{"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/computing-wasserstein-p-distance-between","title":"Computing Wasserstein-p Distance Between Images With Linear Cost","arxiv_id":null,"date":"2022-01-01","proceeding":"CVPR 2022 1","authors":["Yidong Chen","Chen Li","Zhonghua Lu"],"abstract":"    When the images are formulated as discrete measures, computing Wasserstein-p distance between them is challenging due to the complexity of solving the corresponding Kantorovich's problem. In this paper, we propose a novel algorithm to compute the Wasserstein-p distance between discrete measures by restricting the optimal transport (OT) problem on a subset. First, we define the restricted OT problem and prove the solution of the restricted problem converges to antorovich's OT solution. Second, we propose the SparseSinkhorn algorithm for the restricted problem and provide a multi-scale algorithm to estimate the subset. Finally, we implement the proposed algorithm on CUDA and illustrate the linear computational cost in terms of time and memory requirements. We compute Wasserstein-p distance, estimate the transport mapping, and transfer color between color images with size ranges from 64x64 to 1920x1200. (Our code is available at https://github.com/ucascnic/CudaOT)    ","url_abs":"http://openaccess.thecvf.com//content/CVPR2022/html/Chen_Computing_Wasserstein-p_Distance_Between_Images_With_Linear_Cost_CVPR_2022_paper.html","url_pdf":"http://openaccess.thecvf.com//content/CVPR2022/papers/Chen_Computing_Wasserstein-p_Distance_Between_Images_With_Linear_Cost_CVPR_2022_paper.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":"computing-wasserstein-p-distance-between","repo_url":"https://github.com/ucascnic/cudaot","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}