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Actes des rencontres du CIRM

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Yukiko Kenmochi; Phuc Ngo; Nicolas Passat; Hugues Talbot
Digital shapes, digital boundaries and rigid transformations: A topological discussion
Actes des rencontres du CIRM, 3 no. 1: Discrete curvature: Theory and applications (2013), p. 195-201, doi: 10.5802/acirm.68
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Class. Math.: 00X99
Keywords: topology, digitization, geometric transformations

Résumé - Abstract

Curvature is a continuous and infinitesimal notion. These properties induce geometrical difficulties in digital frameworks, and the following question is naturally asked: “How to define and compute curvatures of digital shapes?” In fact, not only geometrical but also topological difficulties are also induced in digital frameworks. The – deeper – question thus arises: “Can we still define and compute curvatures?” This latter question, that is relevant in the context of digitization, i.e., when passing from $\mathbb{R}^n$ to $\mathbb{Z}^n$, can also be stated in $\mathbb{Z}^n$ itself, when applying geometric transformations on digital shapes. This paper proposes a preliminary discussion on this topic.

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