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

ISBN-10: 364232312X

ISBN-13: 9783642323126

ISBN-10: 3642323138

ISBN-13: 9783642323133

This e-book constitutes the refereed lawsuits of the 1st Workshop on functions of Discrete Geometry and Mathematical Morphology, WADGMM 2010, held on the overseas convention on trend acceptance in Istanbul, Turkey, in August 2010. The eleven revised complete papers offered have been conscientiously reviewed and chosen from 25 submissions. The publication was once particularly designed to advertise interchange and collaboration among specialists in discrete geometry/mathematical morphology and strength clients of those equipment from different fields of picture research and trend recognition.

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

**Sample text**

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.

The comparison often relies on a dissimilarity measure that assigns a weight to each edge. Following the notations of [10], we summarise hereafter graph deﬁnitions required in the context of clustering. , E is a subset of {{p, q} ⊆ V | p = q}. Each element of V is called a vertex or a point (of X), and each element of E is called an edge (of X). If V = ∅, we say that X is non-empty. As several graphs are considered in this paper, whenever this is necessary, we denote by V (X) and by E(X) the vertex and edge set of a graph X.

We have proven in [18] that, if Σ is a shape embedded in R3 , then internal vertices have null vertex distortion. This is an important property that we use to deﬁne the restriction of distortion on the boundary of the 3-manifold without considering the tetrahedra in its interior. For triangulated surfaces embedded in R3 , the restriction of discrete distortion to a surface reduces to compare the internal solid angles at vertices with 2π. In this case, distortion at a vertex p can be expressed in a simpler way as Discrete Curvature Estimation Methods for Triangulated Surfaces (π − Θe ), D(p) = 37 (6) e∈st(p) where st(p) is the star of p and Θe are the dihedral angles around the edges e incident to p.

### Applications of Discrete Geometry and Mathematical Morphology: First International Workshop, WADGMM 2010, Istanbul, Turkey, August 22, 2010, Revised Selected Papers by Peer Stelldinger (auth.), Ullrich Köthe, Annick Montanvert, Pierre Soille (eds.)

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