Frank C Langbein
Ex Tenebris Scientia




X.-F. Sun, P. L. Rosin, R. R. Martin, F. C. Langbein

In: Proc. ACM Symp. Solid and Physical Modeling, pp. 11-22, ACM Siggraph 2007.
ISBN 1595936660.

[DOI: 10.1145/1236246.1236252] [Preprint] [CiteSeer]

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. 

@INPROCEEDINGS{Sun2007a,
  author =       {Xianfang Sun and Paul L. Rosin and Ralph R. Martin
                  and Frank C. Langbein},
  title =        {Random Walks for Mesh Denoising},
  booktitle =    {Proc. ACM Symp. Solid and Physical Modeling},
  year =         2007,
  pages =        {11-22},
  address =      {New York, NY, USA},
  publisher =    {ACM Siggraph},
  doi =          {10.1145/1236246.1236252},
  isbn =         1595936660,
  url =          {http://www.langbein.org/research/surfaces/filtering/sun2007a/},
  abstract =     {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.},
}
Cite as Random Walks for Mesh Denoising, http://www.langbein.org/research/manifolds/filtering/sun2007a/print by Frank C Langbein [ 6/December/2008, 19:28].