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Digital shapes, digital boundaries and rigid transformations: A topological discussion
Yukiko Kenmochi1; Phuc Ngo2; Nicolas Passat3; Hugues Talbot1
1 LIGM, Université Paris-Est, France
2 CEA LIST - DIGITEO Labs, France
3 CReSTIC, Université de Reims, France
Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 195-201.

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 ℝ n to ℤ n , can also be stated in ℤ n itself, when applying geometric transformations on digital shapes. This paper proposes a preliminary discussion on this topic.

Published online:
DOI: 10.5802/acirm.68
Classification: 00X99
Keywords: topology, digitization, geometric transformations
Yukiko Kenmochi 1; Phuc Ngo 2; Nicolas Passat 3; Hugues Talbot 1

1 LIGM, Université Paris-Est, France
2 CEA LIST - DIGITEO Labs, France
3 CReSTIC, Université de Reims, France 
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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, Volume 3 (2013) no. 1, pp. 195-201. doi : 10.5802/acirm.68. https://acirm.centre-mersenne.org/articles/10.5802/acirm.68/

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