Show simple item record

dc.contributor.authorVialard, François-Xavier
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
dc.contributor.authorNardi, Giacomo
dc.date.accessioned2014-03-03T12:49:44Z
dc.date.available2014-03-03T12:49:44Z
dc.date.issued2014
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12792
dc.language.isoenen
dc.subjectshape registrationen
dc.subjectBV 2-curvesen
dc.subjectMartingaleen
dc.subjectGeodesicsen
dc.subject.ddc516en
dc.titleA Second-order Total Variation Metric on the Space of Immersed Curvesen
dc.typeDocument de travail / Working paper
dc.description.abstractenThis paper studies the space of BV^2 planar curves endowed with the BV^2 Finsler metric over its tangent space of displacement vector fields. Such a space is of interest for applications in image processing and computer vision because it enables piecewise regular curves that undergo piecewise regular deformations, such as articulations. The main contribution of this paper is the proof of the existence of a shortest path between any two BV^2 curves for this Finsler metric. The method of proof relies on the construction of a martingale on a space satisfying the Radon- Nikodym property and on the invariance under reparametrization of the Finsler metric. This method applies more generally to similar cases such as the space of curves with H^s metrics for s > 3/2. When s >=2 is integer, this space has a strong Riemannian structure and is geodesically complete. Thus, our result shows that the exponential map is surjective, which is complementary to geodesic completeness in infinite dimensions. We propose a finite element discretization of the minimal geodesic problem, and use a gradient descent method to compute a stationary point of a relaxed energy. Numerical illustrations shows the qualitative difference between BV^2 and H^s geodesics.en
dc.publisher.nameUniversité Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages35en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00952672en
dc.subject.ddclabelGéométrieen
dc.description.submittednonen


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record