{"title":"回顾仿射不变性","authors":"Evgeni Begelfor, M. Werman","doi":"10.1109/CVPR.2006.50","DOIUrl":null,"url":null,"abstract":"This paper proposes a Riemannian geometric framework to compute averages and distributions of point configurations so that different configurations up to affine transformations are considered to be the same. The algorithms are fast and proven to be robust both theoretically and empirically. The utility of this framework is shown in a number of affine invariant clustering algorithms on image point data.","PeriodicalId":421737,"journal":{"name":"2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"158","resultStr":"{\"title\":\"Affine Invariance Revisited\",\"authors\":\"Evgeni Begelfor, M. Werman\",\"doi\":\"10.1109/CVPR.2006.50\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper proposes a Riemannian geometric framework to compute averages and distributions of point configurations so that different configurations up to affine transformations are considered to be the same. The algorithms are fast and proven to be robust both theoretically and empirically. The utility of this framework is shown in a number of affine invariant clustering algorithms on image point data.\",\"PeriodicalId\":421737,\"journal\":{\"name\":\"2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06)\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-06-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"158\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CVPR.2006.50\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CVPR.2006.50","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper proposes a Riemannian geometric framework to compute averages and distributions of point configurations so that different configurations up to affine transformations are considered to be the same. The algorithms are fast and proven to be robust both theoretically and empirically. The utility of this framework is shown in a number of affine invariant clustering algorithms on image point data.
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