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

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 development reputation in Istanbul, Turkey, in August 2010. The eleven revised complete papers offered have been conscientiously reviewed and chosen from 25 submissions. The publication used to be in particular designed to advertise interchange and collaboration among specialists in discrete geometry/mathematical morphology and capability clients of those equipment from different fields of picture research and development 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 resources for Applications of Discrete Geometry and Mathematical Morphology: First International Workshop, WADGMM 2010, Istanbul, Turkey, August 22, 2010, Revised Selected Papers**

**Example text**

1 Introduction Most image processing applications require the selection of an image representation suitable for further analysis. The suitability of a given representation can be evaluated by confronting its properties with those required by the application at hand. In practice, images are often represented by decomposing them into primitive or fundamental elements that can be more easily interpreted. Examples of decomposition (or simply representation) schemes are given hereafter: – A functional decomposition decomposes the image into a sum of elementary functions.

The principle underlying concentrated curvature can be extended to combinatorial (triangulated) 3-manifolds, by comparing the total solid angle around a vertex with 4π which is the total solid angle around a point in space. Let p be a vertex of a combinatorial 3-manifold Ω. Vertex distortion at p is thus deﬁned as D(p) = 4π − Sp if p is an interior vertex, and D(p) = 2π − Sp if p is a boundary vertex, where Sp is the solid angle at p within the manifold. We have proven in [18] that, if Σ is a shape embedded in R3 , then internal vertices have null vertex distortion.

Computation of local diﬀerential properties on irregular meshes. In: IMA Conference on Mathematics of Surfaces (NIPS), vol. 1, pp. 19–33 (2000) 8. : Optimizing 3D triangulations using discrete curvature analysis. In: Mathematical Methods for Curves and Surfaces: Oslo 2000, pp. 135–146 (2001) 9. : Curvature estimation for unstructured triangulations of surfaces. Technical report, Los Alamos National Laboratory LA-03-8240 (2003) 10. : Estimating curvature on triangular meshes. International Journal on Shape Modeling 12, 1–29 (2006) 11.