By Alexandra Bac, Jean-Luc Mari
This publication constitutes the court cases of the sixth overseas Workshop on Computational Topology in picture Context, CTIC 2016, held in Marseille, France, in June 2016.
The 24 papers provided during this quantity have been conscientiously reviewed and chosen from 35 submissions. also, this quantity comprises 2 invited papers. CTIC covers quite a lot of issues reminiscent of: topological invariants and their computation, homology, cohomology, linking quantity, basic teams; set of rules optimization in discrete geometry, move of mathematical instruments, parallel computation in multi-dimensional quantity context, hierarchical methods; experimental overview of algorithms and heuristics; combinatorial or multi-resolution versions; discrete or computational topology; geometric modeling guided through topological constraints; computational topological dynamics; and use of topological info in discrete geometry applications.
Read Online or Download Computational Topology in Image Context: 6th International Workshop, CTIC 2016, Marseille, France, June 15-17, 2016, Proceedings PDF
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Additional info for Computational Topology in Image Context: 6th International Workshop, CTIC 2016, Marseille, France, June 15-17, 2016, Proceedings
If the two reached critical vertices are distinct, then there is a unique gradient path from c to each of them, and they both belong to ∂M (c). Otherwise, if the same critical vertex is reached from both endpoints of c, then it is reached through two distinct gradient paths from c, and ∂M (c) is empty. Dually, gradient lines connecting critical 3-cells and faces never merge, and can be extracted by backtracking V starting from critical faces until critical 3-cells are reached. Each critical face d belongs to ∂M (v) of two distinct critical 3-cells, or it does not belong to ∂M (v) for any critical 3-cell v, depending on whether the two reached critical 3-cells are distinct or the same, respectively.
40 K. Pluta et al. Table 1. Examples of Lipschitz quaternions which generate 3D bijective digitized rotations. 5◦ , ω = 2 , − √566 , √566 33 √10 , √ 9 281 281 √ 9 , − √ 9 , −5 262 262 2 1 2 , , 3 3 3 − 23 , − √16 , √16 2 131 Conclusion In this article, we showed the existence of non-simple 3D bijective digitized rotations—ones for which a given rotation axis does not correspond to any of the coordinate axes. The approach is similar to that used by Roussillon and Cœurjolly to prove the conditions for the bijectivity of 2D digitized rotations using Gaussian integers .
Res. 11, 19–60 (2010) 30. : A method for registration of 3-d shapes. IEEE Trans. Pattern Anal. Mach. Intell. fr Abstract. Euclidean rotations in Rn are bijective and isometric maps. Nevertheless, they lose these properties when digitized in Zn . For n = 2, the subset of bijective digitized rotations has been described explicitly by Nouvel and R´emila and more recently by Roussillon and Cœurjolly. 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.