{"title":"曲线拟合的Cramer-Rao下限","authors":"Kenichi Kanatani","doi":"10.1006/gmip.1998.0466","DOIUrl":null,"url":null,"abstract":"<div><p>We point out that the derivation of the Cramer–Rao lower bound for estimating a circular arc center and its radius by Chan and Thomas (<em>Graphical Models Image Process</em>.<strong>57</strong>, 1995, 527–532) has some problems although the final result is correct. Examining the mathematical structure of the problem carefully, we first correct their mistakes and then present a suitable formulation for the problem. We show that the result can be extended to more general problems including line and conic fitting.</p></div>","PeriodicalId":100591,"journal":{"name":"Graphical Models and Image Processing","volume":"60 2","pages":"Pages 93-99"},"PeriodicalIF":0.0000,"publicationDate":"1998-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1006/gmip.1998.0466","citationCount":"63","resultStr":"{\"title\":\"Cramer–Rao Lower Bounds for Curve Fitting\",\"authors\":\"Kenichi Kanatani\",\"doi\":\"10.1006/gmip.1998.0466\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We point out that the derivation of the Cramer–Rao lower bound for estimating a circular arc center and its radius by Chan and Thomas (<em>Graphical Models Image Process</em>.<strong>57</strong>, 1995, 527–532) has some problems although the final result is correct. Examining the mathematical structure of the problem carefully, we first correct their mistakes and then present a suitable formulation for the problem. We show that the result can be extended to more general problems including line and conic fitting.</p></div>\",\"PeriodicalId\":100591,\"journal\":{\"name\":\"Graphical Models and Image Processing\",\"volume\":\"60 2\",\"pages\":\"Pages 93-99\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1006/gmip.1998.0466\",\"citationCount\":\"63\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Graphical Models and Image Processing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S107731699890466X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphical Models and Image Processing","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S107731699890466X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We point out that the derivation of the Cramer–Rao lower bound for estimating a circular arc center and its radius by Chan and Thomas (Graphical Models Image Process.57, 1995, 527–532) has some problems although the final result is correct. Examining the mathematical structure of the problem carefully, we first correct their mistakes and then present a suitable formulation for the problem. We show that the result can be extended to more general problems including line and conic fitting.
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