Characterizing Digital Convexity and Straightness in Terms of “Length” and “Total Absolute Curvature”

摘要

By using the anisotropic version of “length” and “total absolute curvature” proposed by K. Kishimoto and M. Iri (Jpn. J. Appl. Math.6, 1989, 179–207), this paper characterizes digital convexity and digital straightness as follows:1. a bounded digital figureFis digitally convex if and only if the “total absolute curvature” of its boundary is 2π;2. a digital arcs(F) is digitally straight if and only if either of the following conditions is satisfied:(a) the “total absolute curvature” ofs(F) is 0;(b) the “length” ofs(F) is “sufficiently” small.These characterizations indicate that the presented definitions may serve as a bridge between the continuous and digital worlds.