Computational Topology in Image Context: 6th International by Alexandra Bac, Jean-Luc Mari

By Alexandra Bac, Jean-Luc Mari

This e-book constitutes the lawsuits of the sixth foreign Workshop on Computational Topology in photograph 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 includes 2 invited papers. CTIC covers quite a lot of themes equivalent to: 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 techniques; experimental overview of algorithms and heuristics; combinatorial or multi-resolution types; discrete or computational topology; geometric modeling guided through topological constraints; computational topological dynamics; and use of topological details in discrete geometry applications.

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2, pp. 2169–2178 (2006) 8. : Evaluating 3D spatial pyramids for classifying 3D shapes. Comput. Graph. 37, 473–483 (2013) 9. : Intrinsic spatial pyramid matching for deformable 3D shape retrieval. IJMIR 2, 261–271 (2013) 10. : On the use of size functions for shape analysis. Biol. Cybern. 70, 99–107 (1993) 11. : Computational Topology - An Introduction. American Mathematical Society, New York (2010) Persistence-Based Pooling for Shape Pose Recognition 29 12. : Computing persistent homology. Discrete Comput.

Y=x (a) (b) (c) (d) (e) (f) (g) Fig. 3. Evolution of the connectedness of the superlevel-sets Fα of a function f in blue (a) as α (green) decreases from +∞ to −∞ (b–f). This evolution is then encoded in a persistence diagram (g). one of another peak that has a higher maximum. Thus, there exists a vertex up which connects the two components such that f (up ) = dp . up is called a saddle, see Fig. 3(c). The “prominence” of p is then the difference bp − dp . The peak corresponding to the global maximum of f dies when α reaches the minimum value of f on G1 .

Lately we provided a characterization of the set of 2D bijective digitized rigid motions [16]. In this article, our contribution is as follows. We consider an approach similar to that proposed by Roussillon and Cœurjolly to prove the conditions for bijectivity of 2D digitized rotations using arithmetic properties of Gaussian integers [17]—which are complex numbers whose real and imaginary parts are integers [4]. Indeed, the product of two complex numbers has a geometrical interpretation; more precisely, it acts as a rotation when the norm of the multiplier is one.

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