Adaptive Riemannian Optimization for Multi-Scale Diffeomorphic Matching

Adaptive Riemannian Optimization for Multi-Scale Diffeomorphic Matching | 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 Biological Sciences - Article Adaptive Riemannian Optimization for Multi-Scale Diffeomorphic Matching James Gee, Rohit Jena, Pratik Chaudhari This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6289791/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract The paper proposes FireANTs, the first multi-scale Adaptive Riemannian Optimization algorithm for dense diffeomorphic image matching. One of the most critical and understudied aspects of diffeomorphic image matching algorithms are its highly ill-conditioned nature. We quantitatively capture the extent of ill-conditioning in a typical MRI matching task, motivating the need for an adaptive optimization algorithm for diffeomorphic matching. To this end, FireANTs generalizes the concept of momentum and adaptive estimates of the Hessian to mitigate this ill-conditioning in the non-Euclidean space of diffeomorphisms. Unlike common non-Euclidean manifolds, we also formalize considerations for multi-scale optimization of diffeomorphisms. Our rigorous mathematical results and operational contributions lead to a state-of-the-art dense matching algorithm that can be applied to generic image data with remarkable accuracy and robustness. We demonstrate consistent improvements in image matching performance across a spectrum of community-standard medical and biological correspondence matching challenges spanning a wide variety of image modalities, anatomies, resolutions, acquisition protocols, and preprocessing pipelines. This improvement is supplemented by 300x to 3200x speedup over existing CPU-based state-of-the-art algorithms. For the first time, we perform diffeomorphic matching of sub-micron mouse isocortex volumes at native resolution, and generate a 25µm mouse brain atlas in under 25 minutes. Our fast implementation also enables hyperparameter studies that were intractable with existing correspondence matching algorithms. Physical sciences/Mathematics and computing/Computer science Health sciences/Health care/Medical imaging/Brain imaging Health sciences/Health care/Medical imaging/Radiography correspondence matching deformable image matching diffeomorphisms optimization non-Euclidean manifold microscopy neuroimaging Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review Version 1 posted 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. 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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-6289791","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Biological Sciences - Article","associatedPublications":[],"authors":[{"id":438138681,"identity":"548a5f56-4474-4887-86d9-a8e7fd1c68d2","order_by":0,"name":"James Gee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAq0lEQVRIiWNgGAWjYHACxgcwlgSxWpgNSNbCBldJnBZ59+Zj1bw7bPLMGZgP3uYhRovhmWNpt3nPpBVbNrAlWxOnZUaO2W3etsOJGw7wmEkTp2X++2/FvG3/gVr4vxGnRV6Ch42Zt+0AyBY24rQY8KQZS849k5y44TCbseUcomxpP/zww9sddokbjjc/vPGGKFsOAAnGBiDBTIxysC0NMC2jYBSMglEwCnABAMTSMJhIaebfAAAAAElFTkSuQmCC","orcid":"","institution":"University of Pennsylvania","correspondingAuthor":true,"prefix":"","firstName":"James","middleName":"","lastName":"Gee","suffix":""},{"id":438138682,"identity":"af851b04-b47b-480b-84eb-b9e834114942","order_by":1,"name":"Rohit Jena","email":"","orcid":"","institution":"University of Pennsylvania","correspondingAuthor":false,"prefix":"","firstName":"Rohit","middleName":"","lastName":"Jena","suffix":""},{"id":438138683,"identity":"6fb4fd67-b587-446a-99b7-ce701c8fb4dd","order_by":2,"name":"Pratik Chaudhari","email":"","orcid":"","institution":"University of Pennsylvania","correspondingAuthor":false,"prefix":"","firstName":"Pratik","middleName":"","lastName":"Chaudhari","suffix":""}],"badges":[],"createdAt":"2025-03-23 18:35:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6289791/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6289791/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82062790,"identity":"6a8819d1-e87f-4440-af98-8d2438210bdc","added_by":"auto","created_at":"2025-05-06 12:06:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2968509,"visible":true,"origin":"","legend":"Article File","description":"","filename":"FireANTsnaturecomms.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6289791/v1_covered_4b3f37fb-5eb7-40c0-8380-35e4f99b9ca7.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Adaptive Riemannian Optimization for Multi-Scale Diffeomorphic Matching","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"correspondence matching, deformable image matching, diffeomorphisms, optimization, non-Euclidean manifold, microscopy, neuroimaging","lastPublishedDoi":"10.21203/rs.3.rs-6289791/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6289791/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The paper proposes FireANTs, the first multi-scale Adaptive Riemannian Optimization\r\nalgorithm for dense diffeomorphic image matching. One of the most critical and understudied\r\naspects of diffeomorphic image matching algorithms are its highly ill-conditioned nature. We\r\nquantitatively capture the extent of ill-conditioning in a typical MRI matching task, motivating the\r\nneed for an adaptive optimization algorithm for diffeomorphic matching. To this end, FireANTs\r\ngeneralizes the concept of momentum and adaptive estimates of the Hessian to mitigate this\r\nill-conditioning in the non-Euclidean space of diffeomorphisms. Unlike common non-Euclidean\r\nmanifolds, we also formalize considerations for multi-scale optimization of diffeomorphisms.\r\nOur rigorous mathematical results and operational contributions lead to a state-of-the-art dense\r\nmatching algorithm that can be applied to generic image data with remarkable accuracy and\r\nrobustness. We demonstrate consistent improvements in image matching performance across a\r\nspectrum of community-standard medical and biological correspondence matching challenges\r\nspanning a wide variety of image modalities, anatomies, resolutions, acquisition protocols, and\r\npreprocessing pipelines. This improvement is supplemented by 300x to 3200x speedup over\r\nexisting CPU-based state-of-the-art algorithms. For the first time, we perform diffeomorphic\r\nmatching of sub-micron mouse isocortex volumes at native resolution, and generate a 25µm mouse\r\nbrain atlas in under 25 minutes. Our fast implementation also enables hyperparameter studies that\r\nwere intractable with existing correspondence matching algorithms.","manuscriptTitle":"Adaptive Riemannian Optimization for Multi-Scale Diffeomorphic Matching","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-06 11:58:01","doi":"10.21203/rs.3.rs-6289791/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"64216677-0ce2-4fb4-841f-2bd7ed872c6f","owner":[],"postedDate":"May 6th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":46657498,"name":"Physical sciences/Mathematics and computing/Computer science"},{"id":46657499,"name":"Health sciences/Health care/Medical imaging/Brain imaging"},{"id":46657500,"name":"Health sciences/Health care/Medical imaging/Radiography"}],"tags":[],"updatedAt":"2025-05-06T11:58:01+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-06 11:58:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6289791","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6289791","identity":"rs-6289791","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}