Wasserstein Regularization of Imaging Problems
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| Title: | Wasserstein Regularization of Imaging Problems |
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| Authors: | Rabin, Julien, Peyré, Gabriel |
| Contributors: | Centre de Mathématiques et de Leurs Applications (CMLA), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), ANR-08-EMER-0009,NatImages,Adaptivité pour la représentation des images naturelles et des textures(2008) |
| Source: | Proceedings of ICIP'11 ; ICIP 2011 : 2011 IEEE International Conference on Image Processing ; https://hal.science/hal-00591279 ; ICIP 2011 : 2011 IEEE International Conference on Image Processing, Sep 2011, Bruxelles, Belgium |
| Publisher Information: | CCSD |
| Publication Year: | 2011 |
| Collection: | Université Paris-Dauphine: HAL |
| Subject Terms: | Variational model, Energy minimization, Image regularization, Gradient descent, color and contrast modification, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing |
| Subject Geographic: | Bruxelles, Belgium |
| Description: | International audience ; 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. |
| Document Type: | conference object |
| Language: | English |
| Availability: | https://hal.science/hal-00591279 https://hal.science/hal-00591279v1/document https://hal.science/hal-00591279v1/file/wasserstein_variational_prox.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| Accession Number: | edsbas.99817BF |
| Database: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | International audience ; 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. |
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