By Peer Stelldinger (auth.), Ullrich Köthe, Annick Montanvert, Pierre Soille (eds.)

This e-book constitutes the refereed lawsuits of the 1st Workshop on purposes of Discrete Geometry and Mathematical Morphology, WADGMM 2010, held on the overseas convention on development popularity in Istanbul, Turkey, in August 2010. The eleven revised complete papers awarded have been conscientiously reviewed and chosen from 25 submissions. The e-book used to be in particular designed to advertise interchange and collaboration among specialists in discrete geometry/mathematical morphology and strength clients of those tools from different fields of snapshot research and trend recognition.

**Read or Download Applications of Discrete Geometry and Mathematical Morphology: First International Workshop, WADGMM 2010, Istanbul, Turkey, August 22, 2010, Revised Selected Papers PDF**

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**Extra info for Applications of Discrete Geometry and Mathematical Morphology: First International Workshop, WADGMM 2010, Istanbul, Turkey, August 22, 2010, Revised Selected Papers**

**Example text**

The total curvature of each spherical cap is equal to 2π − Θp and does not depend on the radius of the cap. The detailed justiﬁcation can be found in [14]. A simple computation on the number of triangles, edges and vertices within the surface gives the following discrete version of Gauss-Bonnet theorem [25]: Theorem 2. Let Σ be a closed orientable singular flat surface, and χ(Σ) be the Euler characteristic of Σ. Then (2π − Θp ) = 2πχ(Σ). p vertex of Σ 5 Discrete Mean Curvature In this section, we describe two common estimators for mean curvature, the ﬁrst one deﬁned from Laplace-Beltrami operator [19], and the second one based on a cylindrical approximation.

Soc. 60, 471–502 (1990) 15. : Multi-scale Analysis of Discrete Contours for Unsupervised Noise Detection. P. ) IWCIA 2009. LNCS, vol. 5852, pp. 187–200. Springer, Heidelberg (2009) 16. fr/MeaningfulBoxes 17. : Meaningful scales detection along digital contours for unsupervised local noise estimation. IEEE Transaction on Pattern Analysis and Machine Intelligence (accepted, to appear, 2012) 18. : Digital straightness – a review. Discrete Applied Mathematics 139(1-3), 197–230 (2004) 19. : Digital Geometry: Geometric Methods for Digital Picture Analysis.

Then (2π − Θp ) = 2πχ(Σ). p vertex of Σ 5 Discrete Mean Curvature In this section, we describe two common estimators for mean curvature, the ﬁrst one deﬁned from Laplace-Beltrami operator [19], and the second one based on a cylindrical approximation. M. Mesmoudi, L. De Floriani, and P. Magillo Mean Curvature through Discrete Laplace-Beltrami Operator →p be Let H(p) be the mean curvature of a surface at a point (a vertex) p and − n the normal unit vector at p. The Laplace-Beltrami operator K maps p to the →p .