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Stable Spectral Mesh Filtering

  • Artiom Kovnatsky
  • Michael M. Bronstein
  • Alexander M. Bronstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7583)

Abstract

The rapid development of 3D acquisition technology has brought with itself the need to perform standard signal processing operations such as filters on 3D data. It has been shown that the eigenfunctions of the Laplace-Beltrami operator (manifold harmonics) of a surface play the role of the Fourier basis in the Euclidean space; it is thus possible to formulate signal analysis and synthesis in the manifold harmonics basis. In particular, geometry filtering can be carried out in the manifold harmonics domain by decomposing the embedding coordinates of the shape in this basis. However, since the basis functions depend on the shape itself, such filtering is valid only for weak (near all-pass) filters, and produces severe artifacts otherwise. In this paper, we analyze this problem and propose the fractional filtering approach, wherein we apply iteratively weak fractional powers of the filter, followed by the update of the basis functions. Experimental results show that such a process produces more plausible and meaningful results.

Keywords

Computational Geometry and Object Modeling Hierarchy and geometric transformations Laplace-Beltrami operator 3D Mesh filtering 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Artiom Kovnatsky
    • 1
  • Michael M. Bronstein
    • 1
  • Alexander M. Bronstein
    • 2
  1. 1.Institute of Computational Science, Faculty of InformaticsUniversità della Svizzera ItalianaLuganoSwitzerland
  2. 2.School of Electrical EngineeringTel Aviv UniversityIsrael

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