G-LoG Bi-filtration for Medical Image Classification

G-LoG Bi-filtration for Medical Image Classification | 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 G-LoG Bi-filtration for Medical Image Classification Qingsong Wang, Jiaxing He, Bingzhe Hou, Tieru Wu, Yang Cao, Cailing Yao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8920056/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 Building practical filtrations on objects to detect topological and geometric features is an important task in the field of Topological Data Analysis (TDA). In this paper, leveraging the ability of the Laplacian of Gaussian operator to enhance the boundaries of medical images, we define the G-LoG (Gaussian-Laplacian of Gaussian) bi-filtration to generate the features more suitable for multi-parameter persistence module. By modeling volumetric images as bounded functions, then we prove the interleaving distance on the persistence modules obtained from our bi-filtrations on the bounded functions is stable with respect to the maximum norm of the bounded functions. Finally, we conduct experiments on the MedMNIST dataset, comparing our bi-filtration against single-parameter filtration and the established deep learning baselines, including Google AutoML Vision, ResNet, AutoKeras and auto-sklearn. Experiments results demonstrate that our bi-filtration significantly outperforms single-parameter filtration. Notably, a simple Multi-Layer Perceptron (MLP) trained on the topological features generated by our bi-filtration achieves performance comparable to complex deep learning models trained on the original dataset. Persistent homology multi-filtration Gaussian kernel medical imaging Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 08 Apr, 2026 Editor assigned by journal 22 Feb, 2026 Submission checks completed at journal 20 Feb, 2026 First submitted to journal 19 Feb, 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. 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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-8920056","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":621136247,"identity":"c0499b15-1351-47ae-93c4-a830dd84e62b","order_by":0,"name":"Qingsong Wang","email":"","orcid":"","institution":"Jilin University","correspondingAuthor":false,"prefix":"","firstName":"Qingsong","middleName":"","lastName":"Wang","suffix":""},{"id":621136249,"identity":"09a8ca1c-ecc7-4b96-9ef7-b4162f3465be","order_by":1,"name":"Jiaxing He","email":"","orcid":"","institution":"Jilin University","correspondingAuthor":false,"prefix":"","firstName":"Jiaxing","middleName":"","lastName":"He","suffix":""},{"id":621136252,"identity":"39e60920-4b70-4ec3-9cbc-e73633d87be8","order_by":2,"name":"Bingzhe Hou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsUlEQVRIiWNgGAWjYBACAwYGNgaGCjYZEEeCBC1n2HhI1MLYxkCCFnP2HrOHP+fx8RgcYD54m4fBLo+gFsueM+YGktvYgFrYkq15GJKLCTvsRo6ZhCFYC4+ZNA/DgcQGorQkzgFp4f9GgpaDDWBb2IjUcuZYuWHDMTYeycNsxpZzDJKJ0HK8edvDHzXH5PiONz+88abCjrAWKDjGwMAMNoFI9UBQQ7zSUTAKRsEoGHkAAKEFNNLWmZa7AAAAAElFTkSuQmCC","orcid":"","institution":"Jilin University","correspondingAuthor":true,"prefix":"","firstName":"Bingzhe","middleName":"","lastName":"Hou","suffix":""},{"id":621136253,"identity":"4fb2791f-306d-404b-a2f2-d4d011c87192","order_by":3,"name":"Tieru Wu","email":"","orcid":"","institution":"Jilin University","correspondingAuthor":false,"prefix":"","firstName":"Tieru","middleName":"","lastName":"Wu","suffix":""},{"id":621136255,"identity":"25100588-a71f-4f13-b3ac-af978897a774","order_by":4,"name":"Yang Cao","email":"","orcid":"","institution":"Jilin University","correspondingAuthor":false,"prefix":"","firstName":"Yang","middleName":"","lastName":"Cao","suffix":""},{"id":621136256,"identity":"eab65491-e359-4c88-9378-bbcedb59237f","order_by":5,"name":"Cailing Yao","email":"","orcid":"","institution":"Jilin University","correspondingAuthor":false,"prefix":"","firstName":"Cailing","middleName":"","lastName":"Yao","suffix":""}],"badges":[],"createdAt":"2026-02-19 18:23:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8920056/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8920056/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107481306,"identity":"c0fea45d-7323-44d7-9d28-aa21ba13debc","added_by":"auto","created_at":"2026-04-22 02:17:11","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":428570,"visible":true,"origin":"","legend":"","description":"","filename":"GLoG.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8920056/v1_covered_bfd3a756-89e3-4032-8a60-38fbcfdd66c8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"G-LoG Bi-filtration for Medical Image Classification","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-mathematical-imaging-and-vision","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jmiv","sideBox":"Learn more about [Journal of Mathematical Imaging and Vision](http://link.springer.com/journal/10851)","snPcode":"10851","submissionUrl":"https://submission.nature.com/new-submission/10851/3","title":"Journal of Mathematical Imaging and Vision","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Persistent homology, multi-filtration, Gaussian kernel, medical imaging","lastPublishedDoi":"10.21203/rs.3.rs-8920056/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8920056/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Building practical filtrations on objects to detect topological and geometric features is an important task in the field of Topological Data Analysis (TDA). In this paper, leveraging the ability of the Laplacian of Gaussian operator to \n\tenhance the boundaries of medical images, we define the G-LoG (Gaussian-Laplacian of Gaussian) bi-filtration to generate the features more suitable for multi-parameter persistence module. \n\tBy modeling volumetric images as bounded functions, then we prove the interleaving distance on the persistence modules obtained from our bi-filtrations on the bounded functions is stable with respect to the maximum norm of the bounded functions. Finally, we conduct experiments on the MedMNIST dataset, comparing our bi-filtration against single-parameter filtration and the established deep learning baselines, including Google AutoML Vision, ResNet, AutoKeras and auto-sklearn. Experiments results demonstrate that our bi-filtration significantly outperforms single-parameter filtration. 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