Abstract.
The problem of projective reconstruction by minimization of the 2D reprojection error in multiple images is considered. Although bundle adjustment techniques can be used to minimize the 2D reprojection error, these methods being based on nonlinear optimization algorithms require a good starting point. Quasi-linear algorithms with better global convergence properties can be used to generate an initial solution before submitting it to bundle adjustment for refinement. In this paper, we propose a factorization-based method to integrate the initial search as well as the bundle adjustment into a single algorithm consisting of a sequence of weighted least-squares problems, in which a control parameter is initially set to a relaxed state to allow the search of a good initial solution, and subsequently tightened up to force the final solution to approach a minimum point of the 2D reprojection error. The proposed algorithm is guaranteed to converge. Our method readily handles images with missing points.
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References
Bartoli, A. and Sturm, P. 2001. Three new algorithms for projective bundle adjustment with minimum parameters. Technical Report 4236, INRIA.
Beardsley, P. Zisserman, A., and Murray, D. 1997. Sequential updating of projective and affine structure from motion. Int. J. Computer Vision, 23(3):235–259.
Chen, G. and Medioni, G. 1999. Efficient iterative solutions to M-view projective reconstruction problem. In Int. Conf. on Computer Vision & Pattern Recognition, Vol. II, pp. 55–61.
Chen, G. and Medioni, G. 2002. Practical algorithms for stratified structure-from-motion, 20:103–123.
Faugeras, O.D. 1995. Stratification of 3-dimensional vision: Projective, affine, and metric representations. J. of the Optical Society of America-A, 12(3):465–484.
Han, M. and Kanade, T. 2000. Scene reconstruction from multiple uncalibrated views. Technical Report CMU-RI-TR-00-09, Robotics Institute, Carnegie Mellon University.
Han, M. and Kanade, T. 2001. Multiple motion scene reconstruction from uncalibrated views. In IEEE Int. Conf. Computer Vision, Vol. 1, pp. 163–170.
Hartley, R.I. 1993. Euclidean reconstruction from uncalibrated views. In Applications of Invariance in Computer Vision, J. Mundy and A. Zisserman (Eds.), vol. LNCS 825, pp. 237–256.
Heyden, A., Berthilsson, R., and Sparr, G. 1999. An iterative factorization method for projective structure and motion from image sequences. Image and Vision Computing, 1713:981–991.
Jacobs, D.W. 2001. Linear fitting with missing data for structure from motion. Computer Vision and Image Understanding, 82:57–81.
Mahamud, S. and Hebert, M. 2000. Iterative projective reconstruction from multiple views. In Int. Conf. on Computer Vision & Pattern Recognition, vol. 2, pp. 430–437.
Mahamud, S., Hebert, M., Omori, Y., and Ponce, J. 2001. Provably-convergent iterative methods for projective structure from motion. In Int. Conf. on Computer Vision & Pattern Recognition, Kauai, Hawaii, pp. 1018–1025.
Morris, D.D., Kanatani, K., and Kanade, T. 1999. Uncertainty modeling for optimal structure from motion. In Vision Algorithms Theory and Practice, Springer LNCS.
Oliensis, J. 1996. Fast and accurate self-calibration. In IEEE Int. Conf. Computer Vision, pp. 745–752.
Pollefeys, M. and Gool, L.V. 1999. Stratified self-calibration with the modulus constraint. IEEE Trans. Pattern Analysis & Machine Intelligence, 21(8):707–724.
Powell, M.J.D. 1970. A hybrid method for non-linear equations. In Numerical Methods for Non-Linear Algebraic Equations, P. Rabinowitz (Ed.), 87ff.
Shum, H.Y., Ikeuchi, K., and Reddy. R. 1995. Principal component analysis with missing data and its application to polyhedral object modeling. IEEE Trans. Pattern Analysis & Machine Intelligence, 17(9):854–867.
Shum, H.Y., Ke, Q., and Zhang, Z. 1999. Efficient bundle adjustment with virtual key frames: A hierarchical approach to multi-frame structure from motion. In Int. Conf. on Computer Vision & Pattern Recognition.
Sparr, G. 1996. Simultaneous reconstruction of scene structure and camera locations from uncalibrated image sequences. In Int. Conf. Pattern Recognition.
Sturm, P. and Triggs, B. 1996. A factorization based algorithm for multi-image projective structure and motion. In European Conf. on Computer Vision. Cambridge, England, pp. 709–720.
Tomasi, C. and Kanade, T. 1992. Shape and motion from image streams under orthography: A factorization method. Int. J. Computer Vision, 9(2):137–154.
Triggs, B. 1996. Factorization methods for projective structure and motion. In Int. Conf. on Computer Vision & Pattern Recognition, San Francisco, pp. 845–851.
Triggs, B. 1998. Some notes on factorization methods for projective structure and Motion, unpublished.
Triggs, B., McLauchlan, P., Hartley, R., and Fitzgibbon, A. 2000. Bundle adjustment-A modern synthesis. In Vision Algorithms: Theory and Practice, W. Triggs, A. Zisserman, and R. Szeliski (Eds.), vol. LNCS 1883, Springer Verlag, pp. 298–375.
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Hung, Y.S., Tang, W.K. Projective Reconstruction from Multiple Views with Minimization of 2D Reprojection Error. Int J Comput Vision 66, 305–317 (2006). https://doi.org/10.1007/s11263-005-3675-0
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DOI: https://doi.org/10.1007/s11263-005-3675-0