A Novel Multi-wavelet Multi-scale Dynamic Integral Framework for Real-Time Industrial Surface Defect Detection

A Novel Multi-wavelet Multi-scale Dynamic Integral Framework for Real-Time Industrial Surface Defect 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 A Novel Multi-wavelet Multi-scale Dynamic Integral Framework for Real-Time Industrial Surface Defect Detection xiaoyang zheng, hongfei pan, Zhejiang yu, shiyu liu, Zhengyuan Wei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9295493/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Due to the extreme irregular surface defects exhibiting variations in random shape, size, and distribution on industrialproductions, it is difficult for the traditional defect detection models to achieve a good balance between the precisionand efficiency. To address these challenges, this paper contributes to three key innovations: On the one hand, theLegendre wavelet convolution (LWConv) module is devised to reduce the number of parameters in deep learningmodels to improve inference speed and noise-robust. On the other hand, the C2f_Dynamic-Integral (C2f_DI) mod-ule is implemented to enhance and optimize the corner, edge, and interior weight ratios to accurately represent thecomplex features of the defects by using learnable trapezoidal integration kernels. Finally, the improved deformableprogressive pyramid aggregation (IDPPA) is utilized to fuse the multi-scale defect features by alternating convolu-tional modules. In brief, the proposed multi-wavelet multi-scale dynamic integral network based on YOLOv12 isabbreviated to LWDIYOLO-Net. Subsequently, the defect detection performance of LWDIYOLO-Net is validatedon two datasets. On the aluminum plate dataset, LWDIYOLO-Net attains 98.8% mAP50 while processing images at879.6 FPS. On the PCB dataset, LWDIYOLO-Net achieves precision of 98.8%, mAP50 of 99.2%, and F1 score of98.6% by using 2.36 M parameters and 121 FPS. The extensive experiment results demonstrate that LWDIYOLO-Netachieves the faster inference speed and better detection accuracy than those state-of-the-art methods. YOLOv12 Industrial surface defect detection Legendre wavelet Attention mechanism Numerical Integral Full Text Additional Declarations No competing interests reported. Supplementary Files image1.png image7.png image3.png image2.png image5.png image6.png image9.png image8.png image4.png Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 04 May, 2026 Reviewers agreed at journal 17 Apr, 2026 Reviewers agreed at journal 16 Apr, 2026 Reviewers invited by journal 16 Apr, 2026 Editor assigned by journal 16 Apr, 2026 Submission checks completed at journal 16 Apr, 2026 First submitted to journal 01 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. 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-9295493","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":626085703,"identity":"09689d92-448e-4259-87a7-1100cea69ce5","order_by":0,"name":"xiaoyang zheng","email":"","orcid":"","institution":"Chongqing University of Technology","correspondingAuthor":false,"prefix":"","firstName":"xiaoyang","middleName":"","lastName":"zheng","suffix":""},{"id":626085704,"identity":"1d66b0f7-c98f-4dd9-8350-a16b2a53c5d5","order_by":1,"name":"hongfei pan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYBACNvb+xw8kDCTq57M3HyBOCx/PGTYDiwoLxo09xxKI0yIn4cMgUXGmgrHhRo4BkQ6T4D1gcLNNgplxRs7HG28Y7OR0Gwhpke5LeDizTYKNneftZss5DMnGZgcIaZE5YGAs2SbBw9ieu02ah+FA4jaCWiQSDKT/tklIMBzIeUaslhwDCYkzEgYMJ3LYiNTCcyzNQKJCIsGw55ix5RwDIvwi3958GBiVdQny7M0Pb7ypsJMjqAUFSPAQGTXIWkjVMQpGwSgYBSMCAACxN0BmX87d7gAAAABJRU5ErkJggg==","orcid":"","institution":"Chongqing University of Technology","correspondingAuthor":true,"prefix":"","firstName":"hongfei","middleName":"","lastName":"pan","suffix":""},{"id":626085705,"identity":"4d4ec1ce-1582-4122-bd85-0c51886babcc","order_by":2,"name":"Zhejiang yu","email":"","orcid":"","institution":"Chongqing University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Zhejiang","middleName":"","lastName":"yu","suffix":""},{"id":626085707,"identity":"152bd912-2818-4247-b401-c2eb4f4f6887","order_by":3,"name":"shiyu liu","email":"","orcid":"","institution":"Chongqing University of Technology","correspondingAuthor":false,"prefix":"","firstName":"shiyu","middleName":"","lastName":"liu","suffix":""},{"id":626085712,"identity":"20eb4a20-a88f-479b-816e-6560cdd4c441","order_by":4,"name":"Zhengyuan Wei","email":"","orcid":"","institution":"Chongqing University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Zhengyuan","middleName":"","lastName":"Wei","suffix":""}],"badges":[],"createdAt":"2026-04-01 19:23:55","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9295493/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9295493/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107709328,"identity":"53fff055-fc45-4abb-804f-d2a75656f9a2","added_by":"auto","created_at":"2026-04-24 09:35:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":675238,"visible":true,"origin":"","legend":"","description":"","filename":"468198LaTeXDL46819801072021.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9295493/v1_covered_83ba663c-55f4-4b1d-94eb-0f6d5cdaba6f.pdf"},{"id":107625243,"identity":"feb5595c-61f4-40a5-811c-a3d4500c6f77","added_by":"auto","created_at":"2026-04-23 10:25:18","extension":"png","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1342475,"visible":true,"origin":"","legend":"","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-9295493/v1/7a94e0f2079cd5192cc46cac.png"},{"id":107625160,"identity":"df62331a-04e7-43dc-8fd8-bdb445a021bc","added_by":"auto","created_at":"2026-04-23 10:24:51","extension":"png","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1127278,"visible":true,"origin":"","legend":"","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-9295493/v1/8bd173578d967f45ce5077e4.png"},{"id":107625152,"identity":"e19b0326-953d-4cac-9045-27a21f39fdbc","added_by":"auto","created_at":"2026-04-23 10:24:48","extension":"png","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":72019,"visible":true,"origin":"","legend":"","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-9295493/v1/8907872774882ee611c8c03c.png"},{"id":107625213,"identity":"03d16d85-d075-4a91-803e-b3c1d06d7cf8","added_by":"auto","created_at":"2026-04-23 