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Table 2.1. Evaluation of different segmentation algorithms.
Lincoln image
Objective measure
described [174]
[58]
[35]
Number of regions N Ω
52
187
192
189
Correlation
0.9788
0.9879 0.9873 0.9908
Boundary contrast/pixel K b
0.204
0.202
0.200
0.194
K Ω
Region contrast/pixel
0.0294
0.0257 0.0258 0.0293
Biplane image
Number of regions N Ω
35
59
59
76
Correlation
0.9886
0.9892 0.9892 0.9884
K b
Boundary contrast/pixel
0.1499
0.1866 0.1866 0.1782
K Ω
Region contrast/pixel
0.0151
0.0144 0.0144 0.0150
Also, due to merging, the homogeneity of the segmented regions is expected
to increase. For good segmentation, this homogeneity should be very high.
This means that the average contrast K Ω within a region should be low. The
parameter region contrast/pixel, K Ω , shows that the average homogeneity is
reasonably good. Finally, the average boundary contrast K b , for both images
is very much comparable to all the cases. Different segmented images along
with the input are shown in Figures 2.3((a)-(e)) and 2.4((a)-(e)). For a better
display of segmented regions, all segmented images are stretched over a gray
scale of 0-255.
2.7 Some Justifications for Image Data Compression
The segmentation scheme, discussed in this chapter, is well suited for image
data compression. It exploits the benefit of the multilevel thresholding based
on conditional entropy, and partitions an image hierarchically. It also merges
small regions eciently.
The algorithm shows the possibility of globally approximating many seg-
mented regions or patches by a single polynomial function. In other words, one
can think to model different regions in an image by a single polynomial sur-
face. For this, all such regions should have similar graylevels. The segmented
regions to be approximated by a single polynomial can be extracted under
a single threshold. Thresholding based segmentation thus provides an advan-
tage over the split and merge technique of segmentation [133]. The latter does
not provide any group of patches or regions of similar gray levels located at
different places in an image at a time. It is, therefore, preferable to choose a
thresholding technique of segmentation for coding application because, under
such segmentation, a set of approximation parameters can represent many
regions. This set of parameters represents a single surface on which differ-
ent regions are situated at different locations. Hence, one need not code all
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