Discrete convexity: Definition, parametrization, and compatibility with continuous convexity

doi:10.1016/S0734-189X(83)80047-4

Computer Vision, Graphics, and Image Processing

Volume 21, Issue 3, March 1983, Pages 326-344

https://doi.org/10.1016/S0734-189X(83)80047-4 Get rights and content

A definition of convexity in discrete spaces such as Z² is considered. This definition has a great similarity with that used for continuous convex figures in R². We establish a method to describe the measurement of convexity. The convex hull of a connected component S will be defined by the intersection property of the convex connected components containing S. In the last part we prove the compatibility of this definition, applied to discrete components obtained by the sampling of continuous figures, with the definition of continuous convexity on R².

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Discrete convexity: Definition, parametrization, and compatibility with continuous convexity

Computer Graphics and Image Processing

Topologies on Discrete Spaces