Parameter estimation in the three-point perspective projection problem in computer vision

Abstract

A mathematical solution to parameter estimation in the 3-D perspective projection problem is presented. In this paper, the Bairstow method and the direct solution method, which can solve the roots of a fourth order polynomial equation, are used to evaluate the three-point perspective pose estimation 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 roundoff errors came from the cosines law which was used to obtain the perspective projection points' polynomial equation. Here, the authors developed a new method to solve this problem directly without using sinusoidal functions. The evaluation results and advantages are included in a summary.