CHARACTERIZING DIGITAL STRAIGHTNESS AND DIGITAL CONVEXITY BY MEANS OF DIFFERENCE OPERATORS

摘要

We characterize straightness of digital curves in the integer plane by means of difference operators. Earlier definitions of digital rectilinear segments have used, respectively, Rosenfeld’s chord property, word combinatorics, Reveillès’ double Diophantine inequalities, and the author’s refined hyperplanes. We prove that all these definitions are equivalent. We also characterize convexity of integer-valued functions on the integers with the help of difference operators.