Abstract
In this paper, we address the problem of line triangulation, which is to find the position of a line in space given its three projections taken with cameras with known camera matrices. Because of measurement error in line extraction, the problem becomes difficult so that it is necessary to estimate a 3D line to optimally fit measured lines. In this work, the normal errors of measured line are presented to describe the measurement error and based on their statistical property a new geometric-distance optimality criterion is constructed. Furthermore, a simple iterative algorithm is proposed to obtain suboptimal solution of the optimality criterion, which ensures that the solution satisfies the trifocal tensor constraint. Experiments show that our iterative algorithm can achieve the estimation accuracy comparable with the Gold Standard algorithm, but its computational load is substantially reduced.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-319-02895-8_64
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References
Beardsley, P.A., Zisserman, A., Murray, D.W.: Navigation using affine structure from motion. In: Eklundh, J.-O. (ed.) ECCV 1994. LNCS, vol. 801, pp. 85–96. Springer, Heidelberg (1994)
Hartley, R., Sturm, P.: Triangulation. Computer Vision and Image Understanding, 146–157 (1997)
Wu, F., Zhang, Q., Hu, Z.: Efficient suboptimal solutions to the optimal triangulation. International Journal of Computer Vision, 77–106 (2011)
Kanatani, K., Sugaya, Y., Niitsuma, H.: Triangulation from two views revisited: Hartley-Sturm vs. optimal correction. In: The British Machine Vision Conference, pp. 173–182. BMVC Press, Leeds (2008)
Lindstrom, P.: Triangulation made easy. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1554–1561. IEEE Press, New York (2010)
Olsson, C., Kahl, F., Oskarsson, M.: Branch and bound methods for Euclidean registration problems. IEEE Trans. Pattern Anal. Mach. Intell., 783–794 (2009)
Olsson, C., Kahl, F., Hartley, R.: Projective least-squares: global solutions with local optimization. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1216–1223. IEEE Press, New York (2009)
Lu, F., Hartley, R.I.: A fast optimal algorithm for L 2 triangulation. In: Yagi, Y., Kang, S.B., Kweon, I.S., Zha, H. (eds.) ACCV 2007, Part II. LNCS, vol. 4844, pp. 279–288. Springer, Heidelberg (2007)
Hartley, R., Schaffalitzky, F.: L ∞ minimization in geometric reconstruction problems. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 504–509. IEEE Press, New York (2004)
Ke, Q., Kanade, T.: Quasiconvex optimization for robust geometric reconstruction. IEEE Trans. Pattern Anal. Mach. Intell., 1834–1847 (2007)
Kahl, F., Hartley, R.: Multiple-view geometry under the L ∞ -norm. IEEE Trans. Pattern Anal. Mach. Intell., 1603–1617 (2008)
Bartoli, A., Sturm, P.: Structure-from-motion using lines: representation, triangulation, and bundle adjustment. Computer Vision and Image Understanding, 416–441 (2005)
Spetsakis, M., Aloimonos, J.: Structure from motion using line correspondences. International Journal of Computer Vision, 171–183 (1990)
Weng, J., Huang, T., Ahuja, N.: Motion and structure from line correspondences: closed-form solution, uniqueness, and optimization. IEEE Trans. Pattern Anal. Mach. Intell. 318–336 (1992)
Taylor, C.J., Kriegman, D.J.: Structure and motion from line segments in multiple images. IEEE Trans. Pattern Anal. Mach. Intell. 1021–1032 (1995)
Josephson, K., Kahl, F.: Triangulation of Points, Lines and Conics. Journal of Mathematical Imaging and Vision, 215–225 (2008)
Hartley, R., Zisserman, A.: Multiple view geometry in computer vision. Cambridge University Press, Cambridge (2003)
Ressl, C.: Geometry, Constraints and Computation of the Trifocal Tensor. PhD thesis, Technical University of Vienna (2003)
Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (2005)
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Zhang, Q., Wu, Y., Liu, M., Jiao, L. (2013). An Efficient Normal-Error Iterative Algorithm for Line Triangulation. In: Blanc-Talon, J., Kasinski, A., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2013. Lecture Notes in Computer Science, vol 8192. Springer, Cham. https://doi.org/10.1007/978-3-319-02895-8_27
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DOI: https://doi.org/10.1007/978-3-319-02895-8_27
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