A Comparative Study of Data Driven Regularize Optical Flow Estimation Models

A Comparative Study of Data Driven Regularize Optical Flow Estimation Models | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Comparative Study of Data Driven Regularize Optical Flow Estimation Models Bhavana Singh, Pushpendra Kumar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4422440/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 13 You are reading this latest preprint version Abstract Motion estimation has been increasingly important in the field of computer vision in recent years. The motion estimation is conducted using optical flow field. The estimation model of optical flow consists of data term and the regularization term. In this study, we aimed to present and compare six variational models by varying the composition of the data term. The variation is formulated through application of different penalty functions namely, quadratic, Charbonnier and Lorentzian in data term. The quadratic penalty term has linear characteristic which eases its implementation in the model. The Charbonnier function is deployed to increase the robustness of the model against the outliers, and the motive of utilizing Lorentzian function is to test the behaviour of variational model when nonconvexity is incorporated. Further, these penalty functions are convolved with the non-local weighted function to incorporate global motion information. Thus, these established models are solved using various numerical techniques. In the regularization term of all the presented models, fractional order-based derivative called Marchaud is considered. The Marchaud fractional derivative is discretized using Grunwald-Letnikov derivative method. The result obtained from the solution of each model is visualised using a color map and vector field. Moreover, the variational models are also evaluated and compared using numerous evaluation metrics such as, AAE, AEE, AENG, RMS, and WE. A thorough analysis is conducted on variety of datasets including synthetic and real dataset. The comparison results are employed by the different bar graphs, and statistical analysis is also conducted to ensure the scientific validity. Optical flow Penalty function Non-local weight Marchaud fractional order derivative Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 22 Apr, 2025 Reviews received at journal 21 Apr, 2025 Reviewers agreed at journal 10 Apr, 2025 Reviewers agreed at journal 10 Apr, 2025 Reviewers agreed at journal 31 Mar, 2025 Reviews received at journal 06 Mar, 2025 Reviewers agreed at journal 20 Feb, 2025 Reviewers agreed at journal 20 Feb, 2025 Reviewers agreed at journal 25 Sep, 2024 Reviewers invited by journal 23 Sep, 2024 Editor assigned by journal 17 May, 2024 Submission checks completed at journal 15 May, 2024 First submitted to journal 15 May, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4422440","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":486375208,"identity":"6bbbf38e-0913-42c5-9aac-a4f118f0008f","order_by":0,"name":"Bhavana Singh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEklEQVRIie3RMWuDQBTA8Xcc1OVJVguSfoUThxCw+FU8Cpn8AB0yCA5Z7K6kHyJZCp168iAuBefiUumQJYNjl5ZqTZei0rHD/ZcHx/24Bweg0/3DZtxQKkAL2SY6H/F+4Bi53KBUje3NeaJYjzifJqIEN0+9lWukwZn8PDMaQUAYkrzLjsc3hIerhTFT8L4GezEiWMwU4TPJbBs6MULlPMYcWHIAXEbDpF08IDMhud+GrCNsR+1iZgQo1DC54CDI/CT59FLUHfE7wj4mCLYkT3HlshS+F5Md4VOvWBwD1aA3Z0noZPeiummJIPtgjRK/LKjpv7J4bU631fWuzOv6tPb8MfIr0Y/2svWn+zqdTqcb7guwiFxI7hQU7gAAAABJRU5ErkJggg==","orcid":"","institution":"Maulana Azad National Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Bhavana","middleName":"","lastName":"Singh","suffix":""},{"id":486375210,"identity":"2d63d118-4ce9-4e4b-83d4-614970a706a3","order_by":1,"name":"Pushpendra Kumar","email":"","orcid":"","institution":"Maulana Azad National Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Pushpendra","middleName":"","lastName":"Kumar","suffix":""}],"badges":[],"createdAt":"2024-05-15 04:14:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4422440/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4422440/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94568275,"identity":"62d26831-5806-4272-8a8c-7427b6b4164b","added_by":"auto","created_at":"2025-10-28 18:05:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":21009566,"visible":true,"origin":"","legend":"","description":"","filename":"ArticleTitle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4422440/v1_covered_51a4a4c8-99d9-46f0-9753-bcfb4d4103ae.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Comparative Study of Data Driven Regularize Optical Flow Estimation Models","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"multidimensional-systems-and-signal-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mult","sideBox":"Learn more about [Multidimensional Systems and Signal Processing](http://link.springer.com/journal/11045)","snPcode":"11045","submissionUrl":"https://submission.nature.com/new-submission/11045/3","title":"Multidimensional Systems and Signal Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Optical flow, Penalty function, Non-local weight, Marchaud fractional order derivative","lastPublishedDoi":"10.21203/rs.3.rs-4422440/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4422440/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":" Motion estimation has been increasingly important in the field of computer vision in recent years. 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