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Conformal curvature flows: From phase transitions to active vision

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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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Authors and Affiliations

  1. Department of Mathematics Department of Aerospace Engineering, University of Minnesota, 55455, Minneapolis, Minnesota

    Satyanad Kichenassamy, Arun Kumar, Peter Olver, Allen Tannenbaum & Anthony Yezzi Jr.

  2. Department of Electrical Engineering, University of Minnesota, 55455, Minneapolis, Minnesota

    Satyanad Kichenassamy, Arun Kumar, Peter Olver, Allen Tannenbaum & Anthony Yezzi Jr.

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  1. Satyanad Kichenassamy
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  2. Arun Kumar
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  3. Peter Olver
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  4. Allen Tannenbaum
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  5. Anthony Yezzi Jr.
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Communicated by J. Serrin

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Kichenassamy, S., Kumar, A., Olver, P. et al. Conformal curvature flows: From phase transitions to active vision. Arch. Rational Mech. Anal. 134, 275–301 (1996). https://doi.org/10.1007/BF00379537

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