New Algorithms for the Perspective-Three-Point Problem

In this paper, two approaches are used to solve the Perspective-Three-Point Problem (P3P): the symbolic computation approach and the geometric approach. In the symbolic computation 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. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions. The complete solution classification for two special cases with three and four parameters is also given. This work is supported in part by the National Natural Science Foundation of China under an outstanding youth grant (No. 69725002) and by the NKBRSF of China (No. G1998030600). GAO Xiaoshan received his PhD. degree from Institute of Systems Science, The Chinese Academy of Sciences in 1988. Since 1996, he has been a professor in the Institute of Systems Science, Academy of Mathematics and System Science, The Chinese Academy of Sciences. His research interests include automated reasoning, symbolic computation, intelligent CAD and CAI (computer aided instruction). CHEN Hangfei was born in 1974. He received his B.S. degree from the University of Science and Technology of China in 1995 and M.S. degree from the Institute of Systems Science in 1998. He is now a Ph.D. candidate in Pennsylvania State University.