{"title":"扩散在持久性上运行得很快","authors":"Chao Chen, H. Edelsbrunner","doi":"10.1109/ICCV.2011.6126271","DOIUrl":null,"url":null,"abstract":"Interpreting an image as a function on a compact subset of the Euclidean plane, we get its scale-space by diffusion, spreading the image over the entire plane. This generates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian kernel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods.","PeriodicalId":6391,"journal":{"name":"2011 International Conference on Computer Vision","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2011-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"31","resultStr":"{\"title\":\"Diffusion runs low on persistence fast\",\"authors\":\"Chao Chen, H. Edelsbrunner\",\"doi\":\"10.1109/ICCV.2011.6126271\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Interpreting an image as a function on a compact subset of the Euclidean plane, we get its scale-space by diffusion, spreading the image over the entire plane. This generates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian kernel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods.\",\"PeriodicalId\":6391,\"journal\":{\"name\":\"2011 International Conference on Computer Vision\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"31\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2011 International Conference on Computer Vision\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICCV.2011.6126271\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 International Conference on Computer Vision","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICCV.2011.6126271","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Interpreting an image as a function on a compact subset of the Euclidean plane, we get its scale-space by diffusion, spreading the image over the entire plane. This generates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian kernel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods.