A Fundamentally New View of the Perspective Three-Point Pose Problem
The Perspective Three-Point Pose Problem (P3P) is an old and basic problem in the area of camera tracking. While methods for solving it have been largely successful, they are subject to erratic behavior near the so-called danger cylinder. Another difficulty with most of these methods is the need to select the physically correct solution from among various mathematical solutions. This article presents a new framework from which to study P3P for non-collinear control points, particularly near the danger cylinder. A multivariate Newton-Raphson method to approximately solve P3P is introduced. Using the new framework, this is then enhanced by adding special procedures for handling the problematic behavior near the danger cylinder. It produces a point on the cylinder, a compromise between two nearly equal mathematical solutions, only one of which is the cameras actual position. The compromise diminishes the risk of accidentally converging to the other nearby solution. However, it does impose the need, upon receding from the danger cylinder vicinity, to make a selection between two possible approximate solution points. Traditional algebraic methods depend on correctly selecting from up to four points, each time the camera position is recomputed. In the new iterative method, selecting between just two points is only occasionally required. Simulations demonstrate that a considerable improvement results from using this revised method instead of the basic Newton-Raphson method.
perspective pose p3p camera tracking danger cylinder resection