Edge Detection - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 170

contain noise, so whether a pixel is an edge pixel or noise pixel, it depends
on the grey value of the pixel and its surrounding pixels. So, smoothing is
required in order to remove the noise present in the image, and Gaussian
smoothing is the most common filter used.
Fuzzy methods alleviate these problems as they consider the image to be
vague and are better suited for edge information detection and noise filtering
than the traditional methods. Edge detection using fuzzy logic provides an
alternative approach to detect edges. There are various fuzzy and crisp edge
detection methods in the literature (see, e.g. [2,5,10,12-15,19]). Fuzzy methods
consider the image to be fuzzy as the edges are not clearly defined. In medi-
cal images where the images have poor contrast and the edges/boundaries
are not properly visible, edge detection becomes very crucial. Edges may be
detected using a fuzzy edge detector (FEDGE) that uses some fuzzy tem-
plates or fuzzy reasoning that uses linguistic variables. Apart from fuzzy
methods, edges may be detected using the intuitionistic fuzzy method.
The intuitionistic fuzzy method considers a more number of uncertainties
than the fuzzy method, and thus, it seems to be better suited to those types
of images where the presence of uncertainty is high (e.g. medical images,
remotely sensed images).
There are various ways one can detect the edges, and these are
(a) the thresholding-based method, (b) Hough transform method and
(c) boundary-based method.
8.1.1 Thresholding Method
When an edge strength is computed using any of the methods such as
Canny and Prewitt, thresholding is required to know the existence of edges.
Threshold selection is crucial. If the threshold is low, many unwanted edges
and irrelevant features are detected, and if the threshold is high, the image
will have many missed or fragmented edges. If the edge thresholding is
applied to the gradient magnitude image, the resulting edges will be thick
and so some type of edge-thinning post-processing is required. A good edge
detection method uses a smoothing parameter to remove any noise and,
depending on the type of image smoothing parameter, is adjusted to mini-
mize the unwanted noise, and the thresholding parameter is adjusted so that
well-formed edges are produced.
A commonly used approach to compute the appropriate thresholds is
thresholding using hysteresis that is used in Canny's edge detector [3]. It uses
initially a smoothing parameter (σ) to remove the noise. Gradient image is
computed, and then non-maximal suppression is used, which is an edge-
thinning technique. A search is carried out to see if the gradient magnitude
is the local maxima in the gradient direction. It keeps only those pixels on
the edges which have high magnitude. Finally, hysteresis thresholding is
done where unwanted edges are removed. If a simple threshold is used,