Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
A Java3D framework for inspecting and segmenting 3D models
Web3D '08 Proceedings of the 13th international symposium on 3D web technology
Discrete Distortion for Surface Meshes
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Discrete distortion in triangulated 3-manifolds
SGP '08 Proceedings of the Symposium on Geometry Processing
Computing morse decompositions for triangulated terrains: an analysis and an experimental evaluation
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
Concentrated curvature for mean curvature estimation in triangulated surfaces
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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Curvature is one of the most relevant notions that links the metric properties of a surface to its geometry and to its topology (Gauss-Bonnet theorem). In the literature, a variety of approaches exist to compute curvatures in the discrete case. Several techniques are computationally intensive or suffer from convergence problems. In this paper, we discuss the notion of concentrated curvature, introduced by Troyanov [24]. We discuss properties of this curvature and compare with a widely-used technique that estimates the Gaussian curvatures on a triangulated surface. We apply our STD method [13] for terrain segmentation to segment a surface by using different curvature approaches and we illustrate our comparisons through examples.