Chapter 2 – DIGITAL GEOMETRY

Publisher Summary This chapter reviews various topics in digital geometry—the theory of geometrical properties of subsets of digital pictures. This theory provides the foundations for a number of basic array automaton algorithms, for example, border following and region traversal. From a more practical standpoint, it serves as a basis for defining and proving the correctness of various fundamental image analysis operations such as object counting, that is, connected component counting, and chain encoding of region borders. Many other topics are included in the chapter; among these are digital homotopy, dimension , elongatedness, straightness, convexity, and a variety of algorithms for connected component tracking and counting, adjacency tree construction, and border finding. In the process of analyzing a digital picture, one usually begins by extracting subsets of various types from the picture, and this process is called segmentation.

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