ABSTRACT
Real-life images are inherently embedded with various ambiguities. In order to perceive the nature of ambiguities in images, let us consider a 1001 × 1001 grayscale image (see Figure 3.1(a)) that has sinusoidal gray value gradations in horizontal direction. When an attempt is made to mark the boundary of an arbitrary region in the image, an exact boundary can not be defined as a consequence of the presence of steadily changing gray values (gray value gradation). This is evident from Figure 3.1(b) that shows a portion of the image, where it is known that the pixels in the ‘white’ shaded area uniquely belong to a region. However, the boundary (on the left and right sides) of this region is vague as it can lie anywhere in the gray value gradations present in the portion. Value gradation is a common phenomenon in real-life images and hence it is widely accepted (Pal, 1982; Pal, King, and Hashim, 1983; Udupa and Saha, 2003) that regions in an image have fuzzy boundaries.
