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ICIP 2011 : 2011 IEEE International Conference on Image Processing, Bruxelles : Belgium (2011)

Wasserstein Regularization of Imaging Problems

Julien Rabin 1, Gabriel Peyré 2

(01/09/2011)

This paper introduces a novel and generic framework embedding statistical constraints for variational problems. We resort to the theory of Monge-Kantorovich optimal mass transport to define penalty terms depending on statistics from images. To cope with the computation time issue of the corresponding Wasserstein distances involved in this approach, we propose an approximate variational formulation for statistics represented as point clouds. We illustrate this framework on the problem of regularized color specification. This is achieved by combining the proposed approximate Wasserstein constraint on color statistics with a generic geometric-based regularization term in a unified variational minimization problem. We believe that this methodology may lead to some other interesting applications in image processing, such as medical imaging modification, texture synthesis, etc.

1 :	Centre de Mathématiques et de Leurs Applications (CMLA)
	CNRS : UMR8536 – École normale supérieure de Cachan - ENS Cachan
2 :	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine

Domaine

:

Informatique/Traitement du signal et de l'image Sciences de l'ingénieur/Traitement du signal et de l'image

Mots Clés : Variational model – Energy minimization – Image regularization – Gradient descent – color and contrast modification

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Contributeur : Gabriel Peyré <>

Soumis le : Dimanche 8 Mai 2011, 20:41:03

Dernière modification le : Lundi 9 Mai 2011, 09:54:01