A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Meshless parameterization and surface reconstruction
Computer Aided Geometric Design
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
Geometric surface smoothing via anisotropic diffusion of normals
Proceedings of the conference on Visualization '02
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Anisotropic Nonlinear Diffusion in Flow Visualization
VISUALIZATION '99 Proceedings of the 10th IEEE Visualization 1999 Conference (VIS '99)
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Fairing of Point Based Surfaces
CGI '04 Proceedings of the Computer Graphics International
Finite elements on point based surfaces
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Feature-preserving non-local denoising of static and time-varying range data
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Robust statistical estimation of curvature on discretized surfaces
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Voronoi-based variational reconstruction of unoriented point sets
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Multiresolution point-set surfaces
GI '08 Proceedings of graphics interface 2008
Differentials-based segmentation and parameterization for point-sampled surfaces
Journal of Computer Science and Technology
Adaptive feature-preserving non-local denoising of static and time-varying range data
Computer-Aided Design
Feature-preserving denoising of point-sampled surfaces
CEA'09 Proceedings of the 3rd WSEAS international conference on Computer engineering and applications
Extracting lines of curvature from noisy point clouds
Computer-Aided Design
Robust denoising of point-sampled surfaces
WSEAS Transactions on Computers
Curvature-aware adaptive re-sampling for point-sampled geometry
Computer-Aided Design
Technical Section: Variational Bayesian noise estimation of point sets
Computers and Graphics
Error estimates of the finite volume scheme for the nonlinear tensor-driven anisotropic diffusion
Applied Numerical Mathematics
Robust Voronoi-based curvature and feature estimation
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
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The use of point sets instead of meshes became more popular during the last years. We present a new method for anisotropic fairing of a point sampled surface using an anisotropic geometric mean curvature flow. The main advantage of our approach is that the evolution removes noise from a point set while it detects and enhances geometric features of the surface such as edges and corners. We derive a shape operator, principal curvature properties of a point set, and an anisotropic Laplacian of the surface. This anisotropic Laplacian reflects curvature properties which can be understood as the point set analogue of Taubin's curvature-tensor for polyhedral surfaces. We combine these discrete tools with techniques from geometric diffusion and image processing. Several applications demonstrate the efficiency and accuracy of our method.