A Conic Transformation Approach for Solving the Perspective-Three-Point Problem

Abstract

We propose a conic transformation method to solve the Perspective-Three-Point (P3P) problem. In contrast to the current state-of-the-art solvers which formulate the P3P problem by intersecting two conics and constructing a degenerate conic to find the intersection our approach builds upon a new formulation based on a transformation that maps the two conics to a new coordinate system where one of the conics becomes a standard parabola in a canonical form. This enables expressing one variable in terms of the other variable and as a consequence substantially simplifies the problem of finding the conic intersection. Moreover the polynomial coefficients are fast to compute and we only need to determine the real-valued intersection points which avoids the requirement of using computationally expensive complex arithmetic. While the current state-of-the-art methods reduce the conic intersection problem to solving a univariate cubic equation our approach despite resulting in a quartic equation is still faster thanks to this new simplified formulation. Extensive evaluations demonstrate that our method achieves higher speed while maintaining robustness and stability comparable to state-of-the-art methods.