Image Change Detection and Fusion Using MRF Models
289
total number of sites in the image. We plot the average detection, false alarm
and error rates in Fig. 12.4 for a quantitative comparison. We observe rapid
improvement (in accuracy) from 0 to 60 sweeps, with no further improvement
after around 80 sweeps. The detection rate increases from about 60 percent
to more than 90 percent and the average error rate decreases from around 35
percent to less than 5 percent.
We also compare the performance of our algorithm, with a variation ofBruzzone and Prieto's algorithm (abbreviated here as VBPA) described in Bruzzone
and Prieto (2000) and apply it to the same dataset. In their algorithm, the two
original images are replaced by their difference image as the input to the image
change detection algorithm. Similar to our approach, the spatial information
is characterized through an MRF model and the objective of their algorithm
is to determine the most likely change image given the difference image of
images at two different times. However, in Bruzzone and Prieto (2000), the
expectation maximization (EM) algorithm is used for the estimation of means
and variances associated with changed and unchanged regions, respectively.
However, in this experiment, since the ground truth is available to us, we calculate these statistics beforehand. Furthermore, we substitute the IeM algorithm
with the SA algorithm as the optimization algorithm since the SA algorithm is
optimum.
The resulting change image after 500 iterations from VBPA is shown in
Fig. 12.5a while Fig. 12.5b illustrates the change image presented in Fig. 12.3d
for comparison purposes. The error rate of VBPA is 7% while our algorithm
achieves the accuracy less than 1.5%. This is because VBPA uses the differ0.1
-+- Awrage Error Rate
~ Awrage Detection Rate
___ Awrage False Alann Rate
oL---~-=~~~~~~~~~~~~~~
o
20
40
60
80
100
120
140
Number of Iterations
Fig. 12.4. Performance of the MRF based leD algorithm in terms of average detection rate,
average false alarm rate and average error rate
289
total number of sites in the image. We plot the average detection, false alarm
and error rates in Fig. 12.4 for a quantitative comparison. We observe rapid
improvement (in accuracy) from 0 to 60 sweeps, with no further improvement
after around 80 sweeps. The detection rate increases from about 60 percent
to more than 90 percent and the average error rate decreases from around 35
percent to less than 5 percent.
We also compare the performance of our algorithm, with a variation ofBruzzone and Prieto's algorithm (abbreviated here as VBPA) described in Bruzzone
and Prieto (2000) and apply it to the same dataset. In their algorithm, the two
original images are replaced by their difference image as the input to the image
change detection algorithm. Similar to our approach, the spatial information
is characterized through an MRF model and the objective of their algorithm
is to determine the most likely change image given the difference image of
images at two different times. However, in Bruzzone and Prieto (2000), the
expectation maximization (EM) algorithm is used for the estimation of means
and variances associated with changed and unchanged regions, respectively.
However, in this experiment, since the ground truth is available to us, we calculate these statistics beforehand. Furthermore, we substitute the IeM algorithm
with the SA algorithm as the optimization algorithm since the SA algorithm is
optimum.
The resulting change image after 500 iterations from VBPA is shown in
Fig. 12.5a while Fig. 12.5b illustrates the change image presented in Fig. 12.3d
for comparison purposes. The error rate of VBPA is 7% while our algorithm
achieves the accuracy less than 1.5%. This is because VBPA uses the differ0.1
-+- Awrage Error Rate
~ Awrage Detection Rate
___ Awrage False Alann Rate
oL---~-=~~~~~~~~~~~~~~
o
20
40
60
80
100
120
140
Number of Iterations
Fig. 12.4. Performance of the MRF based leD algorithm in terms of average detection rate,
average false alarm rate and average error rate