{"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/a-torus-model-for-optical-flow","title":"A torus model for optical flow","arxiv_id":"1812.00875","date":"2018-11-09","proceeding":null,"authors":["Henry Adams","Johnathan Bush","Brittany Carr","Lara Kassab","Joshua Mirth"],"abstract":"We propose a torus model for high-contrast patches of optical flow. Our model is derived from a database of ground-truth optical flow from the computer-generated video \\emph{Sintel}, collected by Butler et al.\\ in \\emph{A naturalistic open source movie for optical flow evaluation}. Using persistent homology and zigzag persistence, popular tools from the field of computational topology, we show that the high-contrast $3\\times 3$ patches from this video are well-modeled by a \\emph{torus}, a nonlinear 2-dimensional manifold. Furthermore, we show that the optical flow torus model is naturally equipped with the structure of a fiber bundle, related to the statistics of range image patches.","url_abs":"https://arxiv.org/abs/1812.00875v2","url_pdf":"https://arxiv.org/pdf/1812.00875v2.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":"a-torus-model-for-optical-flow","repo_url":"https://bitbucket.org/Cross_Product/optical_flow","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"optical-flow-estimation","task_name":"Optical Flow Estimation"},{"task_slug":"model","task_name":"model"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}