Characterization of the multiplicity of solutions for camera pose given two vertically-aligned landmarks and accelerometer

Characterization of the multiplicity of solutions for camera pose given two vertically-aligned landmarks and accelerometer | 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 Characterization of the multiplicity of solutions for camera pose given two vertically-aligned landmarks and accelerometer Alexander Robert Pruss This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5284866/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 We consider the problem of recovering the position and orientation of a camera equipped with an accelerometer from sensor images of two labeled landmarks whose positions in a coordinate system aligned in a known way with gravity are known. This a variant on the much studied PnP problem of recovering camera position and orientation from n points without any gravitational data. It is proved that in three types of singular cases there are infinitely many solutions, in another type of case there is one, and in a final type of case there are two. A precise characterization of each type of case. In particular, there is always a unique solution in the practically interesting case where the two landmarks are at the same altitude and the camera is at a different altitude. This case is studied by numerical simulation and an implementation on a consumer cellphone. It is also proved that if the two landmarks are unlabeled, then apart from the same singular cases, there are still always one or two solutions. Full Text Additional Declarations No competing interests reported. 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. 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-5284866","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":367454571,"identity":"23133621-a752-4dce-b615-ec75ecde15eb","order_by":0,"name":"Alexander Robert Pruss","email":"data:image/png;base64,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","orcid":"","institution":"Baylor University","correspondingAuthor":true,"prefix":"","firstName":"Alexander","middleName":"Robert","lastName":"Pruss","suffix":""}],"badges":[],"createdAt":"2024-10-17 19:08:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5284866/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5284866/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81137830,"identity":"c314a99e-7703-43c9-9f11-56ff99dc5702","added_by":"auto","created_at":"2025-04-22 16:01:19","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1241864,"visible":true,"origin":"","legend":"","description":"","filename":"camera.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5284866/v1_covered_1a12a038-e3be-4d57-937c-13eeec513edc.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Characterization of the multiplicity of solutions for camera pose given two vertically-aligned landmarks and accelerometer","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-5284866/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5284866/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We consider the problem of recovering the position and orientation of a camera equipped with an accelerometer from sensor images of two labeled landmarks whose positions in a coordinate system aligned in a known way with gravity are known. 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