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Artificial Intelligence - Special issue on geometric reasoning
An analytic solution for the perspective 4-point problem
Computer Vision, Graphics, and Image Processing
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
Algorithmic algebra
Mechanical theorem proving in geometries
Mechanical theorem proving in geometries
Model-based object pose in 25 lines of code
International Journal of Computer Vision - Special issue: image understanding research at the University of Maryland
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Linear N-Point Camera Pose Determination
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
A complete symbolic-numeric linear method for camera pose determination
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
On Pose Recovery for Generalized Visual Sensors
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Journal of Mathematical Imaging and Vision
A general sufficient condition of four positive solutions of the P3P problem
Journal of Computer Science and Technology
On the Probability of the Number of Solutions for the P4P Problem
Journal of Mathematical Imaging and Vision
Camera calibration based on receptive fields
Pattern Recognition
Pose determination and plane measurement using a trapezium
Pattern Recognition Letters
Image and Vision Computing
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
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The unique solution for P3P problem
Proceedings of the 2009 ACM symposium on Applied Computing
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Robotics and Computer-Integrated Manufacturing
An Algorithm for Finding Repeated Solutions to the General Perspective Three-Point Pose Problem
Journal of Mathematical Imaging and Vision
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IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Some necessary conditions on the number of solutions for the P4P problem
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Journal of Symbolic Computation
An efficient method for computing comprehensive Gröbner bases
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International Journal of Computer Vision
A Fundamentally New View of the Perspective Three-Point Pose Problem
Journal of Mathematical Imaging and Vision
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In this paper, we use two approaches to solve the Perspective-Three-Point (P3P) problem: the algebraic approach and the geometric approach. In the algebraic 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. We also give a complete solution classification for the P3P equation system, i.e., we give explicit criteria for the P3P problem to have one, two, three, and four solutions. Combining the analytical solutions with the criteria, we provide an algorithm, CASSC, which may be used to find complete and robust numerical solutions to the P3P problem. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions.