Archive for Rational Mechanics and Analysis

, Volume 134, Issue 3, pp 275–301

Conformal curvature flows: From phase transitions to active vision

Authors

  • Satyanad Kichenassamy
    • Department of Mathematics Department of Aerospace EngineeringUniversity of Minnesota
    • Department of Electrical EngineeringUniversity of Minnesota
  • Arun Kumar
    • Department of Mathematics Department of Aerospace EngineeringUniversity of Minnesota
    • Department of Electrical EngineeringUniversity of Minnesota
  • Peter Olver
    • Department of Mathematics Department of Aerospace EngineeringUniversity of Minnesota
    • Department of Electrical EngineeringUniversity of Minnesota
  • Allen Tannenbaum
    • Department of Mathematics Department of Aerospace EngineeringUniversity of Minnesota
    • Department of Electrical EngineeringUniversity of Minnesota
  • Anthony YezziJr.
    • Department of Mathematics Department of Aerospace EngineeringUniversity of Minnesota
    • Department of Electrical EngineeringUniversity of Minnesota
Article

DOI: 10.1007/BF00379537

Cite this article as:
Kichenassamy, S., Kumar, A., Olver, P. et al. Arch. Rational Mech. Anal. (1996) 134: 275. doi:10.1007/BF00379537

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.

Copyright information

© Springer-Verlag 1996