Fundamental Limits of Subpixel Detectability in Imaging Systems: An Analytical Framework for Uav Detection

Fundamental Limits of Subpixel Detectability in Imaging Systems: An Analytical Framework for Uav Detection | 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 Fundamental Limits of Subpixel Detectability in Imaging Systems: An Analytical Framework for Uav Detection Alexandr Butenko, Beibit Kassimov, Dmitriy Xenofontov, Nurzhan Zikiryaev, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9556944/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract The detection of compact unmanned aerial vehicles (UAVs) in the subpixel imaging regime represents a fundamental limitation of electro-optical surveillance systems. When the projected target footprint falls below the detector pixel pitch, morphological information is lost, and detectability is governed by radiometric energy distribution and statistical noise fluctuations. This work develops a unified analytical framework that, for the first time, jointly integrates subpixel projection geometry, point spread function (PSF) effects, discrete detector sampling, temporal integration, and Neyman–Pearson statistical detection theory into a closed-form performance model. Explicit expressions are derived for detection probability as a function of effective signal-to-noise ratio, pixel occupancy ratio, and temporal integration length. Based on this formulation, the Subpixel Detectability Threshold (SDT) is defined as the minimum effective SNR required to achieve a prescribed detection probability at a fixed false alarm rate. The proposed model establishes a closed-form detectability boundary and reveals a fundamental scaling law for maximum detection range, showing that temporal integration improves detection range only as \(\:{\varvec{N}}^{\left(1/4\right)}\) , thereby quantifying the diminishing returns of Track-Before-Detect processing. Monte Carlo simulations validate the analytical predictions and demonstrate close agreement with theoretical predictions, with minor deviations attributed to finite sampling and threshold estimation effects. Unlike existing algorithm-driven approaches, the proposed framework provides sensor-agnostic, physics-grounded performance limits and offers a quantitative design tool for next-generation imaging-based detection systems operating in the subpixel regime. Subpixel detection Detection theory Electro-optical imaging Point spread function Signal-to-noise ratio Track-Before-Detect Temporal integration Imaging system design Performance limits Small target detection Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 04 May, 2026 Editor assigned by journal 02 May, 2026 Submission checks completed at journal 01 May, 2026 First submitted to journal 28 Apr, 2026 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-9556944","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":634432807,"identity":"f064bf7c-c44a-4b32-a8c2-0f5cac1981c0","order_by":0,"name":"Alexandr 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When the projected target footprint falls below the detector pixel pitch, morphological information is lost, and detectability is governed by radiometric energy distribution and statistical noise fluctuations.\u003c/p\u003e \u003cp\u003eThis work develops a unified analytical framework that, for the first time, jointly integrates subpixel projection geometry, point spread function (PSF) effects, discrete detector sampling, temporal integration, and Neyman\u0026ndash;Pearson statistical detection theory into a closed-form performance model. Explicit expressions are derived for detection probability as a function of effective signal-to-noise ratio, pixel occupancy ratio, and temporal integration length.\u003c/p\u003e \u003cp\u003eBased on this formulation, the Subpixel Detectability Threshold (SDT) is defined as the minimum effective SNR required to achieve a prescribed detection probability at a fixed false alarm rate. The proposed model establishes a closed-form detectability boundary and reveals a fundamental scaling law for maximum detection range, showing that temporal integration improves detection range only as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{N}}^{\\left(1/4\\right)}\\)\u003c/span\u003e\u003c/span\u003e, thereby quantifying the diminishing returns of Track-Before-Detect processing.\u003c/p\u003e \u003cp\u003eMonte Carlo simulations validate the analytical predictions and demonstrate close agreement with theoretical predictions, with minor deviations attributed to finite sampling and threshold estimation effects. Unlike existing algorithm-driven approaches, the proposed framework provides sensor-agnostic, physics-grounded performance limits and offers a quantitative design tool for next-generation imaging-based detection systems operating in the subpixel regime.\u003c/p\u003e","manuscriptTitle":"Fundamental Limits of Subpixel Detectability in Imaging Systems: An Analytical Framework for Uav Detection","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-12 22:29:37","doi":"10.21203/rs.3.rs-9556944/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewersInvited","content":"","date":"2026-05-05T00:51:41+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-05-02T08:22:12+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-05-01T12:08:41+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal on Information Security","date":"2026-04-28T16:58:59+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-on-information-security","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Journal on Information Security](https://link.springer.com/journal/13635)","snPcode":"13635","submissionUrl":"https://submission.springernature.com/new-submission/13635/3","title":"Journal on Information Security","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"acbcef4e-3e70-4a3b-81a7-7670429b23c4","owner":[],"postedDate":"May 12th, 2026","published":true,"recentEditorialEvents":[{"type":"reviewersInvited","content":"3","date":"2026-05-05T00:51:41+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-05-02T08:22:12+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-05-01T12:08:41+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-12T22:29:38+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-12 22:29:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9556944","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9556944","identity":"rs-9556944","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}