loading...
 This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Lines in One Orthographic and Two Perspective Views
July 2003 (vol. 25 no. 7)
pp. 912-917

Abstract—We introduce a linear algorithm to recover the Euclidean motion between an orthographic and two perspective cameras from straight line correspondences filling the gap in the analysis of motion estimation from line correspondences for various projection models. The general relationship between lines in three views is described by the trifocal tensor. Euclidean structure from motion for three perspective views is a special case in which the relationship is defined by a collection of three matrices. Here, we describe the case of two calibrated perspective views and an orthographic view. Similar to the other cases, our linear algorithm requires 13 or more line correspondences to recover 27 coefficients of the trifocal tensor.

[1] 912 K. Astrom, A. Heyden, F. Kahl, and M. Oskarsson, Structure and Motion from Lines Under Affine Projections Int'l Conf. Computer Vision, pp. 285-292, 1999.[2] R. Hartley, Cheirality Invariants Proc. Defense Advanced Research Projects Agency Image Understanding Workshop, pp. 745-753, 1993.[3] R.I. Hartley, "A Linear Method for Reconstruction From Lines and Points," Proc. Int'l Conf. Computer Vision, 1995, pp. 882-887.[4] R.J. Holt and A.N. Netravali, Motion and Structure From Line Correspondences Under Orthographic Projection Int'l J. Imaging Systems and Technology, vol. 8, no. 3, pp. 301-312, 1997.[5] Y. Liu and T. Huang, “A Linear Algorithm for Determining Motion and Structure from Line Correspondences,” Computer Vision, Graphics, and Image Processing, vol. 44, no. 1, pp. 35-57, 1988.[6] Y. Liu, T.S. Huang, and O.D. Faugeras, “Determination of Camera Location from 2D to 3D Line and Point Correspondences,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 28-37, Jan. 1990.[7] A. Marugame, J. Katto, and M. Ohta, Structure Recovery with Multiple Cameras From Scaled Orthographic and Perspective Views Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 7, pp. 628-633, 1999.[8] N. Navab et al., "Scene Augmentation via the Fusing of Industrial Drawings and Uncalibrated Images with a View to Marker-less Calibration," Proc. 2nd IEEE&ACM Int'l Workshop Augmented Reality (IWAR 99), IEEE Press, Piscataway, N.J., 1999, pp. 125-133.[9] N. Navab, Y. Genc, and M. Appel, Lines in One Orthographic and Two Perspective Views Proc. Conf. Computer Vision and Pattern Recognition, pp. 607-614, June 2000.[10] N. Navab and O.D. Faugeras, The Critical Sets of Lines for Camera Displacement Estimation: A Mixed Euclidean-Projective and Constructive Approach Int'l J. Computer Vision, vol. 23, no. 1, pp. 17-44, May 1997.[11] L. Quan and T. Kanade, Affine Structure From Line Correspondences with Uncalibrated Affine Cameras Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 8, pp. 834-845, Aug. 1997.[12] M.E. Spetsakis and J. Aloimonos, “Structure from Motion Using Line Correspondences,” Int'l J. Computer Vision, vol. 4, pp. 171-183, 1990.[13] C. Steger, An Unbiased Detector of Curvilinear Structures Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 2, pp. 113-125, Feb. 1998.[14] C.J. Taylor and D.J. Kriegman, Structure and Motion from Line Segments in Multiple Images IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 11, pp. 1021-1032, Nov. 1995.[15] J. Weng, T.S. Huang, and N. Ahuja, Motion and Structure from Line Correspondences: Closed-Form Solution, Uniqueness, and Optimization Trans. Pattern and Machine Intelligence, vol. 14, no. 3, pp. 318-336, Mar. 1992.[16] Z. Zhang, Estimating Motion and Structure from Correspondences of Line Segments Between Two Perspective Images Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 12, pp. 1129-1139, Dec. 1995.[17] Z. Zhang, P. Anandan, and H.-Y. Shum, What Can Be Determined from a Full and a Weak Perspective Camera Proc. Int'l Conf. Computer Vision, pp. 680-687, 1999.

Index Terms:
Motion from line correspondences, perspective and orthographic cameras, trifocal tensor, camera calibration.
Citation:
Nassir Navab, Yakup Genc, Mirko Appel, "Lines in One Orthographic and Two Perspective Views," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 7, pp. 912-917, July 2003, doi:10.1109/TPAMI.2003.1206519
Usage of this product signifies your acceptance of the Terms of Use.