Thresholding of Medical Images - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 114

Optimal threshold is computed for each region. The threshold for each pixel is
computed by interpolating the results of the subimages. This method gives a
better result, but computational complexity is more in real-time applications.
An alternative method to find local threshold is to look into the local statis-
tics of each pixel around its neighbourhood such as the mean or median or
mean of the difference of minimum and maximum values in the subimage.

6.2.5.2 Multispectral Thresholding

This type of thresholding is used in remotely sensed images where there are
many spectral bands. One simple way is to obtain a threshold for each band
and then combine to obtain a thresholded image.
Though this topic mainly discusses medical image processing using
advanced fuzzy set theories, a brief overview on fuzzy thresholding on med-
ical images is discussed. The methods are not discussed in detail as these
are already presented in the author's other topic on fuzzy image processing.
Approaches related to intuitionistic fuzzy set and Type II fuzzy set will be
discussed in detail with examples on medical images in later sections.

6.3 Fuzzy Methods
In this section, fuzzy methods are discussed briefly so that the readers may
have a clear knowledge on the application of fuzzy sets in thresholding.
There are many fuzzy methods in literature [10-13,16], and few of them are
explained in this section.

6.3.1 Fuzzy Divergence Method

Chaira and Ray's [5,6] fuzzy divergence method is used for optimal thresh-
old selection. The criterion function involves the minimization of the diver-
gence between the thresholded image and an ideally thresholded image. The
gamma membership function is used for finding the membership values of
the pixels in an image. The membership functions for the object and back-
ground regions are as follows:

() exp(

−⋅ − ca m | |) if

i

a ≤ t , forobject

ij 0 ij

(6.1)

μ Aij a =

exp( −⋅ − ca m | |) f at

ij >

, for background

ij 1

where
t is the any chosen threshold
a ij is the ( i , j )th pixel in image A
constant c = 1/( f max − f fmin) )
m 0 and m 1 are the means of object and background regions, respectively