New possibilities with Sobolev active contours

Ganesh Sundaramoorthi*, Anthony Yezzi, Andrea C. Mennucci, Guillermo Sapiro

*Corresponding author for this work

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

8 Scopus citations

Abstract

Recently, the Sobolev metric was introduced to define gradient flows of various geometric active contour energies. It was shown that the Sobolev metric out-performs the traditional metric for the same energy in many cases such as for tracking where the coarse scale changes of the contour are important. Some interesting properties of Sobolev gradient flows are that they stabilize certain unstable traditional flows, and the order of the evolution PDEs are reduced when compared with traditional gradient flows of the same energies. In this paper, we explore new possibilities for active contours made possible by Sobolev active contours. The Sobolev method allows one to implement new energy-based active contour models that were not otherwise considered because the traditional minimizing method cannot be used. In particular, we exploit the stabilizing and the order reducing properties of Sobolev gradients to implement the gradient descent of these new energies. We give examples of this class of energies, which include some simple geometric priors and new edge-based energies. We will show that these energies can be quite useful for segmentation and tracking. We will show that the gradient flows using the traditional metric are either ill-posed or numerically difficult to implement, and then show that the flows can be implemented in a stable and numerically feasible manner using the Sobolev gradient.

Original languageEnglish (US)
Title of host publicationScale Space and Variational Methods in Computer Vision, First International Conference, SSVM 2007, Proceedings
Pages153-164
Number of pages12
StatePublished - Dec 24 2007
Event1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007 - Ischia, Italy
Duration: May 30 2007Jun 2 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4485 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007
CountryItaly
CityIschia
Period05/30/0706/2/07

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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