{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/regularized-discrete-optimal-transport","title":"Regularized Discrete Optimal Transport","arxiv_id":"1307.5551","date":"2013-07-21","proceeding":null,"authors":["Sira Ferradans","Nicolas Papadakis","Gabriel Peyré","Jean-François Aujol"],"abstract":"This article introduces a generalization of the discrete optimal transport,\nwith applications to color image manipulations. This new formulation includes a\nrelaxation of the mass conservation constraint and a regularization term. These\ntwo features are crucial for image processing tasks, which necessitate to take\ninto account families of multimodal histograms, with large mass variation\nacross modes.\n  The corresponding relaxed and regularized transportation problem is the\nsolution of a convex optimization problem. Depending on the regularization\nused, this minimization can be solved using standard linear programming methods\nor first order proximal splitting schemes.\n  The resulting transportation plan can be used as a color transfer map, which\nis robust to mass variation across images color palettes. Furthermore, the\nregularization of the transport plan helps to remove colorization artifacts due\nto noise amplification.\n  We also extend this framework to the computation of barycenters of\ndistributions. The barycenter is the solution of an optimization problem, which\nis separately convex with respect to the barycenter and the transportation\nplans, but not jointly convex. A block coordinate descent scheme converges to a\nstationary point of the energy. We show that the resulting algorithm can be\nused for color normalization across several images. The relaxed and regularized\nbarycenter defines a common color palette for those images. Applying color\ntransfer toward this average palette performs a color normalization of the\ninput images.","url_abs":"http://arxiv.org/abs/1307.5551v1","url_pdf":"http://arxiv.org/pdf/1307.5551v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"regularized-discrete-optimal-transport","repo_url":"https://github.com/gpeyre/2013-SIIMS-regularized-ot","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"color-normalization","task_name":"Color Normalization"},{"task_slug":"colorization","task_name":"Colorization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1307.5551","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}