Archive for Rational Mechanics and Analysis

, Volume 134, Issue 3, pp 275–301 | Cite as

Conformal curvature flows: From phase transitions to active vision

  • Satyanad Kichenassamy
  • Arun Kumar
  • Peter Olver
  • Allen Tannenbaum
  • Anthony YezziJr.


In this paper, we analyze geometric active contour models from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new feature-based Riemannian metrics. This leads to a novel edge-detection paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus an edge-seeking curve is attracted very naturally and efficiently to the desired feature. Comparison with the Allen-Cahn model clarifies some of the choices made in these models, and suggests inhomogeneous models which may in return be useful in phase transitions. We also consider some 3-dimensional active surface models based on these ideas. The justification of this model rests on the careful study of the viscosity solutions of evolution equations derived from a level-set approach.


Phase Transition Evolution Equation Active Surface Surface Model Electromagnetism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Satyanad Kichenassamy
    • 1
    • 2
  • Arun Kumar
    • 1
    • 2
  • Peter Olver
    • 1
    • 2
  • Allen Tannenbaum
    • 1
    • 2
  • Anthony YezziJr.
    • 1
    • 2
  1. 1.Department of Mathematics Department of Aerospace EngineeringUniversity of MinnesotaMinneapolis
  2. 2.Department of Electrical EngineeringUniversity of MinnesotaMinneapolis

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