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Digital Geometry by Azriel Rosenfeld, Reinhard Klette

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CHAPTER 5

Incidence Pseudographs

This chapter treats pictures as graph-theoretic objects; it represents spatial subdivisions with incidence pseudographs. We recall that, in 2D or 3D incidence grids (see Section 2.1.5), pixels or voxels are further refined (e.g., a 2-cell [grid square] has grid edges and grid vertices as additional structural components). We define open and closed subsets of incidence pseudographs and their frontiers in preparation for discussing topologies in the following chapters. We give combinatorial formulas for such subsets in regular incidence grids and give a graph-theoretic treatment of frontier tracing.

5.1 Incidence Structures

In this chapter, we discuss a graph-theoretic generalization of the grid cell incidence ...

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