Conformal curvature flows: From phase transitions to active vision
Résumé
We analyze geometric active contour models from a curve
evolution point of view and propose some modifications based on
gradient flows relative to a certain new feature-based Riemannian
metric. This leads to a novel edge-detection paradigm in which the
feature of interest may be assumed 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-D 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.