Conformal curvature flows: From phase transitions to active vision
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.
- Publication:
-
Archive for Rational Mechanics and Analysis
- Pub Date:
- September 1996
- DOI:
- 10.1007/BF00379537
- Bibcode:
- 1996ArRMA.134..275K