{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T06:07:30Z","timestamp":1743142050728,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":45,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540676850"},{"type":"electronic","value":"9783540450542"}],"license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2000]]},"DOI":"10.1007\/3-540-45054-8_34","type":"book-chapter","created":{"date-parts":[[2007,5,1]],"date-time":"2007-05-01T10:57:52Z","timestamp":1178017072000},"page":"522-538","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Plane + Parallax, Tensors and Factorization"],"prefix":"10.1007","author":[{"given":"Bill","family":"Triggs","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2003,4,18]]},"reference":[{"key":"34_CR1","doi-asserted-by":"crossref","unstructured":"A. Capel, D. and Zisserman. Automated mosaicing with super-resolution zoom. In Int. Conf. Computer Vision & Pattern Recognition, pages 885\u2013891, June 1998.","DOI":"10.1109\/CVPR.1998.698709"},{"key":"34_CR2","unstructured":"S. Carlsson. Duality of reconstruction and positioning from projective views. In P. Anandan, editor, IEEE Workshop on Representation of Visual Scenes. IEEE Press, 1995."},{"issue":"3","key":"34_CR3","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1023\/A:1007961913417","volume":"27","author":"S. Carlsson","year":"1998","unstructured":"S. Carlsson and D. Weinshall. Dual computation of projective shape and camera positions from multiple images. Int.J. Computer Vision, 27(3):227\u2013241, May 1998.","journal-title":"Int.J. Computer Vision"},{"key":"34_CR4","doi-asserted-by":"crossref","unstructured":"A. Criminisi, I. Reid, and A. Zisserman. Duality, rigidity and planar parallax. In European Conf. Computer Vision, pages 846\u2013861. Springer-Verlag, 1998.","DOI":"10.1007\/BFb0054783"},{"key":"34_CR5","doi-asserted-by":"crossref","unstructured":"O. Faugeras and B. Mourrain. On the geometry and algebra of the point and line correspondences between n images. In Int. Conf. Computer Vision, pages 951\u20136, 1995.","DOI":"10.1109\/ICCV.1995.466832"},{"key":"34_CR6","doi-asserted-by":"crossref","unstructured":"O. Faugeras and T. Papadopoulo. Grassmann-Cayley algebra for modeling systems of cameras and the algebraic equations of the manifold of trifocal tensors. Transactions of the Royal society A, 1998.","DOI":"10.1098\/rsta.1998.0214"},{"key":"34_CR7","doi-asserted-by":"crossref","unstructured":"K. Hanna and N. Okamoto. Combining stereo and motion analysis for direct estimation of scene structure. In Int. Conf. Computer Vision & Pattern Recognition, pages 357\u201365, 1993.","DOI":"10.1109\/ICCV.1993.378192"},{"issue":"2","key":"34_CR8","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/A:1007936012022","volume":"22","author":"R. Hartley","year":"1997","unstructured":"R. Hartley. Lines and points in three views and the trifocal tensor. Int.J. Computer Vision, 22(2): 125\u2013140, 1997.","journal-title":"Int.J. Computer Vision"},{"issue":"1","key":"34_CR9","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1007957826135","volume":"22","author":"R. Hartley","year":"1997","unstructured":"R. Hartley. Self calibration of stationary cameras. Int.J. Computer Vision, 22(1):5\u201323, 1997.","journal-title":"Int.J. Computer Vision"},{"key":"34_CR10","doi-asserted-by":"crossref","unstructured":"R. Hartley and G. Debunne. Dualizing scene reconstruction algorithms. In R. Koch and L. Van Gool, editors, Workshop on 3D Structure from Multiple Images of Large-scale Environments SMILE\u201998, pages 14\u201331. Springer-Verlag, 1998.","DOI":"10.1007\/3-540-49437-5_2"},{"key":"34_CR11","unstructured":"R. Hartley and A. Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, 2000."},{"key":"34_CR12","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BF00128130","volume":"7","author":"D. Heeger","year":"1992","unstructured":"D. Heeger and A. Jepson. Subspace methods for recovering rigid motion I: Algorithm and implementation. Int.J. Computer Vision, 7:95\u2013117, 1992.","journal-title":"Int.J. Computer Vision"},{"key":"34_CR13","doi-asserted-by":"crossref","unstructured":"A. Heyden. Reconstruction from image sequences by means of relative depths. In E. Grimson, editor, Int. Conf. Computer Vision, pages 1058\u201363, Cambridge, MA, June 1995.","DOI":"10.1109\/ICCV.1995.466817"},{"key":"34_CR14","unstructured":"A. Heyden and K. \u00c5str\u00f6m. A canonical framework for sequences of images. In IEEE Workshop on Representations of Visual Scenes, Cambridge, MA, June 1995."