Affine Structure from Line Correspondences With Uncalibrated Affine Cameras
|
Abstract—This paper presents a linear algorithm for recovering 3D affine shape and motion from line correspondences with uncalibrated affine cameras. The algorithm requires a minimum of seven line correspondences over three views. The key idea is the introduction of a one-dimensional projective camera. This converts 3D affine reconstruction of "line directions" into 2D projective reconstruction of "points." In addition, a line-based factorization method is also proposed to handle redundant views. Experimental results both on simulated and real image sequences validate the robustness and the accuracy of the algorithm.
[1] 834 J.Y. Aloimonos, "Perspective Approximations," Image and Vision Computing, vol. 8, no. 3, pp. 179-192, Aug. 1990.
[2] N. Ayache, Stereovision and Sensor Fusion.Cambridge, Mass.: MIT Press, 1990.
[3] P. Beardsley, I. Reid, A. Zisserman, and D. Murray, “Active Visual Navigation Using Non-Metric Structure,” Proc. Fifth Int'l Conf. Computer Vision, 1995.
[4] S. Carlsson and D. Weinshall, "Dual Computation of Projective Shape and Camera Positions from Multiple Images," Int'l J. Computer Vision, to appear.
[5] M. Dhome, M. Richetin, J.T. Lapreste, and G. Rives, “Determination of the Attitude of 3D Objects from a Single Perspective View,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 12, pp. 1,265-1,278, Dec. 1989.
[6] O. Faugeras, "What Can Be Seen in Three Dimensions With an Uncalibrated Stereo Rig?" Proc. Second European Conf. Computer Vision, pp. 563-578,Santa Margherita Ligure, Italy, May 1992.
[7] O. Faugeras and B. Mourrain, "On the Geometry and Algebra of the Point and Line Correspondences Between N Images," Proc. Int'l Conf. Computer Vision, pp. 951-956, 1995.
[8] O.D. Faugeras, F. Lustman, and G. Toscani, "Motion and Structure From Point and Line Matches," Proc. First Int'l Conf. Computer Vision,London, June 1987.
[9] G.H. Golub and C.F. van Loan, Matrix Computation.Baltimore: Johns Hopkins Univ. Press, 1989.
[10] R. Hartley, "Lines and Points in Three Views—an Integrated Approach," Technical Report, G.E. CRD, 1994.
[11] R. Hartley, R. Gupta, and T. Chang, “Stereo from Uncalibrated Cameras,” Proc. Conf. Computer Vision and Pattern Recognition, pp. 761-764, June 1992.
[12] J. Highsmith, Adaptive Software Development: A Collaborative Approach to Managing Complex Systems, Dorset House, New York, 2000.
[13] R. Horaud, S. Christy, and F. Dornaika, "Object Pose: The Link Between Weak Perspective, Para Perspective, and Full Perspective," Technical Report, INRIA, Sept. 1994.
[14] J. Koenderink and A. van Doorn, "Affine Structure From Motion," J. Optical Soc. Am. A, vol. 8, no. 2, pp. 377-385, 1991.
[15] C.H. Lee and T. Huang, "Finding Point Correspondences and Determining Motion of a Rigid Object From Two Weak Perspective Views," Computer Vision, Graphics, and Image Processing, vol. 52, pp. 309-327, 1990.
[16] Y. Liu and T.S. Huang, "Estimation of Rigid Body Motion Using Straight Line Correspondences," Computer Vision, Graphics, and Image Processing, vol. 43, no. 1, pp. 37-52, July 1988.
[17] Y. Liu and T.S. Huang, "A Linear Algorithm for Motion Estimation Using Straight Line Correspondences," Computer Vision, Graphics, and Image Processing, vol. 44, no. 1, pp. 35-57, Oct. 1988.
[18] H.C. Longuet-Higgins, "A Computer Program for Reconstructing a Scene From Two Projections," Nature, vol. 293, pp. 133-135, Sept. 1981.
[19] Q.T. Luong, "Matrice fondamentale et autocalibration en vision par ordinateur," Thèse de doctorat, Universitéde Paris-Sud, Orsay, France, Dec. 1992.
[20] Q.T. Luong and T. Vieville, "Canonic Representations for the Geometries of Multiple Projective Views," Technical Report, Univ. of California, Berkeley, Dept. of Electrical Engr. and Computer Science, Oct. 1993.
[21] P.F. McLauchlan, I.D. Reid, and D.W. Murray, "Recursive Affine Structure and Motion From Image Sequences," Proc. Third European Conf. Computer Vision, pp. 217-224,Stockholm, Sweden, 1994.
