Sobolev active contours

Ganesh Sundaramoorthi*, Anthony Yezzi, Andrea Mennucci

*Corresponding author for this work

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

21 Scopus citations


All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L2-type inner product to define the notion of gradient. Recent work has shown that this inner product induces a pathological Riemannian metric on the space of smooth curves. However, there are also undesirable features associated with the gradient flows that this inner product induces. In this paper, we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with Sobolev-type inner products. We call the resulting flows Sobolev active contours. Sobolev metrics induce favorable regularity properties in their gradient flows. In addition, Sobolev active contours favor global translations, but are not restricted to such motions. This is particularly useful in tracking applications. We demonstrate the general methodology by reformulating some standard edge-based and region-based active contour models as Sobolev active contours and show the substantial improvements gained in segmentation and tracking applications.

Original languageEnglish (US)
Title of host publicationVariational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings
Number of pages12
StatePublished - 2005
Externally publishedYes
Event3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, VLSM 2005 - Beijing, China
Duration: Oct 16 2005Oct 16 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3752 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, VLSM 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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