The Laplace-Beltrami operator: A ubiquitous tool for image and shape processing

Aaron Wetzler, Yonathan Aflalo, Anastasia Dubrovina, Ron Kimmel

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

Abstract

The ubiquity of the Laplace-Beltrami operator in shape analysis can be seen by observing the wide variety of applications where it has been found to be useful. Here we demonstrate a small subset of such uses with their latest developments including a scale invariant transform for general triangulated meshes, an effective and efficient method for denoising meshes using Beltrami flows via high dimensional embeddings of 2D manifolds and finally the possibility of viewing the framework of geodesic active contours as a surface minimization having the Laplace-Beltrami operator as its main ingredient.

Original languageEnglish
Title of host publicationMathematical Morphology and Its Applications to Signal and Image Processing - 11th International Symposium, ISMM 2013, Proceedings
Pages302-316
Number of pages15
DOIs
StatePublished - 2013
Event11th International Symposium on Mathematical Morphology, ISMM 2013 - Uppsala, Sweden
Duration: 27 May 201329 May 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7883 LNCS

Conference

Conference11th International Symposium on Mathematical Morphology, ISMM 2013
Country/TerritorySweden
CityUppsala
Period27/05/1329/05/13

Keywords

  • Laplace-Beltrami
  • active contours
  • denoising
  • scale invariant
  • segmentation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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