Edge Detection - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 173

operator and then normalized. Then probability partition of the nor-
malized gradient image is then computed using probabilistic dis-
tribution in order to partition the image into two regions: edge and
smooth regions. The two fuzzy partitions are characterized by the
trapezoidal membership function, and the partitions follow a proba-
bilistic distribution. The membership function represents the condi-
tional probability that a pixel is classified into two regions. Then the
entropy is used to calculate the threshold. The threshold partitions
the image into two regions - edge region and smooth region - which
are determined by minimizing the entropy.
3. Fuzzy median-based edge detector : Ho and Ohnishi [13] presented
FEDGE. It considers several fuzzy edge templates with template val-
ues lying between 0 and 1. As it is a fuzzy case, the input image
is normalized. Each template is placed on the image pixel, and the
fuzzy similarity measure between each template and the subimage
(the image area where the template is placed) is calculated to find the
existence of an edge at that pixel point. This is done for all the tem-
plates. Then using a simple max-min operator, the final edge image
is obtained.
4. Fuzzy divergence-based edge detector : This method is also a template-
based method suggested by Chaira [4]. A set of 16 templates are
used that denote the possible direction of edges in an image. The
centre of each template is placed at each pixel position over a nor-
malized image. It involves the calculation of fuzzy divergence
between the image window and each set of 16 fuzzy templates.
The fuzzy divergence measure at each pixel position in the image,
where the template was centred, is calculated between each of the
elements of the subimage and the template. This is repeated for
all 16 fuzzy templates, and using a simple max operator, the edge
image is obtained.
8.3 Intuitionistic Fuzzy Edge Detection Method
Edge detection using intuitionistic fuzzy set theory is described in detail
in this section. In this method, the membership and non-membership
degrees are considered in a fuzzy image. That means it considers more
uncertainties. Edge detection in medical images is considered to perform
well as medical images contain unclear regions/boundaries. Few intu-
itionistic fuzzy edge detection techniques on medical images are provided
in this chapter.