Ray-LLM: Suppressing Runge’s Phenomenon in Data-SparseFisheye Calibration via Neuro-Symbolic Synthetic Anchoring

Ray-LLM: Suppressing Runge’s Phenomenon in Data-SparseFisheye Calibration via Neuro-Symbolic Synthetic Anchoring | 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 Ray-LLM: Suppressing Runge’s Phenomenon in Data-SparseFisheye Calibration via Neuro-Symbolic Synthetic Anchoring Inho Jake Park This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8645116/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Standard fisheye calibration pipelines, utilizing the Kannala-Brandt model, rely on minimizing the Root-Mean-Square (RMS) reprojection error. While RMS is the statistically optimal estimator under Gaussian noise assumptions, its effectiveness is strictly conditional on the spatial distribution of observations. In practice, acquiring dense feature points at the lens periphery is notoriously labor-intensive, leading to unavoidable data sparsity. We demonstrate that applying the standard RMS objective to such sparse datasets induces a critical failure mode: the solver minimizes global error by overfitting the central region, resulting in unconstrained polynomial oscillations (Runge’s phenomenon) at the edges. To bridge this Data-Solver Gap, we propose Ray-LLM, a physics-informed active calibration framework. Crucially, we maintain the standard RMS optimization pipeline without modifying the solver. Instead, our method employs a Neuro-Symbolic Agent that diagnoses parameter instability and autonomously injects 'Physically-Anchored' synthetic data into sparse zones. This approach effectively acts as a dynamic geometric regularizer, constraining the polynomial coefficients to adhere to physical laws. Experimental results confirm that Ray-LLM enables the unmodified RMS solver to achieve superior geometric rectilinearity and stability in data-starved regimes, offering a labor-free alternative to exhaustive manual data collection. Large Language Model(LLM) Retrieval-Augmented Generation(RAG) Data Sparsity Synthetic Data Generation Physics-Informed Calibration Neuro-Symbolic AI Full Text Additional Declarations No competing interests reported. Supplementary Files RayLLMSuppressingRungesPhenomenoninDataSparseFisheyeCalibrationviaNeuroSymbolicSyntheticAnchoringSupplymentary.pdf Cite Share Download PDF Status: Posted 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. 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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-8645116","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":578498919,"identity":"30a5bc80-8b53-47ce-9c8b-1cc22f5011d2","order_by":0,"name":"Inho Jake Park","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYBACNgYeMG3AByIfVAAJZuYG4rSwgciEMyAtjPi1MKBoSWwDkQS08En3HnxcUHPPmI29x/BD4rzaaP52oJYfFdtwO0zmXLLxjGPFZmw8Z4wlErcdz51xmLGBsefMbdxaJHLMpHnYEmyADAOglmO5DUAtzIxthLT8A2sx/pE451jufKK08LYlmIEYEokNNbkbiNBibDyzL8GYjedYmUXCsQO5G4FaDuLzi/yMHMPHBd8SDPvZmzff+FBTlzvv/OGDD35U4NYCAswQisMASBwGMw/gVY/Qwv4ASNQRUjwKRsEoGAUjEAAA/Z1TWZ4OYnQAAAAASUVORK5CYII=","orcid":"","institution":"Among Solution Co.","correspondingAuthor":true,"prefix":"","firstName":"Inho","middleName":"Jake","lastName":"Park","suffix":""}],"badges":[],"createdAt":"2026-01-20 05:23:34","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8645116/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8645116/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104835564,"identity":"76f6767c-07f0-404c-b85e-7ff47147a683","added_by":"auto","created_at":"2026-03-17 17:46:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1318994,"visible":true,"origin":"","legend":"","description":"","filename":"RayLLMLatex.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8645116/v1_covered_ad4b703c-a1e5-4b17-90b1-7e66b631991d.pdf"},{"id":104817915,"identity":"b39efc93-fd38-4d31-819c-77c1296ed8ec","added_by":"auto","created_at":"2026-03-17 13:53:05","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":3906235,"visible":true,"origin":"","legend":"","description":"","filename":"RayLLMSuppressingRungesPhenomenoninDataSparseFisheyeCalibrationviaNeuroSymbolicSyntheticAnchoringSupplymentary.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8645116/v1/6c107e45ba3ea49c8b3e4a37.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Ray-LLM: Suppressing Runge’s Phenomenon in Data-SparseFisheye Calibration via Neuro-Symbolic Synthetic Anchoring","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Large Language Model(LLM), Retrieval-Augmented Generation(RAG), Data Sparsity, Synthetic Data Generation, Physics-Informed Calibration, Neuro-Symbolic AI","lastPublishedDoi":"10.21203/rs.3.rs-8645116/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8645116/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e Standard fisheye calibration pipelines, utilizing the Kannala-Brandt model, rely on minimizing the Root-Mean-Square (RMS) reprojection error. While RMS is the statistically optimal estimator under Gaussian noise assumptions, its effectiveness is strictly conditional on the spatial distribution of observations. In practice, acquiring dense feature points at the lens periphery is notoriously labor-intensive, leading to unavoidable data sparsity. We demonstrate that applying the standard RMS objective to such sparse datasets induces a critical failure mode: the solver minimizes global error by overfitting the central region, resulting in unconstrained polynomial oscillations (Runge\u0026rsquo;s phenomenon) at the edges. To bridge this Data-Solver Gap, we propose Ray-LLM, a physics-informed active calibration framework. Crucially, we maintain the standard RMS optimization pipeline without modifying the solver. Instead, our method employs a Neuro-Symbolic Agent that diagnoses parameter instability and autonomously injects 'Physically-Anchored' synthetic data into sparse zones. This approach effectively acts as a dynamic geometric regularizer, constraining the polynomial coefficients to adhere to physical laws. Experimental results confirm that Ray-LLM enables the unmodified RMS solver to achieve superior geometric rectilinearity and stability in data-starved regimes, offering a labor-free alternative to exhaustive manual data collection.\u003c/p\u003e","manuscriptTitle":"Ray-LLM: Suppressing Runge’s Phenomenon in Data-SparseFisheye Calibration via Neuro-Symbolic Synthetic Anchoring","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-17 13:53:00","doi":"10.21203/rs.3.rs-8645116/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a90caf32-f99c-4e3a-9056-ed9874d12e83","owner":[],"postedDate":"March 17th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-17T13:53:00+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-17 13:53:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8645116","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8645116","identity":"rs-8645116","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}