HANDLING REPEATED SOLUTIONS TO THE PERSPECTIVE THREE-POINT POSE PROBLEM

Michael Q. Rieck

2010

Abstract

In the Perspective 3-Point Pose Problem (P3P), when the three reference points are equidistant from each other, this distance may be assumed to be one unit in length. A repeated solution to the problem then occurs when and only when 1+R1R2 +R2R3 +R3R1-R21-R22-R23 = 0, where R1;R2 and R3 are the squared distances from the camera’s focal point to the reference points. When the setup only approximately satisfies this equation, two nearly equal solutions can introduce substantial calculation errors. To better handle this circumstance, it may be preferable to behave as though the above equation holds precisely, and then invert a certain two-dimensional transformation to obtain the repeated solution. The inversion involves only a few basic arithmetic operations and square roots. This approach is more efficient, and more reliable, than the standard quartic equation approach to solving P3P, at least in this special case.

Paper Citation

in Harvard Style

Q. Rieck M. (2010). HANDLING REPEATED SOLUTIONS TO THE PERSPECTIVE THREE-POINT POSE PROBLEM . In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2010) ISBN 978-989-674-028-3, pages 395-399. DOI: 10.5220/0002790103950399

in Bibtex Style

@conference{visapp10,
author={Michael Q. Rieck},
title={HANDLING REPEATED SOLUTIONS TO THE PERSPECTIVE THREE-POINT POSE PROBLEM},
booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2010)},
year={2010},
pages={395-399},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002790103950399},
isbn={978-989-674-028-3},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2010)
TI - HANDLING REPEATED SOLUTIONS TO THE PERSPECTIVE THREE-POINT POSE PROBLEM
SN - 978-989-674-028-3
AU - Q. Rieck M.
PY - 2010
SP - 395
EP - 399
DO - 10.5220/0002790103950399