{"title":"The tensors of three affine views","authors":"T. Thórhallsson, D. W. Murray","doi":"10.1109/CVPR.1999.786977","DOIUrl":null,"url":null,"abstract":"In this paper we specialize the projective unifocal, bifocal, and trifocal tensors to the affine case, and show how the tensors obtained relate to the registered tensors encountered in previous work. This enables us to obtain an affine specialization of known projective relations connecting points and lines across two or three views. In the simpler case of affine cameras we give neccessary and sufficient constraints on the components of the trifocal tensor together with a simple geometric interpretation. Finally, we show how the estimation of the tensors from point correspondences is achieved through factorization, and discuss the estimation from line correspondences.","PeriodicalId":20644,"journal":{"name":"Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1999-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"22","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CVPR.1999.786977","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 22
Abstract
In this paper we specialize the projective unifocal, bifocal, and trifocal tensors to the affine case, and show how the tensors obtained relate to the registered tensors encountered in previous work. This enables us to obtain an affine specialization of known projective relations connecting points and lines across two or three views. In the simpler case of affine cameras we give neccessary and sufficient constraints on the components of the trifocal tensor together with a simple geometric interpretation. Finally, we show how the estimation of the tensors from point correspondences is achieved through factorization, and discuss the estimation from line correspondences.
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