{"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}
引用次数: 31
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.