[22] R. Mohr, L. Quan, and F. Veillon, "Relative 3D Reconstruction Using Multiple Uncalibrated Images," Int'l J. Robotics Research, vol. 14, no. 6, pp. 619-632, 1995.
[23] Geometric Invariance in Computer Vision, J.L. Mundy and A. Zisserman, eds. Cambridge, Mass.: MIT Press, 1992.
[24] Y. Otha, K. Maenobu, and T. Sakai, "Obtaining Surface Orientation From Texels Under Perspective Projection," Proc. Seventh Int'l Joint Conf. Artificial Intelligence, pp. 746-751, 1981.
[25] T.Q. Phong, R. Horaud, A. Yassine, and D.T. Pham, "Optimal Estimation of Object Pose from a Single Perspective View," Proc. Fourth Int'l Conf. Computer Vision, pp. 534-539,Berlin, 1993.
[26] C.J. Poelman and T. Kanade, "A Paraperspective Factorization Method for Shape and Motion Recovery," Proc. Third European Conf. Computer Vision, pp. 97-108,Stockholm, May 1994.
[27] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes in C.Cambridge, England: Cambridge Univ. Press, 1988.
[28] L. Quan, Invariants of Six Points and Projective Reconstruction from Three Uncalibrated Images IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 1, pp. 34-46, Jan. 1995.
[29] L. Quan, "Self-Calibration of an Affine Camera From Multiple Views," Int'l J. Computer Vision, vol. 19, no. 1, pp. 93-105, May 1996.
[30] L. Quan and T. Kanade, A Factorization Method for Affine Structure from Line Correspondences IEEE Conf. Computer Vision and Pattern Recognition, June 1996.
[31] L. Quan and R. Mohr, "Affine Shape Representation from Motion Through Reference Points," J. Mathematical Imaging and Vision, vol. 1, pp. 145-151, 1992, also in IEEE Workshop on Visual Motion, New Jersey, pp. 249-254, 1991.
[32] L.S. Shapiro, A. Zisserman, and M. Brady, "3D Motion Recovery via Affine Epipolar Geometry," Int'l J. Computer Vision, vol. 16, no. 2, pp. 147-182, 1995.
[33] A. Shashua, “Algebraic Functions for Recognition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 8, pp. 779-789, 1995.
[34] M. Spetsakis and J. Aloimonos, "Structure From Motion Using Line Correspondences," Int'l J. Computer Vision, vol. 4, pp. 171-183, 1990.
[35] M. Spetsakis and J. Aloimonos, "A Unified Theory of Structure From Motion," Proc. DARPA Image Understanding Workshop, pp. 271-283, 1990.
[36] P. Sturm and B. Triggs, "A Factorization Based Algorithm for Multi-Image Projective Structure and Motion," Proc. Fourth European Conf. Computer Vision, B. Buxton and R. Cipolla, eds. Cambridge, England, Apr. 1996, vol. 1,065, Lecture Notes in Computer Science, pp. 709-720, Springer Verlag.
[37] B. Sturmfels, Algorithms in Invariant Theory.New York: Springer-Verlag, 1993.
[38] C. Tomasi and T. Kanade, "Shape and Motion From Image Streams Under Orthography: A Factorization Method," Int'l J. Computer Vision, vol. 9, no. 2, pp. 137-154, 1992.
[39] P.H.S. Torr, "Motion Segmentation and Outlier Detection," PhD thesis, Univ. of Oxford, Dept. of Engr. Science, 1995.
[40] B. Triggs, Matching Constraints and the Joint Image Proc. Int'l Conf. Computer Vision, pp. 338-343, 1995.
[41] S. Ullman, The Interpretation of Visual Motion.Cambridge, Mass.: MIT Press, 1979.
[42] S. Ullman and R. Basri, "Recognition by Linear Combinations of Models," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 992-1006, 1991.
[43] T. Viéville, Q.T. Luong, and O.D. Faugeras, "Motion of Points and Lines in the Uncalibrated Case," Int'l J. Computer Vision, vol. 17, no. 1, 1995.
[44] D. Weinshall and C. Tomasi, "Linear and Incremental Acquisition of Invariant Shape Models From Image Sequences," Proc. Fourth Int'l Conf. Computer Vision,Berlin, 1993.
[45] 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.
[46] Z. Zhang and O.D. Faugeras, 3D Dynamic Scene Analysis, a Stereo Based Approach.New York: Springer-Verlag, 1992.
Index Terms:
Structure from motion, affine structure, factorization method, line correspondence, affine camera, one-dimensional camera, uncalibrated image.
Citation:
Long Quan, Takeo Kanade, "Affine Structure from Line Correspondences With Uncalibrated Affine Cameras," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 8, pp. 834-845, Aug. 1997, doi:10.1109/34.608285