Bijectivity certification of 3D digitized rotations

Abstract : Euclidean rotations in $\mathbb{R}^n$ are bijective and isometric maps. Nevertheless, they lose these properties when digitized in $\mathbb{Z}^n$. For $n=2$, the subset of bijective digitized rotations has been described explicitly by Nouvel and R\'emila and more recently by Roussillon and C{\oe}urjolly. In the case of 3D digitized rotations, the same characterization has remained an open problem. In this article, we propose an algorithm for certifying the bijectivity of 3D digitized rational rotations using the arithmetic properties of the Lipschitz quaternions.
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6th International Workshop on Computational Topology in Image Context (CTIC 2016), Jun 2016, Marseille, France. 9667, pp.30-41, 2016, Lecture Notes in Computer Science. 〈10.1007/978-3-319-39441-1_4〉
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Soumis le : jeudi 30 novembre 2017 - 15:18:15
Dernière modification le : vendredi 8 décembre 2017 - 01:01:37

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Kacper Pluta, Pascal Romon, Yukiko Kenmochi, Nicolas Passat. Bijectivity certification of 3D digitized rotations. 6th International Workshop on Computational Topology in Image Context (CTIC 2016), Jun 2016, Marseille, France. 9667, pp.30-41, 2016, Lecture Notes in Computer Science. 〈10.1007/978-3-319-39441-1_4〉. 〈hal-01315226v2〉

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