Thresholding of Medical Images - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 134

Using the probabilistic t -conorm, a new membership function is generated,
which is written as

(6.29)

upper lower upper lower

μ () () () () () g = μ g + μ g − μ g ⋅ μ g

Pij ij ij ij ij

For each threshold grey level, fuzzy divergence is computed between the
thresholded image and ideally segmented image. Ideally segmented image
is such that the membership values are all 1 [5,6]:

M 1 N 1

− −

∑ ∑ 21

0

⎣

μ () () g − μ g

DAB (,) = − − ( () ( ) μ g ge

Aij

+ μ ⋅

Aij Bij

B ij

j = 0 i =

μ () () g − μ g

⎦

−− + ( μ ( g ) μ ( g )) ⋅ e Bij Aij (6.30)

Bij A ij

Substituting μ B ( g ij ) = 1, for an ideally thresholded image, we get

M 1 N 1

− −

∑ ∑

⎣

μ () g − 1 1 − μ () g

⎦

DAB (,) = 22 − ( ( ) − μ g ⋅ e − μ ( g ) ⋅ e

Aij A ij

Aij Aij

j = 0 i = 0

where
μ

A

g = μ g

() ()

Aij P ij

B

μ g = μ g

() ()

Bij P ij

Fuzzy divergence is computed for all the threshold grey levels. The thresh-
old grey level at which the fuzzy divergence is minimum is the optimal
threshold. For better segmentation, the threshold is chosen as half of the
optimal threshold.

Example 6.7

Two examples of leucocyte images are shown in Figures 6.7 and 6.8. In
one experiment, images contain a normal cell, and in another experi-
ment, leukemic cell images are used that contain mature and immature
cells. In leukaemia, there is an increase in the number of immature/
abnormal white blood cells. Segmentation becomes difficult when many
leucocytes (mature or immature) are present in the image and cells and
are jumbled together. It is observed that the shapes of the leucocytes are
properly preserved and are accurately distinguishable.

Performance evaluation : In order to verify the performance of segmentation
methods, a ground truth image or manually segmented images are drawn.