Piecewise rigid curve deformation via a Finsler steepest descent
Peyré, Gabriel; Charpiat, Guillaume; Nardi, Giacomo; Vialard, François-Xavier (2015), Piecewise rigid curve deformation via a Finsler steepest descent, Interfaces and Free Boundaries, 18, 1, p. 1-44. 10.4171/IFB/355
TypeArticle accepté pour publication ou publié
Journal nameInterfaces and Free Boundaries
MetadataShow full item record
Abstract (EN)This paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al. , to the setting of Finsler metrics. Such a generalized gradient allows one to take into account a prior on deformations (e.g., piecewise rigid) in order to favor some specific evolutions. We define a Finsler gradient descent method to minimize a functional defined on a Banach space and we prove a convergence theorem for such a method. In particular, we show that the use of non-Hilbertian norms on Banach spaces is useful to study non-convex optimization problems where the geometry of the space might play a crucial role to avoid poor local minima.We show some applications to the curve matching problem. In particular, we characterize piecewise rigid deformations on the space of curves and we study several models to perform piecewise rigid evolution of curves.
Subjects / KeywordsCurve evolution; Finsler space; gradient flow; shape registration
Showing items related by title and author.
Nardi, Giacomo; Vialard, François-Xavier; Peyré, Gabriel; Charpiat, Guillaume (2013) Document de travail / Working paper
Feydy, Jean; Séjourné, Thibault; Vialard, François-Xavier; Amari, Shun-ichi; Trouvé, Alain; Peyré, Gabriel (2018) Document de travail / Working paper