Pre-Image as Karcher Mean using Diffusion Maps: Application to shape and image denoising

Nicolas Thorstensen; Florent Ségonne; Renaud Keriven

Pre-Image as Karcher Mean using Diffusion Maps: Application to shape and image denoising

Nicolas Thorstensen ^{1, 2, 3} Florent Ségonne ^{1, 2, 3} Renaud Keriven ^{1, 2, 3}

1 CERTIS - Centre d'Enseignement et de Recherche en Technologies de l'Information et Systèmes

LIGM - Laboratoire d'Informatique Gaspard-Monge, CSTB - Centre Scientifique et Technique du Bâtiment, ENPC - École des Ponts ParisTech

3 LIGM - Laboratoire d'Informatique Gaspard-Monge

Abstract : In the context of shape and image modeling by manifold learning, we focus on the problem of denoising. A set of shapes or images being known through given samples, we capture its structure thanks to the Diffusion Maps method. Denoising a new element classically boils down to the key-problem of pre-image determination, i.e.recovering a point, given its embedding. We propose to model the underlying manifold as the set of Karcher means of close sample points. This non-linear interpolation is particularly well-adapted to the case of shapes and images. We define the pre-image as such an interpolation having the targeted embedding. Results on synthetic 2D shapes and on real 2D images and 3D shapes are presented and demonstrate the superiority of our pre-image method compared to several state-of-the-art techniques in shape and image denoising based on statistical learning techniques.

Type de document :

Communication dans un congrès

Domaine :

Informatique [cs] / Vision par ordinateur et reconnaissance de formes [cs.CV]

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https://hal-enpc.archives-ouvertes.fr/hal-00834952
Contributeur : Pascal Monasse <>
Soumis le : mardi 18 juin 2013 - 12:10:11
Dernière modification le : jeudi 5 juillet 2018 - 14:25:05
Document(s) archivé(s) le : mardi 4 avril 2017 - 23:34:18

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