Edge Detection - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 171

many important edges are removed. In hysteresis thresholding, two thresh-
olds are used. Initially, to find the start of an edge, an upper threshold is
used. Then, following the image pixel by pixel, a path is traced whenever
the edge strength is above the lower threshold and stops when the value
falls below the lower threshold. In this method, the edges are linked and
continuous. But still a problem lies in selecting the threshold parameter.
8.1.2 Hough Transform Method
This method is a robust feature extraction method developed by Hough [18]
to find the lines in the image. Later, it is extended to detect objects of vary-
ing shapes such as ellipse and circles. This method uses an array called an
accumulator to detect the existence of a line y = mx + b . In Hough transform,
the line characteristics are described in terms of slope m and intercept b .
The straight line is represented as a point ( b , m ) in the parameter space.
Hough transform uses an accumulator, and the dimension of the accumula-
tor is the number of unknown parameters of the line (here it is 2). For each
pixel and its neighbourhood, it determines if the straight line exists at that
pixel. If it exists, it will calculate the parameter of that line and then look for
the accumulator's bin that the parameters fall into and increase the value of
that bin. By looking at the local maxima in the accumulator space, the most
likely lines are extracted. It can also be used for curved shapes such as a
circle and an ellipse that contain three parameters, making Hough trans-
form 3D. Later, generalized Hough transform is proposed that deals with
complicated shapes.
8.1.3 Boundary-Based Method
It is another method for boundary detection introduced by Kass et al. [12].
He developed a novel technique called snake. Snake is an active contour
model which is 'an energy minimizing spline guided by external constraint
forces and influenced by image forces that pull it toward features such as
lines and edges'. Snakes or active contours are computer-generated curves
that find the boundary in an image. This method deals with internal (snake)
and external (image) forces. Internal forces prevent stretching and bending,
and external forces guide towards object boundaries. Traditional snake is
initially close to the boundaries and cannot go into the concavities. Later, it
is modified such that it can be initialized anywhere in the boundary and can
go into the concavities.
As this topic is related to the use of intuitionistic fuzzy/Type II fuzzy set,
an overview of fuzzy edge detection is given so that the readers will have
an idea on fuzzy methods. Fuzzy methods provide better results, but in
some images, these methods fail to produce better edge images. In that case,