ABSTRACT
Digital straight segments (DSS) started gaining special attention since the 1960s from the viewpoint of their theoretical formulation [28, 86, 87, 166, 180]. Many interesting properties of DSS have been discovered in later periods by various researchers, which are mostly related to the theory of words and numbers [7, 32, 117] and continued fractions [113, 115, 119, 143, 209]. With the proliferation of digitization and vectorization of graphical objects and visual imageries, uses of these properties have been investigated by different researchers for different application-specific problems related with computer graphics and image analysis. The most significant among these is to determine whether or not a given digital curve segment S is a DSS, and its algorithmic solutions for several defining criteria have been reported in the literature in the 1980s and
FIGURE 4.1: Polygonal approximation of the image ‘pyramid’.Top-left: 8bit gray-scale image of ‘pyramid’. Top-right: The edge map of ‘pyramid’ is considered to be a real-world digital curve. Note that the edge map is subject to the parameter(s) specified in the edge extraction algorithm. Bottomleft: Polygonal approximation of the edge map with the vertices shown in red color and the edges in blue color. Bottom-right: Polygonal approximation superimposed on the original gray-scale image shows how well the algorithm can approximate a real-world image. (See color insert.)
1990s [50, 73, 74, 122, 142, 195]. In the previous chapter, characterization of digital straightness property of a set of points in a 2-D grid by determining the domain of a candidate DSLS was briefly discussed. In this chapter, we present a more direct approach for determination of the straightness of a digital arc and demonstrate its application in polygonal approximation of boundaries of objects in an image.
