The Beltrami-Mumford-Shah functional

Nir Sochen*, Leah Bar

*Corresponding author for this work

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

2 Scopus citations


We present in this paper a unifying generalization of the Mumford-Shah functional, in the Ambrosio-Totorelli set up, and the Beltrami framework. The generalization of the Ambrosio-Tortorelli is in using a diffusion tensor as an indicator of the edge set instead of a function. The generalization of the Beltrami framework is in adding a penalty term on the metric such that it is defined dynamically from minimization of the functional. We show that we are able, in this way, to have the benefits of true anisotropic diffusion together with a dynamically tuned metric/diffusion tensor. The functional is naturally defined in terms of the vielbein-the metric's square root. Preliminary results show improvement on both the Beltrami flow and the Mumford-Shah flow.

Original languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers
Number of pages11
StatePublished - 2012
Event3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011 - Ein-Gedi, Israel
Duration: 29 May 20112 Jun 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6667 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011


  • Ambrosio-Tortorelli functional
  • Beltrami framework
  • Inhomogeneous diffusion
  • Mumford-Shah functional
  • anisotropic diffusion


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