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CHARACTERIZING DIGITAL STRAIGHTNESS AND DIGITAL CONVEXITY BY MEANS OF DIFFERENCE OPERATORS

Part of: Discrete geometry Special classes of linear operators Difference and functional equations Difference equations

Published online by Cambridge University Press:  31 May 2011

Christer O. Kiselman
Christer O. Kiselman*
Affiliation:
Department of Mathematics, Uppsala University, P.O. Box 480, SE-751 06 Uppsala, Sweden (email: kiselman@math.uu.se, christer@kiselman.eu)
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Abstract

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.

MSC classification

Secondary: 52C99: None of the above, but in this section 39A05: General theory 39A70: Difference operators 47B39: Difference operators
Type
Research Article
Information
Mathematika , Volume 57 , Issue 2 , July 2011 , pp. 355 - 380
Copyright
Copyright © University College London 2011

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