New algorithms for the Perspective-Three-Point Problem

In this paper, two approaches are used to solve the Perspective-Three-Point Problem (P3P): the symbolic computation approach and the geometric approach. In the symbolic computation approach, we use Wu-Ritt’s zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system. This decomposition provides the first complete analytical solution to the P3P problem. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions. The complete solution classification for two special cases with three and four parameters is also given.

[1]  Robert M. Haralick,et al.  Analysis and solutions of the three point perspective pose estimation problem , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[2]  Mongi A. Abidi,et al.  A New Efficient and Direct Solution for Pose Estimation Using Quadrangular Targets: Algorithm and Evaluation , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Bud Mishra,et al.  Algorithmic Algebra , 1993, Texts and Monographs in Computer Science.

[4]  Gao Xiao-Shan.  ON THE THEORY OF RESOLVENTS AND ITS APPLICATIONS , 1999 .

[5]  Bruno Buchberger,et al.  Computer algebra symbolic and algebraic computation , 1982, SIGS.

[6]  William J. Wolfe,et al.  Camera Calibration Using The Perspective View Of A Triangle , 1987, Other Conferences.

[7]  Larry S. Davis,et al.  Exact and Approximate Solutions of the Perspective-Three-Point Problem , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Radu Horaud,et al.  An analytic solution for the perspective 4-point problem , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[9]  Dennis S. Arnon,et al.  Geometric Reasoning with Logic and Algebra , 1988, Artif. Intell..

[10]  David Harwood,et al.  Passive ranging to known planar point sets , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[11]  Lu Yang.  A Simplified Algorithm for Solution Classification of the Perspective-three-Point Problem 1) , 1998 .

[12]  Robert C. Bolles,et al.  Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography , 1981, CACM.

[13]  George E. Collins,et al.  Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .

[14]  Joseph S.-C. Yuan.  A general photogrammetric method for determining object position and orientation , 1989, IEEE Trans. Robotics Autom..

[15]  Michael J. Magee,et al.  The Perspective View of Three Points , 1991, IEEE Trans. Pattern Anal. Mach. Intell..