{"title":"圆锥曲线和正交的三维解释","authors":"Kanatani K., Liu W.","doi":"10.1006/ciun.1993.1043","DOIUrl":null,"url":null,"abstract":"<div><p>Computational techniques involving conics are formulated in the framework of projective geometry, and basic notions of projective geometry such as poles, polars, and conjugate pairs are reformulated as \"computational procedures\" with special emphasis on computational aspects. It is shown that the 3D geometry of three orthogonal lines can be interpreted by computing conics. We then describe an analytical procedure for computing the 3D geometry of a conic of a known shape from its projection. Real image examples are also given.</p></div>","PeriodicalId":100350,"journal":{"name":"CVGIP: Image Understanding","volume":"58 3","pages":"Pages 286-301"},"PeriodicalIF":0.0000,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1006/ciun.1993.1043","citationCount":"77","resultStr":"{\"title\":\"3D Interpretation of Conics and Orthogonality\",\"authors\":\"Kanatani K., Liu W.\",\"doi\":\"10.1006/ciun.1993.1043\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Computational techniques involving conics are formulated in the framework of projective geometry, and basic notions of projective geometry such as poles, polars, and conjugate pairs are reformulated as \\\"computational procedures\\\" with special emphasis on computational aspects. It is shown that the 3D geometry of three orthogonal lines can be interpreted by computing conics. We then describe an analytical procedure for computing the 3D geometry of a conic of a known shape from its projection. Real image examples are also given.</p></div>\",\"PeriodicalId\":100350,\"journal\":{\"name\":\"CVGIP: Image Understanding\",\"volume\":\"58 3\",\"pages\":\"Pages 286-301\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1006/ciun.1993.1043\",\"citationCount\":\"77\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"CVGIP: Image Understanding\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1049966083710430\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"CVGIP: Image Understanding","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1049966083710430","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computational techniques involving conics are formulated in the framework of projective geometry, and basic notions of projective geometry such as poles, polars, and conjugate pairs are reformulated as "computational procedures" with special emphasis on computational aspects. It is shown that the 3D geometry of three orthogonal lines can be interpreted by computing conics. We then describe an analytical procedure for computing the 3D geometry of a conic of a known shape from its projection. Real image examples are also given.
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