Translation, scale, and deformationweighted polar active contours

Maximilian Baust*, Anthony Yezzi, Gozde Unal, Nassir Navab

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Polar active contours have proven to be a powerful segmentation method for many medical as well as other computer vision applications, such as interactive image segmentation or tracking. Inspired by recent work on Sobolev active contours we derive a Sobolev-type function space for polar curves, which is endowed with a metric that allows us to favor origin translations and scale changes over smooth deformations of the curve. The resulting translation, scale, and deformation weighted polar active contours inherit the coarse-to-fine behavior of Sobolev active contours as well as their robustness to local minima and are thus very useful for many medical applications, such as cross-sectional vessel segmentation, aneurysm analysis, or cell tracking.

Original languageEnglish
Pages (from-to)354-365
Number of pages12
JournalJournal of Mathematical Imaging and Vision
Issue number3
Publication statusPublished - Nov 2012
Externally publishedYes


  • Active contours
  • Curve evolution
  • Image segmentation
  • Sobolev spaces


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