Range Image Segmentation Based on Differential Geometry: A Hybrid Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface Parametrization and Curvature Measurement of Arbitrary 3-D Objects: Five Practical Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Curvature approximation for triangulated surfaces
Geometric modelling
On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
Computer Aided Geometric Design
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Optimizing 3D triangulations using discrete curvature analysis
Mathematical Methods for Curves and Surfaces
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
On the angular defect of triangulations and the pointwise approximation of curvatures
Computer Aided Geometric Design
Curvature measures for discrete surfaces
ACM SIGGRAPH 2006 Courses
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Isometric Embeddings in Imaging and Vision: Facts and Fiction
Journal of Mathematical Imaging and Vision
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The interest, in recent years, in the geometric processing of polygonal meshes, has spawned a whole range of algorithms to estimate curvature properties over smooth polygonal meshes. Being a discrete approximation of a C2 continuous surface, these methods attempt to estimate the curvature properties of the original surface. The best known methods are quite effective in estimating the total or Gaussian curvature but less so in estimating the mean curvature. In this work, we present a scheme to accurately estimate the mean curvature of smooth polygonal meshes using a one sided tube formula for the volume above the surface. In the presented comparison, the proposed scheme yielded results whose accuracy is amongst the highest compared to similar techniques for estimating the mean curvature.