Show simple item record

dc.contributor.authorYezzi, Anthony
dc.contributor.authorMennucci, Andrea
dc.date.accessioned2013-09-18T22:11:27Z
dc.date.available2013-09-18T22:11:27Z
dc.date.issued2005-10
dc.identifier.citationYezzi, A. & Mennucci, A. (2005). "Conformal Metrics and True "Gradient Flows" for Curves". Proceedings of the 10th IEEE International Conference on Computer Vision (ICCV 2005), Vol. 1, October 2005, pp.913-919.en_US
dc.identifier.isbn0-7695-2334-X
dc.identifier.issn1550-5499
dc.identifier.urihttp://hdl.handle.net/1853/48978
dc.description© 2005 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.en_US
dc.descriptionDOI: 10.1109/ICCV.2005.60
dc.description.abstractWe wish to endow the manifold M of smooth curves in Rn with a Riemannian metric that allows us to treat continuous morphs (homotopies) between two curves c0 and c1 as trajectories with computable lengths which are independent of the parameterization or representation of the two curves (and the curves making up the morph between them). We may then define the distance between the two curves using the trajectory of minimal length (geodesic) between them, assuming such a minimizing trajectory exists. At first we attempt to utilize the metric structure implied rather unanimously by the past twenty years or so of shape optimization literature in computer vision. This metric arises as the unique metric which validates the common references to a wide variety of contour evolution models in the literature as "gradient flows" to various formulated energy functionals. Surprisingly, this implied metric yields a pathological and useless notion of distance between curves. In this paper, we show how this metric can be minimally modified using conformal factors that depend upon a curve's total arclength. A nice property of these new conformal metrics is that all active contour models that have been called "gradient flows" in the past will constitute true gradient flows with respect to these new metrics under specific time reparameterizations.en_US
dc.language.isoen_USen_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectConformal metricsen_US
dc.subjectGeodesicen_US
dc.subjectGradient flowsen_US
dc.subjectHomotopiesen_US
dc.subjectParameterizationen_US
dc.subjectRiemannian metricen_US
dc.titleConformal Metrics and True "Gradient Flows" for Curvesen_US
dc.typeProceedingsen_US
dc.contributor.corporatenameGeorgia Institute of Technology. School of Electrical and Computer Engineeringen_US
dc.contributor.corporatenameScuola normale superiore (Italy)en_US
dc.publisher.originalInstitute of Electrical and Electronics Engineers
dc.embargo.termsnullen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record