithm can be developed. To accomplish this, an MRF model for images is employed here so that the statistical
correlation of intensity values among neighboring pixels can be exploited.
Bruzzone and Prieto (2000) and Wiemker (1997) have tried to employ the
MRF model for image change detection (ICD). In Bruzzone and Prieto (2000),
the authors subtracted one original image at one time, say tl> from another
original image at a different time, say t2, to obtain a difference image. A change
image was obtained directly from this difference image without using any
knowledge from original images. Two separate algorithms were developed
in their paper, namely distribution estimation and image change detection.
The first algorithm employs the expectation maximization (EM) algorithm to
estimate distributions of the difference image as a two-mode Gaussian mixture
made up of the conditional densities of changed and unchanged pixels. In the
second part, the MRF model was used to smoothen out the change image by
using the iterative conditional mode (ICM) algorithm. A similar approach can
be found in Wiemker (1997). This algorithm can be divided into two parts.
In the first part, a pixel-based algorithm such as image differencing or image
ratioing determines an initial change image that is further refined based on the
MRF model in the second part. Some information is lost while obtaining the
initial change image since the observed data is projected into a binary image
whose intensity values represent change or no change. We observe that studies
by Bruzzone and Prieto (2000) and Wiemker (1997) do not fully utilize all
the information contained in images, and moreover, the preservation of MRF
properties is not guaranteed. In Perez and Heitz (1996), the effect of image
transformations on images that can be modeled by MRFs is studied. It has
been shown that MRF properties may not hold after some transformations
such as resizing of an image and subtraction of one image from another. For
some specific transformations, MRF properties are preserved, but a new set of
potential functions must be obtained. Since a difference image can be looked
upon as a transformation, MRF modeling of a difference image in Bruzzone
and Prieto (2000) and initial change image in Wiemker (1997) may not be
valid. This provides the motivation for the development of an image change
detection (ICD) algorithm that uses additional information available from the
image and preserves MRF properties.
Here, we develop an ICD algorithm that consists of only one part. The observed images, modeled as MRFs, are directly processed by the MAP detector,
which searches for the global optimum. The detector based on the MAP criterion chooses the most likely change image among all possible change images
given the observed images. The resulting probability of error is minimum
among all other detectors (Trees 1968; Varshney 1997). The structure of the
MAP detector is based on statistical models. Therefore, the accuracy of the
12: Teerasit Kasetkasem, Pramod K. Varshney
basis of a quantitative measure. Then, a change is labeled, if this measure exceeds a predefined threshold, and no change is labeled, otherwise. Most of the
comparison techniques described in Singh (1989) only consider information
contained within a pixel even though intensity values of neighboring pixels
of images are known to have significant correlation. Also, changes are more
likely to occur in connected regions than at disjoint points. By using these
facts, a more accurate change detection algorithm can be developed. To accomplish this, an MRF model for images is employed here so that the statistical
correlation of intensity values among neighboring pixels can be exploited.
Bruzzone and Prieto (2000) and Wiemker (1997) have tried to employ the
MRF model for image change detection (ICD). In Bruzzone and Prieto (2000),
the authors subtracted one original image at one time, say tl> from another
original image at a different time, say t2, to obtain a difference image. A change
image was obtained directly from this difference image without using any
knowledge from original images. Two separate algorithms were developed
in their paper, namely distribution estimation and image change detection.
The first algorithm employs the expectation maximization (EM) algorithm to
estimate distributions of the difference image as a two-mode Gaussian mixture
made up of the conditional densities of changed and unchanged pixels. In the
second part, the MRF model was used to smoothen out the change image by
using the iterative conditional mode (ICM) algorithm. A similar approach can
be found in Wiemker (1997). This algorithm can be divided into two parts.
In the first part, a pixel-based algorithm such as image differencing or image
ratioing determines an initial change image that is further refined based on the
MRF model in the second part. Some information is lost while obtaining the
initial change image since the observed data is projected into a binary image
whose intensity values represent change or no change. We observe that studies
by Bruzzone and Prieto (2000) and Wiemker (1997) do not fully utilize all
the information contained in images, and moreover, the preservation of MRF
properties is not guaranteed. In Perez and Heitz (1996), the effect of image
transformations on images that can be modeled by MRFs is studied. It has
been shown that MRF properties may not hold after some transformations
such as resizing of an image and subtraction of one image from another. For
some specific transformations, MRF properties are preserved, but a new set of
potential functions must be obtained. Since a difference image can be looked
upon as a transformation, MRF modeling of a difference image in Bruzzone
and Prieto (2000) and initial change image in Wiemker (1997) may not be
valid. This provides the motivation for the development of an image change
detection (ICD) algorithm that uses additional information available from the
image and preserves MRF properties.
Here, we develop an ICD algorithm that consists of only one part. The observed images, modeled as MRFs, are directly processed by the MAP detector,
which searches for the global optimum. The detector based on the MAP criterion chooses the most likely change image among all possible change images
given the observed images. The resulting probability of error is minimum
among all other detectors (Trees 1968; Varshney 1997). The structure of the
MAP detector is based on statistical models. Therefore, the accuracy of the