Diffeomorphic Reconstruction of a 2D-Simple Non-Parametric Manifold Via Shape Gradient

Diffeomorphic Reconstruction of a 2D-Simple Non-Parametric Manifold Via Shape Gradient | 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 Diffeomorphic Reconstruction of a 2D-Simple Non-Parametric Manifold Via Shape Gradient Shafeequdheen Palengara, Jyotiranjan Nayak, Vijayakrishna Rowthu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7717081/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract We present a variational method for reconstructing 2D simple manifolds from a given fixed level set data using shape gradients. Starting from an initial triangulated surface (mesh), iteratively evolves the mesh by minimizing a shape energy functional that reflects local geometric properties of the surface. The evolution is performed via a gradient descent scheme, guiding the mesh toward accurate alignment with the object's boundary while ensuring smoothness. This approach ensures both geometric fidelity and regularity of the reconstructed shape. The effectiveness of the method is demonstrated through experiments on various synthetic shapes and also for human brain white matter MRI T1 data. AMS Subject Classification (2020): 49Q10, 49Q20, 65D18, 68U10, 53A05, 65K10 Simple Manifold Non-Parametric Surface Shape Gradient Level Set Signed Distance Function Curvature Hamilton-Jacobi equation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 22 Feb, 2026 Reviewers agreed at journal 09 Feb, 2026 Reviewers invited by journal 16 Oct, 2025 Editor assigned by journal 29 Sep, 2025 Submission checks completed at journal 29 Sep, 2025 First submitted to journal 25 Sep, 2025 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7717081","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":535061577,"identity":"a754e256-db5c-4019-8b50-4a6d631a83c8","order_by":0,"name":"Shafeequdheen Palengara","email":"","orcid":"","institution":"SRM University, Andhra Pradesh","correspondingAuthor":false,"prefix":"","firstName":"Shafeequdheen","middleName":"","lastName":"Palengara","suffix":""},{"id":535061578,"identity":"7449b555-f575-460f-9aee-14702236e356","order_by":1,"name":"Jyotiranjan Nayak","email":"","orcid":"","institution":"SRM University, Andhra Pradesh","correspondingAuthor":false,"prefix":"","firstName":"Jyotiranjan","middleName":"","lastName":"Nayak","suffix":""},{"id":535061579,"identity":"f667f44a-0c48-4375-aed0-f3b2f5d9816c","order_by":2,"name":"Vijayakrishna Rowthu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDklEQVRIiWNgGAWjYDACZoYEIJnAwMbAA+bLgYgDD0jRYgzWkkDYLpASiJbEBhgfFzA4zvDwM09NWj4f/9ljD34w3EufH3b4IdAWOzndBhxaDjMkS/Mcy7Fsk8hLN+xhKM7deDvNAKgl2djsAHYtks0MCdI8bBUGbBI8ZhI8DAm5G2cngLQcSNyGW0vyb55/QC38Z8wk/zAkpBvOTv+AVws/M0OaNG9bjgEbQ46ZNNCWBHnpHPy2gLRYzu1LAzoMqEXGIMFwg3ROwYEEA9x+Abon+cabb8kG8v1Ah72pSJCXn52++cOHCjs5XFqA0ZHAxAPnGADRASgDN2A/wPgDmS/fgE/1KBgFo2AUjEQAAFxUVoM39ZbpAAAAAElFTkSuQmCC","orcid":"","institution":"SRM University, Andhra Pradesh","correspondingAuthor":true,"prefix":"","firstName":"Vijayakrishna","middleName":"","lastName":"Rowthu","suffix":""}],"badges":[],"createdAt":"2025-09-26 03:08:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7717081/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7717081/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94716626,"identity":"856d4c07-7f3a-4500-896d-b147733b90b6","added_by":"auto","created_at":"2025-10-30 03:47:37","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4304,"visible":true,"origin":"","legend":"","description":"","filename":"6f351dd58efe4e189c5b24ccbd8aa69a.json","url":"https://assets-eu.researchsquare.com/files/rs-7717081/v1/cff11c90a9a91d323a731cee.json"},{"id":94730311,"identity":"de26f8a6-bc4d-4d81-a1fb-3fad3af6c387","added_by":"auto","created_at":"2025-10-30 07:05:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5725721,"visible":true,"origin":"","legend":"","description":"","filename":"DIFFEOMORPHICRECONSTRUCTIONOFA2DSIMPLE0ANONPARAMETRICMANIFOLDVIASHAPEGRADIENT.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7717081/v1_covered_1107774d-9f0d-4d2c-a8df-7f7a878c6ea3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Diffeomorphic Reconstruction of a 2D-Simple\nNon-Parametric Manifold Via Shape Gradient","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"signal-image-and-video-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"sivp","sideBox":"Learn more about [Signal, Image and Video Processing](http://link.springer.com/journal/11760)","snPcode":"11760","submissionUrl":"https://submission.nature.com/new-submission/11760/3","title":"Signal, Image and Video Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Simple Manifold, Non-Parametric Surface, Shape Gradient, Level Set, Signed Distance Function, Curvature, Hamilton-Jacobi equation","lastPublishedDoi":"10.21203/rs.3.rs-7717081/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7717081/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe present a variational method for reconstructing 2D simple manifolds from a given fixed level set data using shape gradients. 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