Enhancing Vision Transformer with Multiple Fractional-Order Differential Operators for Image Desnowing

Enhancing Vision Transformer with Multiple Fractional-Order Differential Operators for Image Desnowing | 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 Enhancing Vision Transformer with Multiple Fractional-Order Differential Operators for Image Desnowing Yuxuan Li, Yuning Ren This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8011687/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 Image desnowing aims to eliminate the complex visual degradation caused by snowflake noise and is an important branch of image restoration. In this paper, we consider the self-similar complex edges and rough translucent structures of snowflake noise, which can be characterized by fractal dimension. We use multiple fractional-order differential operators to model fractals, thereby enhancing the Vision Transformer (ViT), and propose MF-ViT. MF-ViT is a dedicated deep learning desnowing model based on the specific prior modeling of the fractal features of snowflake noise. Specifically, to enhance fractal feature representation ability, we incorporate fractional differential operators of different orders into the attention and feedforward networks of ViT, which help to handle fractal features. We empirically evaluate the proposed MF-ViT on five benchmark public desnowing datasets. The results show that MF-ViT achieves state-of-the-art performance in both simulation and real-world images with snowflake noise. This paper also provides new model improvement ideas for other machine vision pattern analysis tasks with fractal dimension features. Accepted at MMM 2026 (International Conference on Multimedia Modeling), to appear in Springer LNCS. This is the author-created version of the manuscript. Artificial Intelligence and Machine Learning Image desnowing Image restoration Fractional-order differential operators Fourier transform Fractal modeling Full Text Additional Declarations The authors declare no competing interests. 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. 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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-8011687","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":538715942,"identity":"7bc8419f-baf9-4551-8c21-a9bbc40e4c3a","order_by":0,"name":"Yuxuan Li","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0001-7398-742X","institution":"The University of Sydney","correspondingAuthor":true,"prefix":"","firstName":"Yuxuan","middleName":"","lastName":"Li","suffix":""},{"id":538715943,"identity":"461446da-d28e-4a9f-b709-1eca2bebdf64","order_by":1,"name":"Yuning Ren","email":"","orcid":"","institution":"China University of Political Science and Law","correspondingAuthor":false,"prefix":"","firstName":"Yuning","middleName":"","lastName":"Ren","suffix":""}],"badges":[],"createdAt":"2025-11-02 14:47:06","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8011687/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8011687/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":95223281,"identity":"6e660e18-f47c-42aa-908b-d2dad0b2aa47","added_by":"auto","created_at":"2025-11-05 16:21:58","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1334366,"visible":true,"origin":"","legend":"","description":"","filename":"final.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8011687/v1_covered_b9ededed-e9aa-400b-95ef-5981b252a411.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eEnhancing Vision Transformer with Multiple Fractional-Order Differential Operators for Image Desnowing\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"University of Sydney","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"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":"Image desnowing, Image restoration, Fractional-order differential operators, Fourier transform, Fractal modeling","lastPublishedDoi":"10.21203/rs.3.rs-8011687/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8011687/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eImage desnowing aims to eliminate the complex visual degradation caused by snowflake noise and is an important branch of image restoration. In this paper, we consider the self-similar complex edges and rough translucent structures of snowflake noise, which can be characterized by fractal dimension. We use multiple fractional-order differential operators to model fractals, thereby enhancing the Vision Transformer (ViT), and propose MF-ViT. MF-ViT is a dedicated deep learning desnowing model based on the specific prior modeling of the fractal features of snowflake noise. Specifically, to enhance fractal feature representation ability, we incorporate fractional differential operators of different orders into the attention and feedforward networks of ViT, which help to handle fractal features. We empirically evaluate the proposed MF-ViT on five benchmark public desnowing datasets. The results show that MF-ViT achieves state-of-the-art performance in both simulation and real-world images with snowflake noise. 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