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

This e-book constitutes the refereed court cases of the 1st Workshop on purposes of Discrete Geometry and Mathematical Morphology, WADGMM 2010, held on the foreign 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 ebook used to be in particular designed to advertise interchange and collaboration among specialists in discrete geometry/mathematical morphology and power clients of those equipment from different fields of photograph 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**

N and with shift x0 , y0 . Several subsampling processes can be considered at this stage, but it is necessary to maintain a surjective map fix0 ,y0 which associates any point P of C to its image point in the subsampled contour φxi 0 ,y0 (C). Such a function is illustrated on Fig. 4(c). Then, we can consider the discrete lengths (Lhj i ,x0 ,y0 ) of the maximal segments on the subsampled shapes φxi 0 ,y0 (C) containing fix0 ,y0 (P ) with the increasing sequence of digitization grid steps hi = ih (see Fig.

Symmetry). Starting from an arbitrary dissimilarity measurement, it is possible to construct a hierarchical clustering: if the dissimilarity is increasing with the merging order, an ultrametric distance between any two objects (or clusters) can be deﬁned as the dissimilarity threshold level from which these two objects (or clusters) belong to the same cluster; if if the dissimilarity is not increasing with the merging order, then any increasing function of the merging order can be used. , non reduced to one object).

Mean and Gaussian C curvatures for Triangulated Surfaces. Let Σ be →p be the a piecewise linear triangulated surface and p be a vertex of Σ. Let − n normal vector at p deﬁned by the average of the normal vectors of the triangles incident in p. Let Π be a plane passing by p and containing the normal vector − →p . This plane cuts surface Σ along a polygonal curve C := Σ ∩ Π. We compute n the C curvature kC (p) at point p of curve C as described above. If the normal →p and the polygonal curve C lie in two diﬀerent half planes (see Figure vector − n 3 (c)), then the angle γ of C at p is smaller than π and the C curvature value π − γ is positive.