On the Probability of the Number of Solutions for the P4P Problem

Authors:
Xiao-Shan Gao;Jianliang Tang
Affiliations:
Key Laboratory of Mathematics Mechanization, Institute of Systems Science, Academia Sinica, Beijing, China 100080;College of Science, Shenzhen University, Shenzhen, China 518060
Venue:
Journal of Mathematical Imaging and Vision
Year:
2006

Citing 11
Cited 7

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
Algorithmic algebra

Algorithmic algebra
Three-dimensional computer vision: a geometric viewpoint

Three-dimensional computer vision: a geometric viewpoint
Linear N-Point Camera Pose Determination

IEEE Transactions on Pattern Analysis and Machine Intelligence
Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography

Communications of the ACM
Multiple view geometry in computer visiond

Multiple view geometry in computer visiond
Theory of Reconstruction from Image Motion

Theory of Reconstruction from Image Motion
A New Efficient and Direct Solution for Pose Estimation Using Quadrangular Targets: Algorithm and Evaluation

IEEE Transactions on Pattern Analysis and Machine Intelligence
A Note on the Number of Solutions of the Noncoplanar P4P Problem

IEEE Transactions on Pattern Analysis and Machine Intelligence
Complete Solution Classification for the Perspective-Three-Point Problem

IEEE Transactions on Pattern Analysis and Machine Intelligence

Single view based pose estimation from circle or parallel lines

Pattern Recognition Letters
Classification of the perspective-three-point problem, discriminant variety and real solving polynomial systems of inequalities

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
The unique solution for P3P problem

Proceedings of the 2009 ACM symposium on Applied Computing
An immune evolutionary algorithm based pose estimation method for parallel manipulator

Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation
Pose estimation from circle or parallel lines in a single image

ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
An efficient two-step solution for vision-based pose determination of a parallel manipulator

Robotics and Computer-Integrated Manufacturing
A Novel Solution to the P4P Problem for an Uncalibrated Camera

Journal of Mathematical Imaging and Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper studies the multi-solution phenomenon for the perspective four point (P4P) problem from geometric and algebraic aspects. We give a pure geometric proof that the P4P problem could have up to five solutions. We also give a clear picture on how these five solutions could be realized. We prove that with probability one, the P4P problem has a unique solution which can be represented by a set of rational functions in the parameters. The simulant experiments show that to solve the P4P problem with the rational functions is stable and accurate.