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Robust Software for Computing Camera Motion Parameters

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Abstract

We revisit the method of Tsai, Huang, and Zhu for the computation of camera motion parameters in computer vision. We elucidate some spectral properties of the homography matrices that arise, which are rank-one perturbations of rotation matrices. We show how to correct for noise by finding the rank-one perturbation of a rotation closest to a given matrix. We illustrate some of the inaccuracies and computational failures that can arise when using the formulas given by Tsai, and we propose new formulas that avoid these pitfalls. A computational experiment shows that the new methods are indeed quite robust.

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References

  1. Forsythe, G.E.: How do you solve a quadratic equation. Technical Report CS 40, Stanford University (1966)

  2. Forsythe, G.E.: What is a satisfactory quadratic equation solver? In: Dejon, B., Henrici, P. (eds.) Constructive Aspects of the Fundamental Theorem of Algebra: Proceedings of a Symposium Conducted at the IBM Research Laboratory, Zürich-Rüschlikon, Switzerland, 5–7 June 1967, pp. 53–61. Wiley-Interscience, New York (1969)

    Google Scholar 

  3. Householder, A.: The Theory of Matrices in Numerical Analysis. Blaisdell, New York (1964)

    MATH  Google Scholar 

  4. Nievergelt, Y.: Schmidt-Mirsky matrix approximation with linearly constrained singular values. In: Linear Algebra and Its Applications, pp. 207–219 (1997)

  5. Tsai, R.Y., Huang, T.S., Zhu, W.-L.: Estimating three-dimensional motion parameters of a rigid planar patch, II: singular value decomposition. IEEE Trans. Acoust. Speech Signal Process. 30, 525–534 (1982)

    Article  Google Scholar 

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Authors and Affiliations

  1. HP Labs, 1501 Page Mill Road, Palo Alto, CA, 94304, USA

    Robert Schreiber, Zeyu Li & Harlyn Baker

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  1. Robert Schreiber
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  2. Zeyu Li
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  3. Harlyn Baker
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Correspondence to Robert Schreiber.

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Schreiber, R., Li, Z. & Baker, H. Robust Software for Computing Camera Motion Parameters. J Math Imaging Vis 33, 1–9 (2009). https://doi.org/10.1007/s10851-008-0106-1

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  • DOI: https://doi.org/10.1007/s10851-008-0106-1

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