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An implicit formulation for incorporating different priors into a deformation model

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Auteurs : Gris, Barbara (Auteur de la conférence)
CIRM (Editeur )

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Résumé : One of the goals of shape analysis is to model and characterise shape evolution. We focus on methods where this evolution is modeled by the action of a time-dependent diffeomorphism, which is characterised by its time-derivatives: vector fields. Reconstructing the evolution of a shape from observations then amounts to determining an optimal path of vector fields whose flow of diffeomorphisms deforms the initial shape in accordance with the observations. However, if the space of considered vector fields is not constrained, optimal paths may be inaccurate from a modeling point of view. To overcome this problem, the notion of deformation module allows to incorporate prior information from the data into the set of considered deformations and the associated metric. I will present this generic framework as well as the Python library IMODAL, which allows to perform registration using such structured deformations. More specifically, I will focus on a recent implicit formulation where the prior can be expressed as a property that the generated vector field should satisfy. This imposed property can be of different categories that can be adapted to many use cases, such as constraining a growth pattern or imposing divergence-free fields.

Mots-Clés : shape registration; constrained large deformation; biological data analysis

Codes MSC :
49N45 - Inverse problems in calculus of variations
51P05 - Geometry and physics
53-04 - Explicit machine computation and programs (not the theory of computation or programming)
53Z05 - Applications of differential geometry to physics
58D30 - Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
65D18 - Computer graphics, image analysis, and computational geometry
68-04 - Explicit machine computation and programs (not the theory of computation or programming)
68U10 - Image processing (computing aspects)
92C15 - Developmental biology, pattern formation
49N90 - Applications of optimal control and differential games

    Informations sur la Vidéo

    Réalisateur : Recanzone, Luca
    Langue : Anglais
    Date de Publication : 21/06/2024
    Date de Captation : 28/05/2024
    Sous Collection : Research talks
    Catégorie arXiv : Computer Vision and Pattern Recognition ; Numerical Analysis
    Domaine(s) : Analyse Numérique & Calcul Formel ; Mathématiques pour les Sciences & Technologies
    Format : MP4 (.mp4) - HD
    Durée : 00:38:22
    Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-05-28_Gris.mp4

Informations sur la Rencontre

Nom de la Rencontre : Geometric Sciences in Action: from geometric statistics to shape analysis / Les sciences géometriques en action: des statistiques géometriques à l'analyse de forme
Organisateurs de la Rencontre : Bauer, Martin ; Buet, Blanche ; Le Brigant, Alice ; Pennec, Xavier ; Sommer, Stefan
Dates : 27/05/2024 - 31/05/2024
Année de la rencontre : 2024
URL de la Rencontre : https://conferences.cirm-math.fr/2974.html

Données de citation

DOI : 10.24350/CIRM.V.20184703
Citer cette vidéo: Gris, Barbara (2024). An implicit formulation for incorporating different priors into a deformation model. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20184703
URI : http://dx.doi.org/10.24350/CIRM.V.20184703

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