Thresholding of Medical Images - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 132

Finally, the segmented pixel g seg is computed as follows:

( ) + () () ( )

) × () ()

gi j L wij

, μ g ij wij , μ

+ ()

, g ij ,

L L U U

() =−

(

(6.27)

seg

, 1

()

wij , wij

U

,

L

6.8 Segmenting Leucocyte Images in Blood Cells
Leucocyte segmentation is a special type of segmentation where different
types of leucocytes are segmented with shapes preserved. Thresholding leu-
cocytes is a difficult task. In pathological studies, blood cell parameters such
as red blood cells, white blood cells and platelets, erythrocytes and leuco-
cytes are very essential to detect many diseases such as anaemia, leukaemia,
cancer and any other infection. Out of these blood parameters, leucocyte
(white blood cell) counting is very much essential where counting five types
of leucocytes such as eosinophil, basophil, neutrophil, lymphocytes and
monocytes is done to detect diseases. The five types of leucocytes can be
distinguished by their cytoplasmic granules, the staining properties of the
granules, the size of cell, the proportion of the nucleus to the cytoplasmic
material and the type of nucleolar lobes.
To threshold the leucocytes, any thresholding method can be used, but
the method should be such that it should preserve the shape of the leuco-
cytes. The shape of the nucleus is preserved to distinguish different types
of leucocytes to diagnose diseases. For this, interval Type II fuzzy set and a
modified Cauchy distribution are used to find the membership values of the
image. The optimal threshold is selected by using divergence using Type II
fuzzy set [9].

6.8.1 Cauchy Distribution

The probability density function of Cauchy distribution is

1

fxa (;,) γ =

2

⎞

⎛

⎛
⎜

xa − ⎞

⎟

⎜ ⎟

πγ 1 +

γ

⎝ ⎠

where
a is the location parameter
γ is a scale parameter