Image Enhancement - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 101

The upper and lower membership values are computed as

upper 05 .

μ () [()] g = μ g

lower 2

μ () [()] g = μ g

where μ( g ) is the fuzzified image.
From the two levels, the new membership function is computed as

lower upper

μ () g = μ () g ⋅ + αμ ()( g ⋅ − 1 α ), 0 < α < 1

new

and

g

mean

α=

L

where
g mean is the mean of the grey levels of the window
L is the number of grey levels

This is done for all the windows. The new image obtained is the enhanced
image.

Example 5.4

Three results on abdominal tumour and ovarian cyst will illustrate the
effect of the Type II fuzzy method in image enhancement. The results on
different types of images are shown in Figures 5.7 through 5.9.

For performance evaluation, the linear index of fuzziness is computed for
the original and the enhanced images. It determines the vagueness in the
image, and enhancement takes place when there is a decrease in fuzziness,
that is, if the index of fuzziness is less than the original image, the enhanced
image is better. It gives at least some useful information about the efficacy of
the methods. The linear index of fuzziness is defined as

M M

−
∑∑

− 1 1

2

( )

(5.23)

enh

g

enh

g

L.I. = min( μ ), 1 − μ ()

ij ij

MN ×

i = 0 j = 0

where
μ enh ( g ij ) is the membership value of the enhanced image
M × N is the size of the image