{"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/bayesian-optical-flow-with-uncertainty","title":"Bayesian Optical Flow with Uncertainty Quantification","arxiv_id":"1611.01230","date":"2016-11-04","proceeding":null,"authors":["Jie Sun","Fernando J. Quevedo","Erik Bollt"],"abstract":"Optical flow refers to the visual motion observed between two consecutive\nimages. Since the degree of freedom is typically much larger than the\nconstraints imposed by the image observations, the straightforward formulation\nof optical flow as an inverse problem is ill-posed. Standard approaches to\ndetermine optical flow rely on formulating and solving an optimization problem\nthat contains both a data fidelity term and a regularization term, the latter\neffectively resolves the otherwise ill-posedness of the inverse problem. In\nthis work, we depart from the deterministic formalism, and instead treat\noptical flow as a statistical inverse problem. We discuss how a classical\noptical flow solution can be interpreted as a point estimate in this more\ngeneral framework. The statistical approach, whose \"solution\" is a distribution\nof flow fields, which we refer to as Bayesian optical flow, allows not only\n\"point\" estimates (e.g., the computation of average flow field), but also\nstatistical estimates (e.g., quantification of uncertainty) that are beyond any\nstandard method for optical flow. As application, we benchmark Bayesian optical\nflow together with uncertainty quantification using several types of prescribed\nground-truth flow fields and images.","url_abs":"http://arxiv.org/abs/1611.01230v2","url_pdf":"http://arxiv.org/pdf/1611.01230v2.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":"bayesian-optical-flow-with-uncertainty","repo_url":"https://github.com/deu439/MCMC-optical-flow","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"optical-flow-estimation","task_name":"Optical Flow Estimation"},{"task_slug":"uncertainty-quantification","task_name":"Uncertainty Quantification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}