Surface Parametrization and Curvature Measurement of Arbitrary 3-D Objects: Five Practical Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Curvature approximation of 3D manifolds in 4D space
Computer Aided Geometric Design
Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces
Computer Aided Geometric Design
Optimal triangulation and quadric-based surface simplification
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Optimizing 3D triangulations using discrete curvature analysis
Mathematical Methods for Curves and Surfaces
Normal vector voting: crease detection and curvature estimation on large, noisy meshes
Graphical Models - Special issue: Processing on large polygonal meshes
Intrinsic Surface Properties from Surface Triangulation
ECCV '92 Proceedings of the Second European Conference on Computer Vision
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
Quantitative methods of evaluating image segmentation
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol. 3)-Volume 3 - Volume 3
Ridge-valley lines on meshes via implicit surface fitting
ACM SIGGRAPH 2004 Papers
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
Robust statistical estimation of curvature on discretized surfaces
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Exact and interpolatory quadratures for curvature tensor estimation
Computer Aided Geometric Design
Interactive Rendering of Dynamic Geometry
IEEE Transactions on Visualization and Computer Graphics
Integral invariants for robust geometry processing
Computer Aided Geometric Design
Extracting lines of curvature from noisy point clouds
Computer-Aided Design
A benchmark for 3D mesh segmentation
ACM SIGGRAPH 2009 papers
A new CAD mesh segmentation method, based on curvature tensor analysis
Computer-Aided Design
Morphology analysis of 3D scalar fields based on morse theory and discrete distortion
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Discrete distortion in triangulated 3-manifolds
SGP '08 Proceedings of the Symposium on Geometry Processing
Discrete surface Ricci flow: theory and applications
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Multiresolution Analysis of 3D Images Based on Discrete Distortion
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
SMI 2012: Short Dimension-independent multi-resolution Morse complexes
Computers and Graphics
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 a key feature in shape analysis and its estimation on discrete simplicial complexes benefits many geometry processing applications. However, its study has mostly remained focused on 2D manifolds and computationally practical extensions to higher dimensions remain an active area of computer science research. We examine the existing notions of distortion, an analog of curvature in the discrete setting, and classify them into two categories: intrinsic and extrinsic, depending on whether they use the interior or the dihedral angles of the tessellation. We then propose a generalization of extrinsic distortion to ce:italic D /ce:italic D and derive a weighting that can be used to compute mean curvature on tessellated hypersurfaces. We analyze the behavior of the operator on 3-manifolds in 4D and compare it to the well-known Laplace-Beltrami operator using ground truth hypersurfaces defined by functions of three variables, and a segmentation application, showing it to behave as well or better while being intuitively simple and easy to implement.