Image Segmentation - Bezier and Splines in Image Processing and Machine Vision - page 50

L− 1 s

t ij

i = s +1 j =0

P 2 = . (2.33)

L− 1 L− 1 L− 1 s

t ij + t ij

i = s +1 j = s +1 i = s +1 j =0

p c ( s ), the conditional probability of transition across the boundary, is then
defined as

p c ( s )=( P 1 + P 2 ) / 2 . (2.34)
Expressions (2.32)-(2.34) suggest that a minimum of p c ( s ) will correspond to
a threshold such that most of the transitions are within the class and few are
across the boundary. Therefore, a set of minima of p c ( s ) would be obtained
corresponding to different thresholds in F.
Chanda et al. [35] also used the co-occurrence matrix for thresholding.
They defined an average contrast measure as

s L− 1 L− 1 s

j ) 2 j ) 2

t ij ∗ ( i − t ij ∗ ( i −

i =0 j = s +1 i = s +1 j =0

AV C ( s )= + . (2.35)

s L− 1 L− 1 s

t ij t ij

i =0 j = s +1 i = s +1 j =0

AVC(s) shows a set of maxima corresponding to the thresholds between var-
ious regions in F. In the computation of t ij , they considered only vertical
transitions in the downward direction.

2.6.1 Results and Discussion

Table 2.1 shows some objective measures, which we have already discussed
in the previous sections. Consider two 32-level images (Figure 2.3 and Figure
2.4), each of size 64 64. Figure 2.3(a) is the Lincoln image while Figure 2.4(a)

is the biplane image. Table 2.1 shows the values of different objective measures
in conjunction with the total number of regions or patches, say N Ω , produced
by different segmentation techniques for the images. Note that the number of
regions is an important parameter to justify goodness of segmentation. For
the Lincoln image, the number of segmented regions obtained by the discussed
algorithm is almost one-fourth of those obtained by the other algorithms and
for biplane image, the number of regions is roughly half of those produced by
the algorithms of Rosenfeld, Pal-Deravi, and Chanda et al., respectively.
Usually, with the increase in number of regions, correlation is expected to
increase. The segmentation of both Lincoln and biplane images supports this
fact. But even with a much smaller number of regions for both the images
produced by the proposed scheme, the correlation values are comparable to
those for the segmented images obtained from other algorithms. This indi-
cates successful merging of small regions to the proper neighboring regions.

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