Optimal Transport for Diffeomorphic Registration

Jean Feydy (1, 2) , Benjamin Charlier (3) , François-Xavier Vialard (4, 5) , Gabriel Peyré (2)

1 CMLA - Centre de Mathématiques et de Leurs Applications
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 IMAG - Institut Montpelliérain Alexander Grothendieck
4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
5 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales

This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in diffeomorphic registration methods that, together with the regularization on the deformation, defines the optimal deformation. Most often, these similarity measures are local or non local but simple enough to be computationally fast. We build on recent theoretical and numerical advances in optimal transport to propose fast and global similarity measures that can be used on surfaces or volumetric imaging data. This new similarity measure is computed using a fast generalized Sinkhorn algorithm. We apply this new metric in the LDDMM framework on synthetic and real data, fibres bundles and surfaces and show that better matching results are obtained.

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]; Théorie de l'information et codage [math.IT]; Traitement du signal et de l'image [eess.SP]

Jean Feydy, Benjamin Charlier, François-Xavier Vialard, Gabriel Peyré. Optimal Transport for Diffeomorphic Registration. MICCAI 2017, Sep 2017, Quebec, Canada. ⟨hal-01540455⟩