SOLVING THE THREE-POINT CAMERA POSE PROBLEM IN THE VICINITY OF THE DANGER CYLINDER

Michael Q. Rieck

2012

Abstract

A new theorem in solid geometry is introduced and shown to be quite useful for solving the Perspective 3-Point Pose Problem (P3P) in the general vicinity of the danger cylinder. Also resulting from this is a criterion for partially deciding which mathematical solution is the correct physical solution. Simulations have demonstrated the greater accuracy of the new method for solving P3P, over a standard classical method, under the following condition. The distance from the camera’s optical center to the axis of the danger cylinder must be sufficiently small, compared with the distance from the optical center to the plane containing the control points.

References

  1. DeMenthon, D. and Davis, L. S. (1992). Exact and approximate solutions of the perspective-three-point problem. IEEE Trans. Pattern Analysis and Machine Intelligence, 14(11):1100-1105.
  2. Faugère, J.-C., Moroz, G., Rouillier, F., and El-Din, M. S. (2008). Classification of the perspective-three-point problem, discriminant variety and real solving polynomial systems of inequalities. In ISSAC'08, 21st Int. Symp. Symbolic and Algebraic Computation, pages 79-86. ACM.
  3. Gao, X.-S., Hou, X.-R., Tang, J., and Cheng, H.-F. (2003). Complete solution classification for the perspectivethree-point problem. IEEE Trans. Pattern Analysis and Machine Intelligence, 25(8):930-943.
  4. Grunert, J. A. (1841). Das pothenotische problem in erweiterter gestalt nebst ü ber seine anwendungen in der geodäsie. In Grunerts Archiv für Mathematik und Physik, volume 1, pages 238-248.
  5. Haralick, R. M., Lee, C.-N., Ottenberg, K., and Nölle, N. (1994). Review and analysis of solutions of the three point perspective pose estimation problem. J. Computer Vision, 13(3):331-356.
  6. Merritt, E. L. (1949). Explicit three-point resection in space. Photogrammetric Engineering, 15(4):649-655.
  7. M üller, F. J. (1925). Direkte (exakte) l ösung des einfachen r ückwärtsein-schneidens im raume. In Allegemaine Vermessungs-Nachrichten.
  8. Nistér, D. (2007). A minimal solution to the generalized 3-point pose problem. J. Mathematical Imaging and Vision, 27(1):67-79.
  9. Pisinger, G. and Hanning, T. (2007). Closed form monocular re-projection pose estimation. In ISIP 7807, IEEE Int. Conf. Image Processing, volume 5, pages 197- 200.
  10. Rieck, M. Q. (2010). Handling repeated solutions to the perspective three-point pose problem. In VISAPP 7810, Int. Conf. Computer Vision Theory and Appl., pages 395-399.
  11. Rieck, M. Q. (2011). An algorithm for finding repeated solutions to the general perspective three-point pose problem. J. Mathematical Imaging and Vision. DOI: 10.1007/s10851-011-0278-y (to appear in print).
  12. Smith, A. D. N. (1965). The explicit solution of the single picture resolution problem, with a least squares adjustment to redundant control. Photogrammetric Record, 5(26):113-122.
  13. Sun, F.-M. and Wang, B. (2010). The solution distribution analysis of the p3p problem. In SMC 7810, Int. Conf. Systems, Man and Cybernetics, pages 2033- 2036. IEEE.
  14. Tang, J., Chen, W., and Wang, J. (2008). A study on the p3p problem. In ICIC 7808, 4th Int. Conf. Intelligent Computing, volume 5226, pages 422-429.
  15. Tang, J. and Liu, N. (2009). The unique solution for p3p problem. In SIGAPP 7809, ACM Symp. Applied Computing, pages 1138-1139. ACM.
  16. Thompson, E. H. (1966). Space resection: failure cases. Photogrammetric Record, 5(27):201-204.
  17. Wolfe, W. J., Mathis, D., Sklair, C. W., and Magee, M. (1991). The perspective view of three points. IEEE Trans. Pattern Analysis and Machine Intelligence, 13(1):66-73.
  18. Xiaoshan, G. and Hangfei, C. (2001). New algorithms for the perspective-three-point problem. J. Comput. Sci. & Tech., 16(3):194-207.
  19. Zhang, C.-X. and Hu, Z.-Y. (2005). A general sufficient condition of four positive solutions of the p3p problem. J. Comput. Sci. & Technol., 20(6):836-842.
  20. Zhang, C.-X. and Hu, Z.-Y. (2006). Why is the danger cylinder dangerous in the p3p problem? Acta Automatica Sinica, 32(4):504-511.
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Paper Citation


in Harvard Style

Q. Rieck M. (2012). SOLVING THE THREE-POINT CAMERA POSE PROBLEM IN THE VICINITY OF THE DANGER CYLINDER . In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2012) ISBN 978-989-8565-04-4, pages 335-340. DOI: 10.5220/0003725403350340


in Bibtex Style

@conference{visapp12,
author={Michael Q. Rieck},
title={SOLVING THE THREE-POINT CAMERA POSE PROBLEM IN THE VICINITY OF THE DANGER CYLINDER},
booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2012)},
year={2012},
pages={335-340},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003725403350340},
isbn={978-989-8565-04-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2012)
TI - SOLVING THE THREE-POINT CAMERA POSE PROBLEM IN THE VICINITY OF THE DANGER CYLINDER
SN - 978-989-8565-04-4
AU - Q. Rieck M.
PY - 2012
SP - 335
EP - 340
DO - 10.5220/0003725403350340