Image Segmentation - Bezier and Splines in Image Processing and Machine Vision - page 40

be reduced. Hence, its maximization with respect to s is expected to provide
a good object/background segmentation.
Next, we provide a schematic description of the algorithm.
c. Algorithm Cond threshold ( X , th )
begin

Compute Co-occurrence matrix, t = [ t ij ] L×L .
s = 0 ; max = 0 ;
th = 0 ; th is the threshold for segmentation
while ( s<L 1) do

compute H T C by (2.16)
if ( H T C ( s ) > max ) then begin

−

th = s ;
max = H T C ( s )

end

s=s+1;
endwhile ;

end ;
Here, we use I ( p i )= e 1 −p i in equation (2.16).

2.4.1 Partition/Decomposition Principle for Gray Images

Explore the possibility of using the object/ background thresholding algorithm
( Cond threshold ) for the extraction of homogeneous patches from a graylevel
image. To partition the image into several subimages, one should keep in mind
the following points:
•

Each subimage consisting of different regions should be approximated well
by some low order function.

• Number of subimages should be as low as possible.

• Homogeneity within a region and contrast between regions should be rea-

sonably good.

In order to achieve this goal, one can use either a multilevel thresholding algo-
rithm [174, 58, 35] or an object/background thresholding algorithm. The mul-
tilevel thresholding algorithm depends on the number of local minima in the
histogram of the image. The extraction of these minima from the histogram
information sometimes may not be very reliable, because some of them may
not be strong enough to be detected by the objective function being used. The
object/background algorithm, on the other hand, relies on a single threshold
to extract the object from the background. Consider a scheme that repeatedly
uses an object/background segmentation algorithm for extraction of homoge-
neous patches.
Consider an L-level image F 0 ( x, y ). The input gray image F 0 ( x, y ) initially
provides a threshold, s on application of the object/background thresholding
algorithm. The threshold, s partitions the image F 0 ( x, y ) into two subim-
ages F 01 ( x, y )and F 02 ( x, y ). The graylevels in F 01 ( x, y ) lie in the interval