Discrete distortion for surface meshes

TitleDiscrete distortion for surface meshes
Publication TypeJournal Articles
Year of Publication2009
AuthorsMesmoudi M, De Floriani L, Magillo P
JournalImage Analysis and Processing–ICIAP 2009
Pagination652 - 661
Date Published2009///

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.