{"title":"FRIDU:功能地图细化与引导图像扩散","authors":"Avigail Cohen Rimon, Mirela Ben-Chen, Or Litany","doi":"10.1111/cgf.70203","DOIUrl":null,"url":null,"abstract":"<p>We propose a novel approach for refining a given correspondence map between two shapes. A correspondence map represented as a <i>functional map</i>, namely a change of basis matrix, can be additionally treated as a 2D image. With this perspective, we train an <i>image diffusion model</i> directly in the space of functional maps, enabling it to generate accurate maps conditioned on an inaccurate initial map. The training is done purely in the functional space, and thus is highly efficient. At inference time, we use the pointwise map corresponding to the current functional map as <i>guidance</i> during the diffusion process. The guidance can additionally encourage different functional map objectives, such as orthogonality and commutativity with the Laplace-Beltrami operator. We show that our approach is competitive with state-of-the-art methods of map refinement and that guided diffusion models provide a promising pathway to functional map processing.</p>","PeriodicalId":10687,"journal":{"name":"Computer Graphics Forum","volume":"44 5","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/cgf.70203","citationCount":"0","resultStr":"{\"title\":\"FRIDU: Functional Map Refinement with Guided Image Diffusion\",\"authors\":\"Avigail Cohen Rimon, Mirela Ben-Chen, Or Litany\",\"doi\":\"10.1111/cgf.70203\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We propose a novel approach for refining a given correspondence map between two shapes. A correspondence map represented as a <i>functional map</i>, namely a change of basis matrix, can be additionally treated as a 2D image. With this perspective, we train an <i>image diffusion model</i> directly in the space of functional maps, enabling it to generate accurate maps conditioned on an inaccurate initial map. The training is done purely in the functional space, and thus is highly efficient. At inference time, we use the pointwise map corresponding to the current functional map as <i>guidance</i> during the diffusion process. The guidance can additionally encourage different functional map objectives, such as orthogonality and commutativity with the Laplace-Beltrami operator. We show that our approach is competitive with state-of-the-art methods of map refinement and that guided diffusion models provide a promising pathway to functional map processing.</p>\",\"PeriodicalId\":10687,\"journal\":{\"name\":\"Computer Graphics Forum\",\"volume\":\"44 5\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2025-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1111/cgf.70203\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Graphics Forum\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/cgf.70203\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Graphics Forum","FirstCategoryId":"94","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/cgf.70203","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
FRIDU: Functional Map Refinement with Guided Image Diffusion
We propose a novel approach for refining a given correspondence map between two shapes. A correspondence map represented as a functional map, namely a change of basis matrix, can be additionally treated as a 2D image. With this perspective, we train an image diffusion model directly in the space of functional maps, enabling it to generate accurate maps conditioned on an inaccurate initial map. The training is done purely in the functional space, and thus is highly efficient. At inference time, we use the pointwise map corresponding to the current functional map as guidance during the diffusion process. The guidance can additionally encourage different functional map objectives, such as orthogonality and commutativity with the Laplace-Beltrami operator. We show that our approach is competitive with state-of-the-art methods of map refinement and that guided diffusion models provide a promising pathway to functional map processing.
期刊介绍:
Computer Graphics Forum is the official journal of Eurographics, published in cooperation with Wiley-Blackwell, and is a unique, international source of information for computer graphics professionals interested in graphics developments worldwide. It is now one of the leading journals for researchers, developers and users of computer graphics in both commercial and academic environments. The journal reports on the latest developments in the field throughout the world and covers all aspects of the theory, practice and application of computer graphics.