Archive for Rational Mechanics and Analysis
, Volume 134, Issue 3, pp 275301
First online:
Conformal curvature flows: From phase transitions to active vision
 Satyanad KichenassamyAffiliated withDepartment of Mathematics Department of Aerospace Engineering, University of MinnesotaDepartment of Electrical Engineering, University of Minnesota
 , Arun KumarAffiliated withDepartment of Mathematics Department of Aerospace Engineering, University of MinnesotaDepartment of Electrical Engineering, University of Minnesota
 , Peter OlverAffiliated withDepartment of Mathematics Department of Aerospace Engineering, University of MinnesotaDepartment of Electrical Engineering, University of Minnesota
 , Allen TannenbaumAffiliated withDepartment of Mathematics Department of Aerospace Engineering, University of MinnesotaDepartment of Electrical Engineering, University of Minnesota
 , Anthony YezziJr.Affiliated withDepartment of Mathematics Department of Aerospace Engineering, University of MinnesotaDepartment of Electrical Engineering, University of Minnesota
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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 featurebased Riemannian metrics. This leads to a novel edgedetection paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus an edgeseeking curve is attracted very naturally and efficiently to the desired feature. Comparison with the AllenCahn 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 3dimensional 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 levelset approach.
 Title
 Conformal curvature flows: From phase transitions to active vision
 Journal

Archive for Rational Mechanics and Analysis
Volume 134, Issue 3 , pp 275301
 Cover Date
 199609
 DOI
 10.1007/BF00379537
 Print ISSN
 00039527
 Online ISSN
 14320673
 Publisher
 SpringerVerlag
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 Authors

 Satyanad Kichenassamy ^{(1)} ^{(2)}
 Arun Kumar ^{(1)} ^{(2)}
 Peter Olver ^{(1)} ^{(2)}
 Allen Tannenbaum ^{(1)} ^{(2)}
 Anthony Yezzi Jr. ^{(1)} ^{(2)}
 Author Affiliations

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