Diffeomorphic matching of distributions: a new approach for unlabelled point-sets and sub-manifolds matching

Joan Alexis Glaunès; Alain Trouvé; Laurent Younes

hal-00263647, version 1

Diffeomorphic matching of distributions: a new approach for unlabelled point-sets and sub-manifolds matching

Joan Alexis Glaunès () ¹, Alain Trouvé () ², Laurent Younes ³

Computer Vision and Pattern Recognition, 2004. CVPR 2004 2 (2004) 712-718

Abstract: In the paper, we study the problem of optimal matching of two generalized functions (distributions) via a diffeomorphic transformation of the ambient space. In the particular case of discrete distributions (weighted sums of Dirac measures), we provide a new algorithm to compare two arbitrary unlabelled sets of points, and show that it behaves properly in limit of continuous distributions on sub-manifolds. As a consequence, the algorithm may apply to various matching problems, such as curve or surface matching (via a sub-sampling), or mixings of landmark and curve data. As the solution forbids high energy solutions, it is also robust towards addition of noise and the technique can be used for nonlinear projection of datasets. We present 2D and 3D experiments.

1: Laboratoire Analyse, Géométrie et Application (LAGA)
CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis
2: Centre de Mathématiques et de Leurs Applications (CMLA)
CNRS : UMR8536 – École normale supérieure de Cachan - ENS Cachan
3: Center for Imaging Science (CIS)
Johns Hopkins University

hal-00263647, version 1
http://hal.archives-ouvertes.fr/hal-00263647
oai:hal.archives-ouvertes.fr:hal-00263647
From: Joan Alexis Glaunès <>
Submitted on: Wednesday, 12 March 2008 17:30:54
Updated on: Wednesday, 12 March 2008 17:30:54

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