A Real-Time 2D-3D Registration Algorithm for Spine Surgery Navigation Using Accelerated Gradient Optimization

A Real-Time 2D-3D Registration Algorithm for Spine Surgery Navigation Using Accelerated Gradient Optimization | 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 Real-Time 2D-3D Registration Algorithm for Spine Surgery Navigation Using Accelerated Gradient Optimization Jun-Ming Zhang, Yan-Yan Zhang, Ying-Ying Yan, Xiao-Xiao Xuan, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8380892/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Two-dimensional to three-dimensional (2D–3D) medical image registration plays a critical role in image-guided spinal surgery, enabling accurate alignment between intraoperative fluoroscopy and preoperative CT volumes. However, existing methods often suffer from slow convergence or high computational demands, limiting their use in time-sensitive clinical settings. To address this challenge, we propose a semi-automatic 2D–3D registration algorithm that integrates a grid-based initialization strategy with Nesterov-accelerated gradient (NAG) optimization. The method first coarsely aligns anatomical landmarks via vertebral segmentation on a grid, then refines the transformation parameters by maximizing a novel similarity metric—Normalized Cross-Correlation–Gradient Difference–Projection Distance Error (NGE)—using momentum-enhanced gradient descent. Evaluated on clinical spine datasets, our approach achieves a root mean square (RMS) registration error of 0.82 ± 0.15 mm with an average processing time of 15.2 seconds per case, outperforming conventional gradient descent (28.7 s) and Gauss–Newton (22.4 s) methods in both speed and accuracy. These results demonstrate the algorithm’s potential for real-time surgical navigation, where rapid and sub-millimeter precision is essential. 2D-3D image registration real-time 2D-3D registration GPU acceleration surgical navigation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 06 Mar, 2026 Reviews received at journal 04 Feb, 2026 Reviews received at journal 31 Jan, 2026 Reviewers agreed at journal 26 Jan, 2026 Reviewers agreed at journal 25 Jan, 2026 Reviewers agreed at journal 16 Jan, 2026 Reviewers invited by journal 14 Jan, 2026 Editor assigned by journal 12 Jan, 2026 Editor invited by journal 22 Dec, 2025 Submission checks completed at journal 22 Dec, 2025 First submitted to journal 22 Dec, 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. 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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-8380892","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":575831205,"identity":"d8907ec7-26e9-4ad5-966d-59f206ce4b4c","order_by":0,"name":"Jun-Ming Zhang","email":"","orcid":"","institution":"Jiyang College, Zhejiang A\u0026F University","correspondingAuthor":false,"prefix":"","firstName":"Jun-Ming","middleName":"","lastName":"Zhang","suffix":""},{"id":575831206,"identity":"0db8a40d-4889-4480-aa14-ddd53b8719ef","order_by":1,"name":"Yan-Yan Zhang","email":"","orcid":"","institution":"Jiyang College, Zhejiang A\u0026F 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However, existing methods often suffer from slow convergence or high computational demands, limiting their use in time-sensitive clinical settings. To address this challenge, we propose a semi-automatic 2D\u0026ndash;3D registration algorithm that integrates a grid-based initialization strategy with Nesterov-accelerated gradient (NAG) optimization. The method first coarsely aligns anatomical landmarks via vertebral segmentation on a grid, then refines the transformation parameters by maximizing a novel similarity metric\u0026mdash;Normalized Cross-Correlation\u0026ndash;Gradient Difference\u0026ndash;Projection Distance Error (NGE)\u0026mdash;using momentum-enhanced gradient descent. Evaluated on clinical spine datasets, our approach achieves a root mean square (RMS) registration error of 0.82\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15 mm with an average processing time of 15.2 seconds per case, outperforming conventional gradient descent (28.7 s) and Gauss\u0026ndash;Newton (22.4 s) methods in both speed and accuracy. These results demonstrate the algorithm\u0026rsquo;s potential for real-time surgical navigation, where rapid and sub-millimeter precision is essential.\u003c/p\u003e","manuscriptTitle":"A Real-Time 2D-3D Registration Algorithm for Spine Surgery Navigation Using Accelerated Gradient Optimization","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-19 05:12:44","doi":"10.21203/rs.3.rs-8380892/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-06T09:51:59+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-04T17:39:55+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-31T17:17:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"329554816701906542255274839718914085187","date":"2026-01-26T07:43:50+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"239146430142528033862929848203089481017","date":"2026-01-25T08:44:48+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"177918373246200648460299812333076081506","date":"2026-01-16T21:15:07+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-14T16:01:21+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-13T03:41:04+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-12-22T11:54:02+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-22T10:11:12+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Medical Imaging","date":"2025-12-22T10:03:00+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-medical-imaging","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmim","sideBox":"Learn more about [BMC Medical Imaging](http://bmcmedimaging.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/bmim/default.aspx","title":"BMC Medical Imaging","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a516b1ff-f6f4-439e-982d-861712788c58","owner":[],"postedDate":"January 19th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-22T13:53:14+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-19 05:12:44","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8380892","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8380892","identity":"rs-8380892","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}