{"title":"使用Mumford-Shah函数的图像平滑和放大的PDE方法","authors":"A. Tsai, A. Yezzi, A. Willsky","doi":"10.1109/ACSSC.2000.911001","DOIUrl":null,"url":null,"abstract":"We first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah (1989) paradigm from a curve evolution perspective. In particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Next, we generalize the data fidelity term of the original Mumford-Shah functional to incorporate a spatially varying penalty. This more general model leads us to a novel partial differential equation (PDE) based approach for simultaneous image magnification, segmentation, and smoothing.","PeriodicalId":10581,"journal":{"name":"Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154)","volume":"24 1","pages":"473-477 vol.1"},"PeriodicalIF":0.0000,"publicationDate":"2000-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A PDE approach to image smoothing and magnification using the Mumford-Shah functional\",\"authors\":\"A. Tsai, A. Yezzi, A. Willsky\",\"doi\":\"10.1109/ACSSC.2000.911001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah (1989) paradigm from a curve evolution perspective. In particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Next, we generalize the data fidelity term of the original Mumford-Shah functional to incorporate a spatially varying penalty. This more general model leads us to a novel partial differential equation (PDE) based approach for simultaneous image magnification, segmentation, and smoothing.\",\"PeriodicalId\":10581,\"journal\":{\"name\":\"Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154)\",\"volume\":\"24 1\",\"pages\":\"473-477 vol.1\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2000-10-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ACSSC.2000.911001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ACSSC.2000.911001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A PDE approach to image smoothing and magnification using the Mumford-Shah functional
We first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah (1989) paradigm from a curve evolution perspective. In particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Next, we generalize the data fidelity term of the original Mumford-Shah functional to incorporate a spatially varying penalty. This more general model leads us to a novel partial differential equation (PDE) based approach for simultaneous image magnification, segmentation, and smoothing.