Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd 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
Random walk approach to image enhancement
Signal Processing - Special section on digital signal processing for multimedia communications and services
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
Anisotropic diffusion of surfaces and functions on surfaces
ACM Transactions on Graphics (TOG)
Geometric surface smoothing via anisotropic diffusion of normals
Proceedings of the conference on Visualization '02
On the geodesic paths approach to color image filtering
Signal Processing
Mesh Smoothing via Mean and Median Filtering Applied to Face Normals
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Non-iterative, feature-preserving mesh smoothing
ACM SIGGRAPH 2003 Papers
ACM SIGGRAPH 2003 Papers
Fuzzy Vector Median-Based Surface Smoothing
IEEE Transactions on Visualization and Computer Graphics
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Efficiently combining positions and normals for precise 3D geometry
ACM SIGGRAPH 2005 Papers
A sharpness dependent filter for mesh smoothing
Computer Aided Geometric Design - Special issue: Geometry processing
A Bayesian method for probable surface reconstruction and decimation
ACM Transactions on Graphics (TOG)
Random Walks for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Random walks, constrained multiple hypothesis testing and image enhancement
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Efficient linear system solvers for mesh processing
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Performance bounds for estimating vector systems
IEEE Transactions on Signal Processing
Fast mesh segmentation using random walks
Proceedings of the 2008 ACM symposium on Solid and physical modeling
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This paper considers an approach to mesh denoising based on the concept of random walks. The proposed method consists of two stages: a face normal filtering procedure, followed by a vertex position updating procedure which integrates the denoised face normals in a least-squares sense. Face normal filtering is performed by weighted averaging of normals in a neighbourhood. The weights are based on the probability of arriving at a given neighbour after a random walk of a virtual particle starting at a given face of the mesh and moving a fixed number of steps. The probability of a particle stepping from its current face to a given neighboring face is determined by the angle between the two face normals, using a Gaussian distribution whose width is adaptively adjusted to enhance the feature-preserving property of the algorithm. The vertex position updating procedure uses the conjugate gradient algorithm for speed of convergence. Analysis and experiments show that random walks of different step lengths yield similar denoising results. In particular, iterative application of a one-step random walk in a progressive manner effectively preserves detailed features while denoising the mesh very well. We observe that this approach is faster than many other feature-preserving mesh denoising algorithms.