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 attractiveness in Istanbul, Turkey, in August 2010. The eleven revised complete papers provided have been rigorously reviewed and chosen from 25 submissions. The booklet was once particularly designed to advertise interchange and collaboration among specialists in discrete geometry/mathematical morphology and power clients of those tools from different fields of snapshot 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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**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**

Hierarchical data representations in the context of classiﬁcation and data clustering were put forward during the ﬁfties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we brieﬂy survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satisﬁed.

Graph theory is the correct setting for formalising clustering concepts as already recognised in [5] and [6], see also the enlightening paper [7] as well as the detailed survey and connections between graph theory and clustering in [8] (and [9] for clustering on directed graphs). For this reason, Sec. 2 presents brieﬂy background notions and notations of graph theory used throughout this paper. Then, fundamental concepts of hierarchical clustering methods where the spatial location of the data points is usually not taken into account are reviewed in Sec.

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. Otherwise, the angle γ of C at p is larger than π and the C curvature value π − γ is negative. This C curvature value corresponds to the normal curvature at vertex p. →p , we obtain a set of normal C curvature values When plane Π turns around − n bounded by two extremal values kC,1 (p) ≤ kC,2 (p) . Values kC,1 (p) and kC,2 (p) correspond to the principal curvatures.

### 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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