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

This booklet constitutes the refereed complaints of the 1st Workshop on purposes of Discrete Geometry and Mathematical Morphology, WADGMM 2010, held on the overseas convention on development acceptance in Istanbul, Turkey, in August 2010. The eleven revised complete papers offered have been rigorously reviewed and chosen from 25 submissions. The ebook 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 photograph research and development recognition.

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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**

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However, since the dividing area value Discrete Curvature Estimation Methods for Triangulated Surfaces 31 can be arbitrary small, then a convergence problems arises. In [19], areas are chosen to give a small error bound, but the convergence is not discussed. In [28], counterexamples on the convergence of some curvature estimation methods are given. In [4], the authors show that the angle deﬁcit is asymptotically equivalent to a homogenous polynomial of degree two in the principal curvature. They show that for general meshes, the angle deﬁcit method does not give accurate estimation of Gaussian curvature.

Montanvert, and P. ): WADGMM 2010, LNCS 7346, pp. 28–42, 2012. c Springer-Verlag Berlin Heidelberg 2012 Discrete Curvature Estimation Methods for Triangulated Surfaces 29 curvature returned up to date under some diﬀerent variants, usually area dependent, and became a very relevant tool for curvature estimation. The aim of this paper is to present a new method to discretely estimate mean curvature through concentrated curvature which was used until now to estimate Gaussian curvature. Consequently, principal curvatures can be deduced through concentrated curvature.

Discrete distortion in triangulated 3-manifolds. Computer Graphics Forum 27(5), 1333–1340 (2008) 19. : Discrete diﬀerential-geometry operators for triangulated 2-manifolds. , Polthier, K. ) Proceedings VisMath 2002, pp. 35–57 (2002) 20. : Morse Theory. Princeton University Press, New Jersey (1963) 21. : Perception-based 3D triangle mesh segmentation using fast marching watersheds. In: IEEE Conference on Computer Vision and Pattern Recognition, vol. 2. IEEE Computer Society (2003) 22. : Surface parametrization and curvature measurement of arbitrary 3D objects: ﬁve practical methods.