A Stable Direct Solution of Perspective-Three-Point Problem

The perspective-three-point problem (P3P) is a classical problem in computer vision. The existing direct solutions of P3P have at least 3 limitations: (1) the numerical instability when using different vertex permutations, (2) the degeneration in the geometric singularity case, and (3) the dependence on particular equation solvers. A new direct solution of P3P is presented to deal with these limitations. The main idea is to reduce the number of unknown parameter by using a geometric constraint we called “perspective similar triangle” (PST). The PST method achieves high stability in the permutation problem and in presence of image noise, and does not rely on particular equation solvers. Furthermore, reliable results can be retrieved even in “danger cylinder”, a typical kind of geometric singularity of P3P, where all existing direct solutions degenerate significantly.