Archive for Rational Mechanics and Analysis

, Volume 134, Issue 3, pp 275–301

Conformal curvature flows: From phase transitions to active vision

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

Abstract

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.

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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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