The Perspective View of Three Points
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exact and Approximate Solutions of the Perspective-Three-Point Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
Review and analysis of solutions of the three point perspective pose estimation problem
International Journal of Computer Vision
New algorithms for the perspective-three-point problem
Journal of Computer Science and Technology
Complete Solution Classification for the Perspective-Three-Point Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
A general sufficient condition of four positive solutions of the P3P problem
Journal of Computer Science and Technology
A Minimal Solution to the Generalised 3-Point Pose Problem
Journal of Mathematical Imaging and Vision
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Theoretical and Methodological Issues
The unique solution for P3P problem
Proceedings of the 2009 ACM symposium on Applied Computing
An Algorithm for Finding Repeated Solutions to the General Perspective Three-Point Pose Problem
Journal of Mathematical Imaging and Vision
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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 camera's 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.