},{"key":"34_CR15","doi-asserted-by":"crossref","unstructured":"A. Heyden and K. \u00c5str\u00f6m. Algebraic varieties in multiple view geometry. In European Conf. Computer Vision, pages 671\u2013682. Springer-Verlag, 1996.","DOI":"10.1007\/3-540-61123-1_180"},{"key":"34_CR16","doi-asserted-by":"crossref","unstructured":"A. Heyden and K. Astrom. Euclidean reconstruction from constant intrinsic parameters. In Int. Conf. Pattern Recognition, pages 339\u201343, Vienna, 1996.","DOI":"10.1109\/ICPR.1996.546045"},{"key":"34_CR17","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1002\/(SICI)1099-1476(19970910)20:13<1135::AID-MMA908>3.0.CO;2-9","volume":"20","author":"A. Heyden","year":"1997","unstructured":"A. Heyden and K. \u00c5strom. Algebraic properties of multilinear constraints. Mathematical Methods in the Applied Sciences, 20:1135\u20131162, 1997.","journal-title":"Mathematical Methods in the Applied Sciences"},{"key":"34_CR18","doi-asserted-by":"crossref","unstructured":"A. Heyden, R. Berthilsson, and G. Sparr. An iterative factorization method for projective structure and motion from image sequences. Image & Vision Computing, 17(5), 1999.","DOI":"10.1016\/S0262-8856(99)00002-5"},{"key":"34_CR19","doi-asserted-by":"crossref","unstructured":"M. Irani and P. Anadan. Parallax geometry of pairs of points for 3d scene analysis. In European Conf. Computer Vision, pages 17\u201330. Springer-Verlag, 1996.","DOI":"10.1007\/BFb0015520"},{"key":"34_CR20","doi-asserted-by":"crossref","unstructured":"M. Irani and P. Anadan. Factorization with uncertainty. In European Conf. Computer Vision. Springer-Verlag, 2000.","DOI":"10.1007\/3-540-45054-8_35"},{"key":"34_CR21","doi-asserted-by":"crossref","unstructured":"M. Irani, P. Anadan, and M. Cohen. Direct recovery of planar-parallax from multiple frames. In Vision Algorithms: Theory and Practice. Springer-Verlag, 1999.","DOI":"10.1007\/3-540-44480-7_6"},{"key":"34_CR22","doi-asserted-by":"crossref","unstructured":"M. Irani, P. Anadan, and D. Weinshall. From reference frames to reference planes: Multi-view parallax geometry and applications. In European Conf. Computer Vision, pages 829\u2013845. Springer-Verlag, 1998.","DOI":"10.1007\/BFb0054782"},{"issue":"6","key":"34_CR23","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1109\/34.683770","volume":"20","author":"M. Irani","year":"1998","unstructured":"M. Irani and P. Anandan. A unified approach to moving object detection in 2d and 3d scenes. IEEE Trans. Pattern Analysis & Machine Intelligence, 20(6):577\u2013589, June 1998.","journal-title":"IEEE Trans. Pattern Analysis & Machine Intelligence"},{"key":"34_CR24","doi-asserted-by":"crossref","unstructured":"R. Kumar, P. Anandan, M. Irani, J. Bergen, and K. Hanna. Representation of scenes from collections of images. In IEEE Workshop on Representations of Visual Scenes, pages 10\u201317, June 1995.","DOI":"10.1109\/WVRS.1995.476847"},{"key":"34_CR25","doi-asserted-by":"crossref","unstructured":"J. Oliensis. Multiframe structure from motion in perspective. In IEEE Workshop on Representation of Visual Scenes, pages 77\u201384, June 1995.","DOI":"10.1109\/WVRS.1995.476855"},{"key":"34_CR26","doi-asserted-by":"crossref","unstructured":"J. Oliensis and Y. Gene. Fast algorithms for projective multi-frame structure from motion. In Int. Conf. Computer Vision, pages 536\u2013542, Corfu, Greece, 1999.","DOI":"10.1109\/ICCV.1999.791269"},{"key":"34_CR27","doi-asserted-by":"crossref","unstructured":"C.J. Poelman and T. Kanade. A parapersective factorization method for shape and motion recovery. In European Conf. Computer Vision, pages 97\u2013108, Stockholm, 1994. Springer-Verlag.","DOI":"10.1007\/BFb0028338"},{"key":"34_CR28","doi-asserted-by":"crossref","unstructured":"A. Shashua and S. Avidan. The rank 4 constraint in multiple (\u2265 3) view geometry. In European Conf. Computer Vision, pages 196\u2013206, Cambridge, 1996.","DOI":"10.1007\/3-540-61123-1_139"},{"key":"34_CR29","unstructured":"A. Shashua and M. Werman. On the trilinear tensor of three perspective views and its underlying geometry. In Int. Conf. Computer Vision, Boston, MA, June 1995."},{"key":"34_CR30","unstructured":"C. E. Springer. Geometry and Analysis of Projective Spaces. Freeman, 1964."