Quantitative Kernel Estimation from Traffic Signs using Slanted Edge Spatial Frequency Response as a Sharpness Metric

Quantitative Kernel Estimation from Traffic Signs using Slanted Edge Spatial Frequency Response as a Sharpness Metric | 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 Article Quantitative Kernel Estimation from Traffic Signs using Slanted Edge Spatial Frequency Response as a Sharpness Metric Amit Pandey, Mohd. Zubair Akhtar, Nandana Kappuva Veettil, Bernhard Wunderle, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6725582/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Feb, 2026 Read the published version in Scientific Reports → Version 1 posted 15 You are reading this latest preprint version Abstract The sharpness is a critical optical property of automotive cameras, measured by the Spatial Frequency Response (SFR) within the end of line (EOL) test after manufacturing. This work presents a method to estimate the blurring kernel of automotive camera for state monitoring. To achieve this, Principal Component Analysis (PCA) is performed, using synthetic kernels generated by Zemax. The PCA model is built with approximately 1300 base kernels representing spatially variant point spread functions (PSFs). This model generates kernel samples during the estimation process. Synthetic images are created by convolving the synthetic kernels with reference traffic sign images and compared with real-life data captured by an automotive camera. These synthetic data are utilized for algorithm development, and later on validation is performed on real-life data. The algorithm extracts two 45 x 45 pixels regions of interest (ROIs) containing slanted edges from the blurred image and crops matching ROIs from a reference sharp image. Each candidate kernel blurs the reference ROIs, and the resulting Spatial Frequency Response (SFR) is compared with the blurred ROIs’ SFR. Differential evolution optimization minimizes the SFR difference, selecting the kernel that best matches the observed blur. The final kernel is evaluated against the true kernel for accuracy. Structural similarity index measure (SSIM) between the original and estimated blurred ROIs ranges from 0.808 to 0.945. For true vs. estimated kernels, SSIM varies from 0.92 to 0.98. Pearson correlation coefficients range from 0.84 to 0.99, Cosine similarity from 0.86 to 0.98, and mean squared error (MSE) from 1.1 x 10-5 to 8.3 x 10-5. Validation on real-life camera images shows that the SSIM between estimated ROI is >0.82 indicating a sufficient level of accuracy in kernel estimation to detect potential degradation of the camera. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 19 Feb, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 25 Nov, 2025 Reviews received at journal 24 Nov, 2025 Reviews received at journal 24 Nov, 2025 Reviews received at journal 22 Nov, 2025 Reviewers agreed at journal 19 Nov, 2025 Reviewers agreed at journal 17 Nov, 2025 Reviewers agreed at journal 14 Nov, 2025 Editor assigned by journal 14 Nov, 2025 Editor invited by journal 06 Nov, 2025 Reviews received at journal 10 Aug, 2025 Reviewers agreed at journal 10 Aug, 2025 Reviewers agreed at journal 08 Aug, 2025 Reviewers invited by journal 08 Aug, 2025 Submission checks completed at journal 02 Aug, 2025 First submitted to journal 29 Jul, 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. 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-6725582","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":502600424,"identity":"8ab1c2e3-8beb-4cfa-9815-f1100bff2266","order_by":0,"name":"Amit Pandey","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYFACxgYIfYCB8QFjgwSIQVBLYwNUC7PBQeK0wKw5wMAmcbCBgbAW/mmH2x8w7rDL4zveY1b9cYcFA9/xBvxaJG4nNjYwnkkuljxzxuzGwTMSDJJnCFkD1tLGnLjhRg5QS5sEg8GNBPw65CFa6hM33H9jVgDWcv8Bfi0GEC2HgbbwmDFAbCHgLkOglhmJZ44nzjyTVixxtk2CR/IMAYfJ3U5/8OHjjurEvuOHN36obKuT4zt+gIA1IJDYACI5DEAkDxHqGWCRyf6AONWjYBSMglEw4gAALVBS6zDdnogAAAAASUVORK5CYII=","orcid":"","institution":"Technische Hochschule Ingolstadt","correspondingAuthor":true,"prefix":"","firstName":"Amit","middleName":"","lastName":"Pandey","suffix":""},{"id":502600425,"identity":"1c61d2da-e180-4f2c-b673-1847c42c9a30","order_by":1,"name":"Mohd. Zubair Akhtar","email":"","orcid":"","institution":"Technische Hochschule Ingolstadt","correspondingAuthor":false,"prefix":"","firstName":"Mohd.","middleName":"Zubair","lastName":"Akhtar","suffix":""},{"id":502600426,"identity":"a9613dd9-5ef5-4fa2-a80a-4dea8d3f0ac1","order_by":2,"name":"Nandana Kappuva Veettil","email":"","orcid":"","institution":"Technische Hochschule Ingolstadt","correspondingAuthor":false,"prefix":"","firstName":"Nandana","middleName":"Kappuva","lastName":"Veettil","suffix":""},{"id":502600427,"identity":"34600212-84cd-431b-a1e5-3d4971e355ad","order_by":3,"name":"Bernhard Wunderle","email":"","orcid":"","institution":"Technische Universität Chemnitz","correspondingAuthor":false,"prefix":"","firstName":"Bernhard","middleName":"","lastName":"Wunderle","suffix":""},{"id":502600428,"identity":"6aa73b79-c794-401b-bafd-4367b0ad9a2b","order_by":4,"name":"Gordon Elger","email":"","orcid":"","institution":"Technische Hochschule Ingolstadt","correspondingAuthor":false,"prefix":"","firstName":"Gordon","middleName":"","lastName":"Elger","suffix":""}],"badges":[],"createdAt":"2025-05-22 13:38:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6725582/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6725582/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-026-40556-w","type":"published","date":"2026-02-19T15:57:36+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":103251067,"identity":"7a597c9b-9fff-4eb9-a175-a61acc705883","added_by":"auto","created_at":"2026-02-23 16:03:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1540493,"visible":true,"origin":"","legend":"","description":"","filename":"InfieldkernelestimationOpticaCopy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6725582/v1_covered_99ae80d8-d1ba-432a-a656-be6822686834.