Wasserstein Regularization of Imaging Problem
Peyré, Gabriel; Rabin, Julien (2011), Wasserstein Regularization of Imaging Problem, 18th IEEE International Conference on Image Processing (ICIP), 2011 - Proceedings, IEEE, p. 1541-1544
TypeCommunication / Conférence
External document linkhttp://hal.archives-ouvertes.fr/hal-00591279/fr/
Conference titleICIP 2011 : 2011 IEEE International Conference on Image Processing
Book title18th IEEE International Conference on Image Processing (ICIP), 2011 - Proceedings
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Abstract (EN)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.
Subjects / Keywordscolor and contrast modification; Gradient descent; Image regularization; Energy minimization; Variational model
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