Thresholding of Medical Images - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 112

image, global threshold does not work better. Local or window-based thresh-
olding methods may be very much effective where the image is divided into
several windows or regions and there is one threshold (or one set of thresh-
olds) for each window. The threshold value depends on the local statistics of the
region such as the variance and mean of the image. It may be termed as regional
thresholding. It works well when the intensities are not uniform and multiple
objects are present with different grey levels. Such types of images are the real-
time images, for example, medical images where the images are not uniform
due to improper illumination or lightning condition or any other. One possible
way for local threshold [14] is replacing each pixel by the mean and standard
deviation of its local neighbourhood of size b × b , which may be calculated as

T ( i , j ) = m ( i , j ) + k · σ( i , j )

where m , σ and k are the local mean, variance and bias setting, respectively.
Rodriguez [18] suggested a non-fuzzy/crisp method on segmenting medi-
cal images using windowed thresholding based on Otsu's method [15], where
the image in the object class ( C 0 ) and background class ( C 1 ) is separated using
a threshold t . Between-class variance σ 2 and within-class variance σ 2 are cal-
culated for the image, and the optimal threshold is selected by maximizing
the ratio of between-class variance to within-class variance with respect to
the threshold t , that is, maximizing the separability of the histogram:

2

σ
σ

b

η =

2

w

This approach works better than any other image thresholding methods. It
performs better where the contrast of the background and object region is
low but sensitive to noise. So, a variation of Otsu's method was suggested
where the image is divided into windows of size (1/2) × (1/4) of the image
and filtered the image using a Gaussian filter of σ = 0.5. The standard devia-
tion is calculated for each window:

jM +

iM +

1
2

∑ ∑

2

( )

S.D. = fkl (,) − μ ( ,) i j

w

k M =− 1 ljM =−

where
M = ( W − 1)/2, W denotes the width of the window
μ (, )

∑

iM +

∑

jM +

2

ij = 1 / W f kl ( ,)

k M =− 1 ljM =−

The final threshold of each window is Otsu's threshold minus the standard
deviation.
So, Threshold window = Threshold Otsu −S.D window