Random walks for feature-preserving mesh denoising

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Abstract

An approach to mesh denoising based on the concept of random walks is examined. The proposed method consists of two stages: face normal filtering, followed by vertex position updating to integrate the denoised face normals in a least-squares manner. Face normal filtering is performed by weighted averaging of normals in a neighbourhood. A novel approach to determining weights is to compute the probability of arriving at each neighbour following a fixed-length random walk of a virtual particle starting at a given face of the mesh. The probability of the particle stepping from its current face to some neighbouring face is a function of the angle between the two face normals, based on a Gaussian distribution whose variance 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. Our experiments show that, in fact, iterative application of a one-step random walk in a progressive manner effectively preserves detailed features while denoising the mesh very well. This approach is faster than many other feature-preserving mesh denoising algorithms.

References (43)

  • M. Desbrun et al.

    Implicit fairing of irregular meshes using diffusion and curvature flow

  • Desbrun, M., Meyer, M., Schröder, P., Barr, A.H., 2000. Anisotropic feature-preserving denoising of height fields and...
  • J.R. Diebel et al.

    A Bayesian method for probable surface reconstruction and decimation

    ACM Transactions on Graphics

    (2006)
  • D.A. Field

    Laplacian smoothing and Delaunay triangulations

    Communications in Numerical Methods in Engineering

    (1988)
  • S. Fleishman et al.

    Bilateral mesh denoising

    ACM Transactions on Graphics

    (2003)
  • L. Grady

    Random walks for image segmentation

    IEEE Transactions on Pattern Analysis and Machine Intelligence

    (2006)
  • K. Hildebrandt et al.

    Anisotropic filtering of non-linear surface features

    Computer Graphics Forum

    (2004)
  • T.R. Jones et al.

    Non-iterative, feature-preserving mesh smoothing

    ACM Transactions on Graphics

    (2003)
  • T.R. Jones et al.

    Normal improvement for point rendering

    IEEE Computer Graphics and Applications

    (2004)
  • B. Kim et al.

    Geofilter: Geometric selection of mesh filter parameters

    Computer Graphics Forum

    (2005)
  • L. Kobbelt et al.

    Interactive multi-resolution modeling on arbitrary meshes

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