Abstract
A factorization method is proposed for recovering camera motion and object shapes from point correspondences observed in multiple images with perspective projection. For any factorization-based approaches for perspective images, scaling parameters called projective depths must be estimated in order to obtain a measurement matrix that could be decomposed into motion and shape. One possible approach, proposed by Sturm and Triggs[11], is to compute projective depths from fundamental matrices and epipoles. The estimation process of the fundamental matrices, however, might be unstable if the measurement noise is large or the cameras and the object points are nearly in critical configurations. In this paper, the authors propose an algorithm by which the projective depths are iteratively estimated so that the measurement matrix is made to be as close as possible to rank 4. This estimation process requires no fundamental matrix computation and is therefore robust against measurement noise. Camera motion and shape in 3D projective space are then recovered by factoring the measurement matrix computed from the obtained projective depths. The authors also derive metric constraints for a perspective camera model in the case where the intrinsic camera parameters are available and show that these constraints can be linearly solved for a projective transformation which relates projective and Euclidean descriptions of the scene structure. Using this transformation, the projective motion and shape obtained in the previous factorization step is upgraded to metric descriptions, that is, represented with respect to the Euclidean coordinate frame. The validity of the proposed method is confirmed by experiments with real images.
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References
S. Christy, R. Horaud, ”Euclidean Reconstruction: from Paraperspective to Perspective”, Proc. 4th European Conf. on Computer Vision, Cambridge, vol.2, pp. 129–140, 1996
O. D. Faugeras, “What can be seen in three dimensions with an uncalibrated stereo rig?”, Proc. 2nd European Conf. on Computer Vision, Santa Margherita Ligure, pp.563–578, 1992
O. D. Faugeras, “Three-Dimensional Computer Vision”, MIT Press, Cambridge, 1993
R. Hartley, R. Gupta, and T. Chang, “Stereo from Uncalibrated Cameras”, Proc. Computer Vision and Pattern Recognition, Champaign, pp.761–764, 1992
R. I. Hartley, “In Defense of the 8-point Algorithm”, Proc. 5th Int. Conf. on Computer Vision”, Cambridge, pp.1064–1070, 1995
A. Heyden, “Projective Structure and Motion from Image Sequences Using Subspace Methods”, Proc. 10th Scandinavian Conference on Image Analysis, Lappenraanta, 1997
K. Kanatani, “Statistical Optimization for Geometric Computation: Theory and Practice”, Elsevier Science, Amsterdam, 1996
S. J. Maybank, “The projective geometry of ambiguous surface”, Phil. Trans. of the Royal Society of London: A, vol.332, pp.1–47, 1990
C. J. Poelman and T. Kanade, “A Paraperspective Factorization Method for Shape and Motion Recovery”, Proc. 3rd European Conference on Computer Vision, vol.2, pp.97–108, 1994
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, “Numerical Recipes in C: The Art of Scientific Computing”, Cambridge University Press, Cambridge, 1988
P. Sturm and B. Triggs, “A Factorization Based Algorithm for Multi-Image Projective Structure and Motion”, Proc. 4th European Conf. on Computer Vision, Cambridge, vol.2, pp.709–720, 1996
C. Tomasi and T. Kanade, “Shape and Motion from Image Streams under Orthography: a Factorization Method”, International Journal of Computer Vision, vol.9, no.2, pp. 137–154, 1992
B. Triggs, “Factorization Methods for Projective Structure and Motion”, Proc. Computer Vision and Pattern Recognition, San Francisco, pp.845–851, 1996
D. Weinshall and C. Tomasi, “Linear and Incremental Acquisition of Invariand Shape Models from Image Sequences”, Proc. 4th International Conference on Computer Vision”, pp.675–682, 1993
Z. Zhang, “Determining the Epipolar Geometry and its Uncertainty: A Review”, Technical Report RR-2927, INRIA, 1996
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© 1998 Springer-Verlag Berlin Heidelberg
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Ueshiba, T., Tomita, F. (1998). A factorization method for projective and Euclidean reconstruction from multiple perspective views via iterative depth estimation. In: Burkhardt, H., Neumann, B. (eds) Computer Vision — ECCV'98. ECCV 1998. Lecture Notes in Computer Science, vol 1406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055674
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DOI: https://doi.org/10.1007/BFb0055674
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