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Mathematical Problems in Engineering
Volume 2015, Article ID 147397, 6 pages
http://dx.doi.org/10.1155/2015/147397
Research Article

Singular Points in the Optical Center Distribution of P3P Solutions

1School of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan 030024, China
2Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China

Received 27 April 2015; Revised 15 June 2015; Accepted 21 June 2015

Academic Editor: Erik Cuevas

Copyright © 2015 Lihua Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. A. Grunert, “Das pothenotische problem in erweiterter gestalt nebst über seine anwendungen in der geodäsie,” Grunerts Archiv für Mathematik und Physik, vol. 1, pp. 238–248, 1841. View at Google Scholar
  2. M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Communications of the Association for Computing Machinery, vol. 24, no. 6, pp. 381–395, 1981. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. D. G. Lowe, “Fitting parameterized three-dimensional models to images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 5, pp. 441–450, 1991. View at Publisher · View at Google Scholar · View at Scopus
  4. V. Lepetit and P. Fua, “Monocular model-based 3D tracking of rigid objects: a survey,” Foundations and Trends in Computer Graphics and Vision, vol. 1, no. 1, pp. 1–89, 2005. View at Publisher · View at Google Scholar
  5. C. McGlove, E. Mikhail, and J. Bethel, Manual of Photogrametry, American Society for Photogrammetry and Romote Sensing, 5th edition, 2004.
  6. D. Nistér and H. Stewénius, “A minimal solution to the generalised 3-point pose problem,” Journal of Mathematical Imaging and Vision, vol. 27, no. 1, pp. 67–79, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. Qingxuan, Z. Ping, and S. Hanxu, “The study of positioning with igh-precision by single camera based on P3P algorithm,” in Proceedings of the IEEE International Conference on Industrial Informatics (INDIN' 06), pp. 1385–1388, August 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Quan and Z. Lan, “Linear N-point camera pose determination,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 8, pp. 774–780, 1999. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Tang, W. Chen, and J. Wang, “A study on the P3P problem,” in Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues, vol. 5226 of Lecture Notes in Computer Science, pp. 422–429, Springer, Berlin, Germany, 2008. View at Publisher · View at Google Scholar
  10. J. Tang and N. Liu, “The unique solution for P3P problem,” in Proceedings of the 2009 ACM Symposium on Applied Computing (SAC '09), pp. 1138–1139, ACM, New York, NY, USA, 2009. View at Publisher · View at Google Scholar
  11. W. J. Wolfe, “A Special Case Solution to the Perspective 3-Point Problem,” http://faculty.csuci.edu/william.wolfe/csuci/articles/perspectiveview/new_p3p_article/wolfe_p3p_special_case.pdf.
  12. B. M. Haralick, C.-N. Lee, K. Ottenberg, and M. Nölle, “Review and analysis of solutions of the three point perspective pose estimation problem,” International Journal of Computer Vision, vol. 13, no. 3, pp. 331–356, 1994. View at Publisher · View at Google Scholar · View at Scopus
  13. X.-S. Gao, X.-R. Hou, J. Tang, and H.-F. Cheng, “Complete solution classification for the perspective-three-point problem,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 8, pp. 930–943, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. X.-S. Gao and J.-L. Tang, “On the probability of the number of solutions for the P4P Problem,” Journal of Mathematical Imaging and Vision, vol. 25, no. 1, pp. 79–86, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. Q. Rieck, “An algorithm for finding repeated solutions to the general perspective three-point pose problem,” Journal of Mathematical Imaging and Vision, vol. 42, no. 1, pp. 92–100, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. M. Q. Rieck, “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 (VISAPP '12), vol. 2, pp. 335–340, February 2012. View at Scopus
  17. M. Q. Rieck, “A fundamentally new view of the perspective three-point pose problem,” Journal of Mathematical Imaging and Vision, vol. 48, no. 3, pp. 499–516, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. C.-X. Zhang and Z.-Y. Hu, “Why is the danger cylinder dangerous in the P3P Problem?” Acta Automatica Sinica, vol. 32, no. 4, pp. 504–511, 2006. View at Google Scholar · View at MathSciNet
  19. C.-X. Zhang and Z.-Y. Hu, “A general sufficient condition of four positive solutions of the P3P Problem,” Journal of Computer Science and Technology, vol. 20, no. 6, pp. 836–842, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. F.-M. Sun and B. Wang, “A note on the roots distribution and stability of the PnP Problem,” Acta Automatica Sinica, vol. 36, no. 9, pp. 1213–1219, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Y.-H. Wu and Z.-Y. Hu, “PnP problem revisited,” Journal of Mathematical Imaging and Vision, vol. 24, no. 1, pp. 131–141, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. B. Wang, C.-X. Zhang, and Z.-Y. Hu, “Geometric interpretation of the multi-solution phenomenon in the P3P problem,” IEEE Transactions on Pattern Analysis and Machine Intelligence. Under revision.
  23. B. Wang, C.-X. Zhang, and Z.-Y. Hu, “The relationship between solutions of the P3P problem and roots of its resulting quartic equation,” Tech. Rep. TR-CASIA-NLPR-RV-2015-03-07, 2015. View at Google Scholar
  24. W. J. Wolfe, D. Mathis, C. W. Sklair, and M. Magee, “The perspective view of three points,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 1, pp. 66–73, 1991. View at Publisher · View at Google Scholar · View at Scopus