Optimal matching between curves in a manifold

07/11/2017
Publication GSI2017
OAI : oai:www.see.asso.fr:17410:22575
contenu protégé  Document accessible sous conditions - vous devez vous connecter ou vous enregistrer pour accéder à ou acquérir ce document.
- Accès libre pour les ayants-droit
 

Résumé

This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared using a Riemannian metric that is invariant under the action of the reparameterization group. This group induces a quotient structure classically interpreted as the "shape space". We introduce a simple algorithm allowing to compute geodesics of the quotient shape space using a canonical decomposition of a path in the associated principal bundle. We consider the particular case of elastic metrics and show simulations for open curves in the plane, the hyperbolic plane and the sphere.

Optimal matching between curves in a manifold

Collection

application/pdf Optimal matching between curves in a manifold Alice Le Brigant, Marc Arnaudon, Frédéric Barbaresco
Détails de l'article
contenu protégé  Document accessible sous conditions - vous devez vous connecter ou vous enregistrer pour accéder à ou acquérir ce document.
- Accès libre pour les ayants-droit

This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared using a Riemannian metric that is invariant under the action of the reparameterization group. This group induces a quotient structure classically interpreted as the "shape space". We introduce a simple algorithm allowing to compute geodesics of the quotient shape space using a canonical decomposition of a path in the associated principal bundle. We consider the particular case of elastic metrics and show simulations for open curves in the plane, the hyperbolic plane and the sphere.
Optimal matching between curves in a manifold

Auteurs

Optimal matching between curves in a manifold
Drone Tracking Using an Innovative UKF
Jean-Louis Koszul et les structures élémentaires de la Géométrie de l’Information
Poly-Symplectic Model of Higher Order Souriau Lie Groups Thermodynamics for Small Data Analytics
Session Geometrical Structures of Thermodynamics (chaired by Frédéric Barbaresco, François Gay-Balmaz)
Opening and closing sessions (chaired by Frédéric Barbaresco, Frank Nielsen, Silvère Bonnabel)
GSI'17-Closing session
GSI'17 Opening session
Démonstrateur franco-britannique "IRM" : gestion intelligente et homéostatique des radars multifonctions
Principes & applications de la conjugaison de phase en radar : vers les antennes autodirectives
Nouvelles formes d'ondes agiles en imagerie, localisation et communication
Compréhension et maîtrise des tourbillons de sillage
Wake vortex detection, prediction and decision support tools
Ordonnancement des tâches pour radar multifonction avec contrainte en temps dur et priorité
Symplectic Structure of Information Geometry: Fisher Metric and Euler-Poincaré Equation of Souriau Lie Group Thermodynamics
Reparameterization invariant metric on the space of curves
Probability density estimation on the hyperbolic space applied to radar processing
SEE-GSI'15 Opening session
Lie Groups and Geometric Mechanics/Thermodynamics (chaired by Frédéric Barbaresco, Géry de Saxcé)
Opening Session (chaired by Frédéric Barbaresco)
Invited speaker Charles-Michel Marle (chaired by Frédéric Barbaresco)
Koszul Information Geometry & Souriau Lie Group 4Thermodynamics
MaxEnt’14, The 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
Koszul Information Geometry & Souriau Lie Group Thermodynamics
Robust Burg Estimation of stationary autoregressive mixtures covariance
Koszul Information Geometry and Souriau Lie Group Thermodynamics
Koszul Information Geometry and Souriau Lie Group Thermodynamics
Oral session 7 Quantum physics (Steeve Zozor, Jean-François Bercher, Frédéric Barbaresco)
Opening session (Ali Mohammad-Djafari, Frédéric Barbaresco)
Tutorial session 1 (Ali Mohammad-Djafari, Frédéric Barbaresco, John Skilling)
Prix Thévenin 2014
SEE/SMF GSI’13 : 1 ère conférence internationale sur les Sciences  Géométriques de l’Information à l’Ecole des Mines de Paris
Synthèse (Frédéric Barbaresco)
POSTER SESSION (Frédéric Barbaresco)
ORAL SESSION 16 Hessian Information Geometry II (Frédéric Barbaresco)
Information/Contact Geometries and Koszul Entropy
lncs_8085_cover.pdf
Geometric Science of Information - GSI 2013 Proceedings
Médaille Ampère 2007

Média

Voir la vidéo

Métriques

0
0
2.07 Mo
 application/pdf
bitcache://928c402b8e4b0e7c6026ca9a415873bda7c7bc8c

Licence

Creative Commons Aucune (Tous droits réservés)

Sponsors

Sponsors Platine

alanturinginstitutelogo.png
logothales.jpg

Sponsors Bronze

logo_enac-bleuok.jpg
imag150x185_couleur_rvb.jpg

Sponsors scientifique

logo_smf_cmjn.gif

Sponsors

smai.png
logo_gdr-mia.png
gdr_geosto_logo.png
gdr-isis.png
logo-minesparistech.jpg
logo_x.jpeg
springer-logo.png
logo-psl.png

Organisateurs

logo_see.gif
<resource  xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
                xmlns="http://datacite.org/schema/kernel-4"
                xsi:schemaLocation="http://datacite.org/schema/kernel-4 http://schema.datacite.org/meta/kernel-4/metadata.xsd">
        <identifier identifierType="DOI">10.23723/17410/22575</identifier><creators><creator><creatorName>Frédéric Barbaresco</creatorName></creator><creator><creatorName>Marc Arnaudon</creatorName></creator><creator><creatorName>Alice Le Brigant</creatorName></creator></creators><titles>
            <title>Optimal matching between curves in a manifold</title></titles>
        <publisher>SEE</publisher>
        <publicationYear>2018</publicationYear>
        <resourceType resourceTypeGeneral="Text">Text</resourceType><subjects><subject>optimal matching</subject><subject>manifold-valued curves</subject><subject>elastic metric</subject></subjects><dates>
	    <date dateType="Created">Thu 8 Mar 2018</date>
	    <date dateType="Updated">Thu 8 Mar 2018</date>
            <date dateType="Submitted">Mon 22 Oct 2018</date>
	</dates>
        <alternateIdentifiers>
	    <alternateIdentifier alternateIdentifierType="bitstream">928c402b8e4b0e7c6026ca9a415873bda7c7bc8c</alternateIdentifier>
	</alternateIdentifiers>
        <formats>
	    <format>application/pdf</format>
	</formats>
	<version>37296</version>
        <descriptions>
            <description descriptionType="Abstract">This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared using a Riemannian metric that is invariant under the action of the reparameterization group. This group induces a quotient structure classically interpreted as the "shape space". We introduce a simple algorithm allowing to compute geodesics of the quotient shape space using a canonical decomposition of a path in the associated principal bundle. We consider the particular case of elastic metrics and show simulations for open curves in the plane, the hyperbolic plane and the sphere.
</description>
        </descriptions>
    </resource>
.