10:25:12","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":1315389,"visible":true,"origin":"","legend":"","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-9295493/v1/2e2cbcb8106e2f349d3bfe78.png"},{"id":107625157,"identity":"9756f394-6f7b-4c32-bcd1-c57d6f0965a4","added_by":"auto","created_at":"2026-04-23 10:24:50","extension":"png","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":2230336,"visible":true,"origin":"","legend":"","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-9295493/v1/e6aad288a4b3a623f438cab2.png"},{"id":107625135,"identity":"beb45a79-d851-4768-8f23-08d89e388ddf","added_by":"auto","created_at":"2026-04-23 10:24:46","extension":"png","order_by":5,"title":"","display":"","copyAsset":false,"role":"supplement","size":970816,"visible":true,"origin":"","legend":"","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-9295493/v1/0c70c5bb9bfe3baef49f783a.png"},{"id":107707244,"identity":"bec1f09c-cabf-4fc4-986b-83bf841f5e01","added_by":"auto","created_at":"2026-04-24 09:19:53","extension":"png","order_by":6,"title":"","display":"","copyAsset":false,"role":"supplement","size":2441308,"visible":true,"origin":"","legend":"","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-9295493/v1/9cbfd096d6a4c4f72b68e0fc.png"},{"id":107625134,"identity":"8f9d680a-8cca-4248-9eeb-46c3a7796b32","added_by":"auto","created_at":"2026-04-23 10:24:46","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"supplement","size":1835521,"visible":true,"origin":"","legend":"","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-9295493/v1/8feec3755a060133282258aa.png"},{"id":107625170,"identity":"c84df80e-9c89-4718-8c99-b34a8c1d5ccd","added_by":"auto","created_at":"2026-04-23 10:24:57","extension":"png","order_by":8,"title":"","display":"","copyAsset":false,"role":"supplement","size":1109186,"visible":true,"origin":"","legend":"","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-9295493/v1/40721f986d476f6d5107ea87.png"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eA Novel Multi-wavelet Multi-scale Dynamic Integral Framework for Real-Time Industrial Surface Defect Detection\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"journal-of-real-time-image-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"rtip","sideBox":"Learn more about [Journal of Real-Time Image Processing](http://link.springer.com/journal/11554)","snPcode":"11554","submissionUrl":"https://submission.nature.com/new-submission/11554/3","title":"Journal of Real-Time Image Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"YOLOv12, Industrial surface defect detection, Legendre wavelet, Attention mechanism, Numerical Integral","lastPublishedDoi":"10.21203/rs.3.rs-9295493/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9295493/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Due to the extreme irregular surface defects exhibiting variations in random shape, size, and distribution on industrialproductions, it is difficult for the traditional defect detection models to achieve a good balance between the precisionand efficiency. To address these challenges, this paper contributes to three key innovations: On the one hand, theLegendre wavelet convolution (LWConv) module is devised to reduce the number of parameters in deep learningmodels to improve inference speed and noise-robust. On the other hand, the C2f_Dynamic-Integral (C2f_DI) mod-ule is implemented to enhance and optimize the corner, edge, and interior weight ratios to accurately represent thecomplex features of the defects by using learnable trapezoidal integration kernels. Finally, the improved deformableprogressive pyramid aggregation (IDPPA) is utilized to fuse the multi-scale defect features by alternating convolu-tional modules. In brief, the proposed multi-wavelet multi-scale dynamic integral network based on YOLOv12 isabbreviated to LWDIYOLO-Net. Subsequently, the defect detection performance of LWDIYOLO-Net is validatedon two datasets. On the aluminum plate dataset, LWDIYOLO-Net attains 98.8% mAP50 while processing images at879.6 FPS. On the PCB dataset, LWDIYOLO-Net achieves precision of 98.8%, mAP50 of 99.2%, and F1 score of98.6% by using 2.36 M parameters and 121 FPS. The extensive experiment results demonstrate that LWDIYOLO-Netachieves the faster inference speed and better detection accuracy than those state-of-the-art methods.","manuscriptTitle":"A Novel Multi-wavelet Multi-scale Dynamic Integral Framework for Real-Time Industrial Surface Defect Detection","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-23 10:23:57","doi":"10.21203/rs.3.rs-9295493/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-05-05T03:39:15+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"339402341112035000937051259745226462501","date":"2026-04-17T05:52:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"157033371266428769907733778161108673250","date":"2026-04-17T01:14:40+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-17T00:52:51+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-16T14:26:59+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-16T07:15:15+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Real-Time Image Processing","date":"2026-04-01T19:12:39+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-real-time-image-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"rtip","sideBox":"Learn more about [Journal of Real-Time Image Processing](http://link.springer.com/journal/11554)","snPcode":"11554","submissionUrl":"https://submission.nature.com/new-submission/11554/3","title":"Journal of Real-Time Image Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d053e7ee-b220-4262-b241-a25791b392d7","owner":[],"postedDate":"April 23rd, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-05-05T03:39:15+00:00","index":57,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-23T10:23:57+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-23 10:23:57","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9295493","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9295493","identity":"rs-9295493","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}