2009 | OriginalPaper | Buchkapitel
Discrete Distortion for Surface Meshes
verfasst von : Mohammed Mostefa Mesmoudi, Leila De Floriani, Paola Magillo
Erschienen in: Image Analysis and Processing – ICIAP 2009
Verlag: Springer Berlin Heidelberg
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Discrete distortion for two- and three-dimensional combinatorial manifolds is a discrete alternative to Ricci curvature known for differentiable manifolds. Here, we show that distortion can be successfully used to estimate mean curvature at any point of a surface. We compare our approach with the continuous case and with a common discrete approximation of mean curvature, which depends on the area of the star of each vertex in the triangulated surface. This provides a new, area-independent, tool for curvature estimation and for morphological shape analysis. We illustrate our approach through experimental results showing the behavior of discrete distortion.