Stable spectral mesh filtering

Artiom Kovnatsky*, Michael M. Bronstein, Alexander M. Bronstein

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationComputer Vision, ECCV 2012 - Workshops and Demonstrations, Proceedings
PublisherSpringer Verlag
Number of pages9
EditionPART 1
ISBN (Print)9783642338625
StatePublished - 2012
Externally publishedYes
EventComputer Vision, ECCV 2012 - Workshops and Demonstrations, Proceedings - Florence, Italy
Duration: 7 Oct 201213 Oct 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume7583 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceComputer Vision, ECCV 2012 - Workshops and Demonstrations, Proceedings


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


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