Generalized Gradients: Priors on Minimization Flows

This paper tackles an important aspect of the variational problem underlying active contours: optimization by gradient flows. Classically, the definition of a gradient depends directly on the choice of an inner product structure. This consideration is largely absent from the active contours literature. Most authors, explicitely or implicitely, assume that the space of admissible deformations is ruled by the canonical L2 inner product. The classical gradient flows reported in the literature are relative to this particular choice. Here, we investigate the relevance of using (i) other inner products, yielding other gradient descents, and (ii) other minimizing flows not deriving from any inner product. In particular, we show how to induce different degrees of spatial consistency into the minimizing flow, in order to decrease the probability of getting trapped into irrelevant local minima. We report numerical experiments indicating that the sensitivity of the active contours method to...

• Type: Journal
• Year: 2007
• Where: IJCV
• Authors: Guillaume Charpiat, Pierre Maurel, Jean-Philippe Pons, Renaud Keriven, Olivier D. Faugeras
• Keywords: Active Contours, Gradient, IJCV 2007, Inner Product