},{"key":"34_CR31","doi-asserted-by":"crossref","unstructured":"G. Stein and A. Shashua. Model-based brightness constraints: On direct estimation of structure and motion. In Int. Conf. Computer Vision & Pattern Recognition, pages 400\u2013406, 1997.","DOI":"10.1109\/CVPR.1997.609356"},{"key":"34_CR32","doi-asserted-by":"crossref","unstructured":"P. Sturm and B. Triggs. A factorization based algorithm for multi-image projective structure and motion. In European Conf. Computer Vision, pages 709\u201320, Cambridge, U.K., 1996. Springer-Verlag.","DOI":"10.1007\/3-540-61123-1_183"},{"key":"34_CR33","doi-asserted-by":"crossref","unstructured":"R. Szeliski and S-B. Kang. Direct methods for visual scene reconstruction. In IEEE Workshop on Representation of Visual Scenes, pages 26\u201333, June 1995.","DOI":"10.1109\/WVRS.1995.476849"},{"issue":"2","key":"34_CR34","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/BF00129684","volume":"9","author":"C. Tomasi","year":"1992","unstructured":"C. Tomasi and T. Kanade. Shape and motion from image streams under orthography: a factorization method. Int.J. Computer Vision, 9(2): 137\u201354, 1992.","journal-title":"Int.J. Computer Vision"},{"key":"34_CR35","unstructured":"B. Triggs. The geometry of projective reconstruction I: Matching constraints and the joint image. Submitted to Int.J. Computer Vision."},{"key":"34_CR36","doi-asserted-by":"crossref","unstructured":"B. Triggs. Matching constraints and the joint image. In E. Grimson, editor, Int. Conf. Computer Vision, pages 338\u201343, Cambridge, MA, June 1995.","DOI":"10.1109\/ICCV.1995.466920"},{"key":"34_CR37","doi-asserted-by":"crossref","unstructured":"B. Triggs. Factorization methods for projective structure and motion. In Int. Conf. Computer Vision & Pattern Recognition, pages 845\u201351, San Francisco, CA, 1996.","DOI":"10.1109\/CVPR.1996.517170"},{"key":"34_CR38","doi-asserted-by":"crossref","unstructured":"B. Triggs. Linear projective reconstruction from matching tensors. In British Machine Vision Conference, pages 665\u201374, Edinburgh, September 1996.","DOI":"10.5244\/C.10.62"},{"key":"34_CR39","unstructured":"B. Triggs. Autocalibration and the absolute quadric. In Int. Conf. Computer Vision & Pattern Recognition, Puerto Rico, 1997."},{"issue":"8","key":"34_CR40","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/S0262-8856(97)00016-4","volume":"15","author":"B. Triggs","year":"1997","unstructured":"B. Triggs. Linear projective reconstruction from matching tensors. Image & Vision Computing, 15(8):617\u201326, August 1997.","journal-title":"Image & Vision Computing"},{"key":"34_CR41","doi-asserted-by":"crossref","unstructured":"B. Triggs. Autocalibration from planar scenes. In European Conf. Computer Vision, pages 189\u2013105, Freiburg, June 1998.","DOI":"10.1007\/BFb0055661"},{"key":"34_CR42","doi-asserted-by":"crossref","unstructured":"D. Weinshall, P. Anandan, and M. Irani. From ordinal to euclidean reconstruction with partial scene calibration. In R. Koch and L. Van Gool, editors, 3D Structure from Multiple Images of Large-scale Environments SMILE\u201998, pages 208\u2013223. Springer-Verlag, 1998.","DOI":"10.1007\/3-540-49437-5_14"},{"key":"34_CR43","doi-asserted-by":"crossref","unstructured":"D. Weinshall, M. Werman, and A. Shashua. Shape tensors for efficient and learnable indexing. In IEEE Workshop on Representation of Visual Scenes, pages 58\u201365, June 1995.","DOI":"10.1109\/WVRS.1995.476853"},{"key":"34_CR44","doi-asserted-by":"crossref","unstructured":"L. Zelnik-Manor and M. Irani. Multi-frame alignment of planes. In Int. Conf. Computer Vision & Pattern Recognition, pages 151\u2013156, 1999.","DOI":"10.1109\/CVPR.1999.786932"},{"key":"34_CR45","doi-asserted-by":"crossref","unstructured":"L. Zelnik-Manor and M. Irani. Multi-view subspace constraints on homographies. In Int. Conf. Computer Vision, pages 710\u2013715, 1999.","DOI":"10.1109\/ICCV.1999.790291"}],"container-title":["Lecture Notes in Computer Science","Computer Vision - ECCV 2000"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-45054-8_34","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,16]],"date-time":"2025-01-16T00:10:36Z","timestamp":1736986236000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-45054-8_34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000]]},"ISBN":["9783540676850","9783540450542"],"references-count":45,"URL":"https:\/\/doi.org\/10.1007\/3-540-45054-8_34","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2000]]},"assertion":[{"value":"18 April 2003","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}