Digital shapes, digital boundaries and rigid transformations: A topological discussion

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 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.
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Yukiko Kenmochi, Phuc Ngo, Nicolas Passat, Hugues Talbot. Digital shapes, digital boundaries and rigid transformations: A topological discussion. Courbure discrète : théorie et applications , 2013, Luminy, France. pp.195-201. ⟨hal-00984287v2⟩

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