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

This booklet constitutes the refereed lawsuits of the 1st Workshop on purposes 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 conscientiously reviewed and chosen from 25 submissions. The publication used to be particularly designed to advertise interchange and collaboration among specialists in discrete geometry/mathematical morphology and power clients of those equipment from different fields of picture research and trend recognition.

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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

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2 Background Notions In this section, we briefly review some fundamental notions on curvature (see [5] for details). Let C be a curve having parametric representation (c(t))t∈R . The curvature k(p) of C at a point p = c(t) is given by k(p) = 1 |c (t) ∧ c”(t)| = , ρ |c (t)|3 where ρ, called the curvature radius, corresponds to the radius of the osculatory circle tangent to C at p. →p be the normal vector to n Let S be a smooth surface (at least C 2 ). Let − the surface at a point p. Let Π be the plane which contains the normal vector − →p .

Non-overlapping clustering methods can be defined as partitional in the sense that they realise a partition of the input objects (a partition of a set is defined as division of this set in disjoint non-empty subsets such that their union is equal to this set). Non-partitional clustering allows for overlap between clusters, see [13] for an early reference on this topic and [14] for recent developments. The third property refers to the relation between clusters. It indicates whether the clustering method is hierarchical (also called ordered) or non-hierarchical (unordered).

7th Symp. on Computational Geometry (SCG 1991), pp. 162–165. ACM Press (1991) 2. : The self-similarity of digital straight lines. In: Proc. 10th Int. Conf. Pattern Recognition (ICPR 1990), Atlantic City, NJ, vol. 1, pp. 485–490 (1990) 3. : Algorithmique et g´eom´etrie pour la caract´erisation des courbes et des surfaces. PhD thesis, Universit´e Lyon 2 (December 2002) 4. : A comparative evaluation of length estimators of digital curves. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(2), 252–258 (2004) 5.

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