Discrete Distortion for Surface Meshes

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.

• Type: Conference
• Year: 2009
• Where: ICIAP
• Authors: Mohammed Mostefa Mesmoudi, Leila De Floriani, Paola Magillo
• Keywords: Common Discrete Approximation, Discrete Distortion, ICIAP 2009, Image Processing, Mean Curvature