{"title":"A canonical framework for sequences of images","authors":"A. Heyden, K. Astrom","doi":"10.1109/WVRS.1995.476851","DOIUrl":"https://doi.org/10.1109/WVRS.1995.476851","url":null,"abstract":"This paper deals with the problem of analysing sequences of images of rigid point objects taken by uncalibrated cameras. It is assumed that the correspondences between the points in the different images are known. The paper introduces a new framework for this problem. Corresponding points in a sequence of n images are related to each other by a fixed n-linear form. This form is an object invariant property, closely linked to the motion of the camera relative to the fixed world. We first describe a reduced setting in which these multilinear forms are easier to understand and analyse. This new formulation of the multilinear forms is then extended to the calibrated case. This formulation makes apparent the connection between camera motion, camera matrices and multilinear forms and the similarities between the calibrated and uncalibrated cases. These new ideas are then used to derive simple linear methods for extracting camera motion from sequences of images.","PeriodicalId":447791,"journal":{"name":"Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95)","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115986441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"About the correspondences of points between N images","authors":"O. Faugeras, B. Mourrain","doi":"10.1109/WVRS.1995.476850","DOIUrl":"https://doi.org/10.1109/WVRS.1995.476850","url":null,"abstract":"We analyze the correspondence of points between an arbitrary number of images, from an algebraic and geometric point of view. We use the formalism of the Grassmann-Cayley algebra as the simplest way to make both geometric and algebraic statements in a very synthetic and effective way (i.e. allowing actual computation if needed). We propose a systematic way to describe the algebraic relations which are satisfied by the coordinates of the images of a 3D point. They are of three types: bilinear relations arising when we consider pairs of images among the N and which are the well-known epipolar constraints, trilinear relations arising when we consider triples of images among the N, and quadrilinear relations arising when we consider four-tuples of images among the N. Moreover, we show how two trilinear relations imply the bilinear ones (i.e. the epipolar constraints). We also show how these trilinear constraints can be used to predict the image coordinates of a point in a third image, given the coordinates of the images in the other two images, even in cases where the prediction by the epipolar constraints fails (points in the trifocal plane, or optical centers aligned). Finally, we show that the quadrilinear relations are in the ideal generated by the bilinearities and trilinearities, and do not bring in any new information. This completes the algebraic description of correspondence between any number of cameras.","PeriodicalId":447791,"journal":{"name":"Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129708938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"IEEE Workshop on Represenfafion of Visual Scenes","authors":"","doi":"10.1109/WVRS.1995.476845","DOIUrl":"https://doi.org/10.1109/WVRS.1995.476845","url":null,"abstract":"","PeriodicalId":447791,"journal":{"name":"Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129354877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}