On the Probability of the Number of Solutions for the P4P Problem

  • Xiao-Shan Gao
  • Jianliang Tang


This paper studies the multi-solution phenomenon for the perspective four point (P4P) problem from geometric and algebraic aspects. We give a pure geometric proof that the P4P problem could have up to five solutions. We also give a clear picture on how these five solutions could be realized. We prove that with probability one, the P4P problem has a unique solution which can be represented by a set of rational functions in the parameters. The simulant experiments show that to solve the P4P problem with the rational functions is stable and accurate.


camera calibration pose determination perspective four point problem P4P probability number of solutions 


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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  • Xiao-Shan Gao
    • 1
  • Jianliang Tang
    • 2
  1. 1.Key Laboratory of Mathematics Mechanization, Institute of Systems Science, Academia SinicaBeijingChina
  2. 2.College of ScienceShenzhen UniversityShenzhenChina

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