9.2.1 Dilation
Dilation is an operation that "grows" or "thickens" objects in a binary image The specific manner and extent of this thickening is controlled by a shape referred to as a structuring element. Figure 9.4 illustrates how dilation works. Figure 9.4(a) shows a simple binary image containing a rectangular object. Figure 9.4(b) is a structuring element, a five-pixel-long diagonal line in this case. Computationally, structuring elements typically are represented by a matrix of 0s and 1s; sometimes it is convenient to show only the 1s, as illustrated in the figure. In addition, the origin of the structuring element must be clearly identified. Figure 9.4(b) shows the origin of the structuring element using a black outline. Figure 9.4(c) graphically depicts dilation as a process that translates the origin of the structuring element throughout the domain of the image and checks to see where it overlaps with 1-valued pixels. The output image Fig. 9.4(d) is 1 at each location of the origin such that the structuring element overlaps at least one 1-valued pixel in the input image.