Abstract
In this chapter, we introduce basic 2D digital geometry. The main topic in 2D geometry is curves. A 2D digital curve is a simple path in \(\Sigma_{2}\). A simple closed digital curve is usually the boundary of a connected component. We first discuss how we precisely define a curve in a graph and Euclidean space, then we discuss how we represent digital curves. Digital curves have two important applications in computer graphics and computer vision: (a) Construction of a digital line when two end points are given, and (b) Determination of a closed digital curve to identify a connected region in computer vision. At the end of this chapter, we present two classic theorems related to 2D digital geometry: Pick’s theorem and Minkowski’s theorem. In addition, we discuss the basic concept of image segmentation, one of the major applications of 2D digital planes.
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