Global regularizing flows with topology preservation for active contours and polygons

Ganesh Sundaramoorthi*, Anthony Yezzi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


Active contour and active polygon models have been used widely for image segmentation. In some applications, the topology of the object(s) to be detected from an image is known a priori, despite a complex unknown geometry, and it is important that the active contour or polygon maintain the desired topology. In this work, we construct a novel geometric flow that can be added to image-based evolutions of active contours and polygons in order to preserve the topology of the initial contour or polygon. We emphasize that, unlike other methods for topology preservation, the proposed geometric flow continually adjusts the geometry of the original evolution in a gradual and graceful manner so as to prevent a topology change long before the curve or polygon becomes close to topology change. The flow also serves as a global regularity term for the evolving contour, and has smoothness properties similar to curvature flow. These properties of gradually adjusting the original flow and global regularization prevent geometrical inaccuracies common with simple discrete topology preservation schemes. The proposed topology preserving geometric flow is the gradient flow arising from an energy that is based on electrostatic principles. The evolution of a single point on the contour depends on all other points of the contour, which is different from traditional curve evolutions in the computer vision literature.

Original languageEnglish (US)
Pages (from-to)803-812
Number of pages10
JournalIEEE Transactions on Image Processing
Issue number3
StatePublished - Mar 2007
Externally publishedYes


  • Active contours
  • Global flows
  • Global regularization
  • Polygons
  • Topology preservation
  • Variational methods

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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