A Mathematical Solution for The Perspective Three-Point Problem

Abstract

In this paper different mathematical solutions and a new approach to the 3-D perspective projection problem in computer vision are presented. The Bairstow method and the direct solution method, which can solve the roots of a fourth-order polynomial equation, are used to evaluate the perspective three-point problem. When the known triangle size increases, the error will also increase. To avoid this numerical error, the round-off error generated from the computation process needs to be reduced. Most of the round-off errors come from the Law of Cosines, which is used to obtain the perspective projection points' polynomial equation. A different formulation of the existing method is developed to solve this problem directly without using the trigonometric function. The evaluation results and advantages are explored.