Solution Classification for Perspective-Three-Point Problem Base on PST Method

Abstract:

The perspective-n-point (PnP) problem is originated from camera calibration. It is to determine the position and orientation of the camera with respect to a scene object from n correspondent points. And a new stable algorithm by using a geometric constraint called perspective similar triangle (PST) can give new equations to solve P3P. The PST method achieves high stability in the permutation problem and in presence of image noise. Using the complete discrimination system, we obtain the solution classification of the new equation for the P3P problem. The solution classification gives a set of formulas to determine the number of real solutions to the P3P problem. Based on the formulas, we may know whether the parameters give multiple solutions or not and are critical or not which is very important to present robust algorithm.

• Periodical: Applied Mechanics and Materials (Volumes 475-476)
• Pages: 1067-1070
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.475-476.1067
• Online since: December 2013
• Authors: Ming Liang Li, Jian Liang Tang*
• Keywords: Complete Discrimination System, Perspective Similar Triangle, Perspective-Three-Point Problem, Revised Sign Lists, Solution Classification

References

[1] Martin A. Fisher and Robert C. Bolles. Random sample Consensus: A Paradigm for Model Fitting with Application to Image Analysis and Automated Cartography. CACM, 24(6): 381-395, (1981).

DOI: 10.1145/358669.358692

[2] R. Haralick, C. Lee, K. Ottenberg, M. Nolle, Review and analysis of solutions of the three point perspective pose estimation problem, International Journal of Computer Vision 13(3) (1994) 331-356.

DOI: 10.1007/bf02028352

[3] L. Quan, Z. Lan, Linear n-point camera pose determination, IEEE Transactions on Pattern Analysis and Machine Intelligence 21(8) (1999) 774-780.

DOI: 10.1109/34.784291

[4] Xiao-Shan Gao and Xiao-Rong Hou etc. Complete Solution Classification for the Perspective-Three-point Problem. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(8) (2003) 930-943.

DOI: 10.1109/tpami.2003.1217599

[5] Shiqi LI and Chi Xu. A Stable Direct Solution of Perspective-Three-Point Problem. International Journal of Pattern Recognition and Artificial Intelligence, 25(1) (2011) 627-646.

DOI: 10.1142/s0218001411008774

[6] L. Yang, Resent advances on determining the number of real roots of parametric polynomials, J. Symbolic Computation, 1999, 28: 225-242.

DOI: 10.1006/jsco.1998.0274

[7] L. Yang, J.Z. Zhang, and X.R. Hou, Non-linear Equation System and Automated Theorem Proving, Shanghai Press of Science Technology and Education, 1996. (in Chinese).