Abstract
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.
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Mesmoudi, M.M., De Floriani, L., Magillo, P. (2009). Discrete Distortion for Surface Meshes. In: Foggia, P., Sansone, C., Vento, M. (eds) Image Analysis and Processing – ICIAP 2009. ICIAP 2009. Lecture Notes in Computer Science, vol 5716. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04146-4_70
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DOI: https://doi.org/10.1007/978-3-642-04146-4_70
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