[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127953-en":3,"doc-seo-127953-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},127953,687207024643,"Oliver","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Scale-Free Image Keypoints Using Differentiable Persistent Homology","Keypoint detection is central to computer vision, yet learning-based approaches often remain scale-dependent and lack flexibility in how salient points are defined. This paper presents MorseDet, a topology-driven detector that uses Morse theory and persistent homology to learn scale-stable keypoints. A new loss function based on a subgradient notion in persistent homology supports topological learning, yielding competitive keypoint repeatability and a principled theoretical foundation.","POLITECNICO DI TORINO Repository ISTITUZIONALE  \nScale-Free Image Keypoints Using Differentiable Persistent Homology  \nOriginal  \nScale-Free Image Keypoints Using Differentiable Persistent Homology / Barbarani, Giovanni; Vaccarino, Francesco; Trivigno, Gabriele; Guerra, Marco; Berton, Gabriele; Masone, Carlo. -ELETTRONICO. -235:(2024), pp. 2990-3002.(Intervento presentato al convegno 41st International Conference on Machine Learning tenutosi a Vienna (AUT) nel 21- 27 July 2024) .  \nAvailability:  \nThis version is available at: 11583/2989658 since: 2024-08-29T17:40:19Z  \nPublisher:  \nML Research Press  \nPublished DOI:  \nTerms of use:  \nThis article is made available under terms and conditions as specified in the corresponding bibliographic description in the repository  \nPublisher copyright  \n(Article begins on next page)  \n07 November 2024  \nScale-Free Image Keypoints Using Differentiable Persistent Homology  \nGiovanni Barbarani 1 Francesco Vaccarino 1 Gabriele Trivigno 2 Marco Guerra 3 Gabriele Berton 2  \nCarlo Masone 2  \nAbstract  \nIn computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency, and lack flexibility. This paper introducesa novel approach that leverages Morse theory and persistent homology, powerful tools rooted in algebraic topology. We propose a novel loss function based on the recent introduction of a notion of subgradient in persistent homology, paving the way toward topological learning. Our detector, MorseDet, is the first topology-based learning model for feature detection, which achieves competitive performance in keypoint repeatability and introduces a principled and theoretically robust approach to the problem.  \n1. Introduction  \nThe ability to extract salient points (keypoints) and associated features from an image is a cornerstone of computer vision, as it underpins several applications such as visual localization (Sarlin et al., 2019 ; Sattler et al., 2018 ; Toft et al., 2020), SLAM (Mur-Artal et al., 2015 ; Durrant-Whyte & Bailey, 2006 ; Bailey & Durrant-Whyte, 2006), Structurefrom-Motion and 3D reconstruction (Schnberger & Frahm, 2016 ; Heinly et al., 2015 ; Schnberger et al., 2016), as well as retrieval and place recognition (Barbarani et al., 2023 ; Noh et al., 2017) . Traditional pipelines relied on handcrafted filters that were engineered to detect salient points such as corners (Harris & Stephens, 1988), blobs (Tuytelaars & Van Gool, 2000 ; Lowe, 2004 ; Mikolajczyk & Schmid, 2004) or edges (Bhardwaj & Mittal, 2012) . These keypoints would then be associated with a feature vector obtained typ-  \n1Department of Mathematical Sciences ”Giuseppe Luigi Lagrange”, Politecnico di Torino, Italy 2Department of Control and Computer Engineering, Politecnico di Torino, Italy 3Institut Fourier, Universit Grenoble Alpes, France. Correspondence to: Giovanni Barbarani \u003C[giovanni.barbarani@gmail.com](giovanni.barbarani@gmail.com) >.  \nProceedings of the 41 st International Conference on Machine Learning, Vienna, Austria. PMLR 235, 2024 . Copyright 2024 by the author(s) .  \nically from local derivatives of the image (Calonder et al., 2010 ; Bay et al., 2006 ; Lowe, 2004) .  \nIdeally, a good feature detector should provide keypoints with the following desirable properties: high repeatability (i.e., consistent across image pairs) and scale-invariance, while being robust to noise and distortion (Ghahremani et al., 2020 ; Revaud et al., 2019 ; Lowe, 2004) . Scale-Space theory (Lindeberg, 1994) provides a formulation of the concept of keypoint that guarantees the properties mentioned above (Lindeberg, 1994 ; Lowe, 2004 ; Ghahremani et al., 2020), and it operates by building a scale-space feature pyramid from the image, in which keypoints are detected as local extrema. Many classical handcrafted detectors exploit this theoretical framework (Mikolajczyk & Schmid, 2004 ; Bay et al., 2006)","cbCaisC9h879GLHQ","https://ap.wps.com/l/cbCaisC9h879GLHQ","pdf",6547298,1,14,"English","en",105,"# Abstract\n# Introduction\n## Keypoint detection and limitations of existing methods\n## Proposed differentiable topological formulation","[{\"question\":\"What problem does the paper address in keypoint detection?\",\"answer\":\"It targets scale dependency and limited flexibility in learning-based keypoint detectors, which typically rely on heuristic definitions of where keypoints should be.\"},{\"question\":\"What is MorseDet and how does it detect keypoints?\",\"answer\":\"MorseDet is a topology-based learning model that uses Morse theory and persistent homology to connect keypoints with differentiable topological invariants.\"},{\"question\":\"How does the proposed method achieve scale stability?\",\"answer\":\"By providing a differentiable formulation for locating local maxima with built-in guarantees related to scale independence, avoiding the patch-wise heuristics that cause scale dependence.\"}]","Scale-Free Image Keypoints Using Differentiable Persistent Homology | 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problem does the paper address in keypoint detection?","Question",{"text":76,"@type":77},"It targets scale dependency and limited flexibility in learning-based keypoint detectors, which typically rely on heuristic definitions of where keypoints should be.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What is MorseDet and how does it detect keypoints?",{"text":81,"@type":77},"MorseDet is a topology-based learning model that uses Morse theory and persistent homology to connect keypoints with differentiable topological invariants.",{"name":83,"@type":74,"acceptedAnswer":84},"How does the proposed method achieve scale stability?",{"text":85,"@type":77},"By providing a differentiable formulation for locating local maxima with built-in guarantees related to scale independence, avoiding the patch-wise heuristics that cause scale 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