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Complete Solution Classification for the Perspective-Three-Point Problem
August 2003 (vol. 25 no. 8)
pp. 930-943

Abstract—In this paper, we use two approaches to solve the Perspective-Three-Point (P3P) problem: the algebraic approach and the geometric approach. In the algebraic approach, we use Wu-Ritt's zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system. This decomposition provides the first complete analytical solution to the P3P problem. We also give a complete solution classification for the P3P equation system, i.e., we give explicit criteria for the P3P problem to have one, two, three, and four solutions. Combining the analytical solutions with the criteria, we provide an algorithm, CASSC, which may be used to find complete and robust numerical solutions to the P3P problem. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions.

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Index Terms:
Perspective-Three-Point problem, pose determination, analytical solutions, solution classification, geometric criteria, Wu-Ritt's zero decomposition method.
Xiao-Shan Gao, Xiao-Rong Hou, Jianliang Tang, Hang-Fei 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, Aug. 2003, doi:10.1109/TPAMI.2003.1217599
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