Conformal curvature flows: From phase transitions to active vision

Satyanad Kichenassamy, Arun Kumar, Peter Olver, Allen Tannenbaum, Anthony Yezzi

Research output: Contribution to journalArticlepeer-review

307 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)275-301
Number of pages27
JournalArchive For Rational Mechanics And Analysis
Volume134
Issue number3
DOIs
StatePublished - Sep 1 1996

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