## Digital geometry in image processing by Jayanta Mukhopadhyay, (College teacher); et al

By Jayanta Mukhopadhyay, (College teacher); et al

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Extra resources for Digital geometry in image processing

Sample text

Let us consider the case of 2-D skeletonization first. We define a point simple, if its deletion still preserves the topology of the picture. A simple point can be characterized in various ways. The following theorem [155, 175] states a characterization of simple points in 2-D. 1. Let p be a non-isolated border point in a digital picture. Let S be its foreground pixel set, and let S = S − {p}. Then the following are equivalent: 1. p is a simple point. 2. p is adjacent to just one component of N (p) S.

In this case, C1 and C2 are the foreground components, and B1 and B2 are background components. The respective adjacency tree formed by nodes corresponding to components and edges between two adjacent components is shown in Fig. 19(b). However, if the pattern of Fig. 15 is taken in a (4, 8) grid, the set of connected components and their adjacency tree differ significantly (see Fig. 20). From these figures, we may observe the following for an adjacency tree, which is also in general true. These properties are discussed in [36].

3 Boundary and Interior . . . . . . . . . . . . . . . . . . 1 Contour Tracing . . . . . . . . . . . . . . 2 Chain Code . . . . . . . . . . . . . . . . 3 Neighborhood Plane Set (NPS) . . . . . . Topology Preserving Operations . . . . . . . . . . . . . . . . . 1 Skeletonization . . . . . . . . . . . . . . . . . . . . . . 2 Adjacency Tree . . . . . . . . . . . . . . . .