New Algorithms for the Perspective-Three-Point Problem

Xiao-Shan Gao, Hangfei Chen

Abstract: 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.