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Quantitative Kernel Estimation from Traffic Signs using Slanted Edge Spatial Frequency Response as a Sharpness Metric","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6725582/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6725582/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The sharpness is a critical optical property of automotive cameras, measured by the Spatial Frequency Response (SFR) within the end of line (EOL) test after manufacturing. This work presents a method to estimate the blurring kernel of automotive camera for state monitoring. To achieve this, Principal Component Analysis (PCA) is performed, using synthetic kernels generated by Zemax. The PCA model is built with approximately 1300 base kernels representing spatially variant point spread functions (PSFs). This model generates kernel samples during the estimation process. Synthetic images are created by convolving the synthetic kernels with reference traffic sign images and compared with real-life data captured by an automotive camera. These synthetic data are utilized for algorithm development, and later on validation is performed on real-life data. The algorithm extracts two 45 x 45 pixels regions of interest (ROIs) containing slanted edges from the blurred image and crops matching ROIs from a reference sharp image. Each candidate kernel blurs the reference ROIs, and the resulting Spatial Frequency Response (SFR) is compared with the blurred ROIs’ SFR. Differential evolution optimization minimizes the SFR difference, selecting the kernel that best matches the observed blur. The final kernel is evaluated against the true kernel for accuracy. Structural similarity index measure (SSIM) between the original and estimated blurred ROIs ranges from 0.808 to 0.945. For true vs. estimated kernels, SSIM varies from 0.92 to 0.98. Pearson correlation coefficients range from 0.84 to 0.99, Cosine similarity from 0.86 to 0.98, and mean squared error (MSE) from 1.1 x 10-5 to 8.3 x 10-5. Validation on real-life camera images shows that the SSIM between estimated ROI is \u003e0.82 indicating a sufficient level of accuracy in kernel estimation to detect potential degradation of the camera.","manuscriptTitle":"Quantitative Kernel Estimation from Traffic Signs using Slanted Edge Spatial Frequency Response as a Sharpness Metric","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-27 08:40:46","doi":"10.21203/rs.3.rs-6725582/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-25T18:35:43+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-25T02:26:58+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-24T10:51:24+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-22T12:25:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"312259341908292864868024439285316658034","date":"2025-11-19T09:37:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"207182080749581050214204540250583619203","date":"2025-11-17T07:46:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"236178349223379445812482156714892594722","date":"2025-11-14T12:00:11+00:00","index":"hide","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-14T09:09:51+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-11-06T17:30:34+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-10T19:25:49+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"289035480234075634565182875099383454846","date":"2025-08-10T11:36:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"116783099542518860252111596161817956538","date":"2025-08-08T09:45:46+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-08T09:14:20+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-02T12:14:06+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-07-29T10:00:04+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"814ed62a-48c4-493e-b813-fa704ed74b28","owner":[],"postedDate":"August 27th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-02-23T16:01:00+00:00","versionOfRecord":{"articleIdentity":"rs-6725582","link":"https://doi.org/10.1038/s41598-026-40556-w","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-02-19 15:57:36","publishedOnDateReadable":"February 19th, 2026"},"versionCreatedAt":"2025-08-27 08:40:46","video":"","vorDoi":"10.1038/s41598-026-40556-w","vorDoiUrl":"https://doi.org/10.1038/s41598-026-40556-w","workflowStages":[]},"version":"v1","identity":"rs-6725582","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6725582","identity":"rs-6725582","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}