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that across the boundary, i.e., MI > 1. A very simple measure of within
region interaction is the number of transitions within the region. Similarly,
the between region interaction can be defined as the number of transitions
across the border of the region. Thus, MI can be computed as
Number of transitions within a region
Number of transitions across the border of the region .
MI =
(2.26)
Note that MI cannot be computed directly from the co-occurence matrix
discussed earlier because more than one isolated regions may contribute to
the computation of t ij for a particular (i, j). In the present context we need to
consider only the transitions with respect to one region. This is a very simple,
yet effective, measure of interaction.
Small regions detected by MI are the potential candidates for merge and
they are merged if the magnitude of the average gradient computed over their
region boundaries is less than a preassigned positive value. This criterion will
avoid merging small but informative regions. High contrast small regions are
usually informative, e.g., the white spot in the eye ball in a face image. The
average gradient over a region, say Ω 1 , may be computed as
G ( i, j )
p
G =
,
(2.27)
( i, j ) ∈ ∂Ω 1
where p is the perimeter of the region Ω 1 and G(i, j) is the gradient at the
position (i, j). The average gradient over other regions can likewise be com-
puted. We have used the following gradient functions. Let g i,j and g k,l be two
adjacent pixels belonging to two different regions, say, Ω i and Ω k , then
G ( i, j )= max
|
g i,j
g k,l
|
(2.28)
k
∈N 3 ( i, j ),
where N 3 ( i, j ) is the 3
3 neighborhood of ( i, j ). Note that rechecking of the
segmentation criteria may be avoided because of merging small regions with
low gradients across the boundary positions. It is expected that the condition
will be satisfied and our computational experience indeed supports this fact.
However, to ensure the validity of the condition, one can once more check the
thresholding after merging.
Single Pixel Merge : Sometimes, single pixel region can occur in a thresh-
olded image. This should be merged to the neighboring region having the
closest gray value in the 3
×
×
3 neighborhood of the single pixel region.
2.5 Evaluation of Segmentation
Evaluation of segmentation is very important, though adequate attention is
not always paid. For evaluation of segmentation, one can consider region ho-
mogeneity and contrast along the boundary points. A good segmentation tech-
nique should create homogeneous regions or patches with high contrast at the
 
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