# PERSPECTIVE-THREE-POINT (P3P) BY DETERMINING THE SUPPORT PLANE

### Zhaozheng Hu, Takashi Matsuyama

#### Abstract

This paper presents a new approach to solve the classic perspective-three-point (P3P) problem. The basic conception behind is to determine the support plane, which is defined by the three control points. Computation of the plane normal is formulated as searching for the maximum likelihood on the Gaussian hemisphere by exploiting the geometric constraints of three known angles and length ratios from the control points. The distances of the control points are then computed from the normal and the calibration matrix by homography decomposition. The proposed algorithm has been tested with real image data. The computation errors for the plane normal and the distances are less than 0.35 degrees, and 0.8cm, respectively, within 1~2m camera-to-plane distances. The multiple solutions to P3P problem are also illustrated.

#### References

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#### Paper Citation

#### in Harvard Style

Hu Z. and Matsuyama T. (2011). **PERSPECTIVE-THREE-POINT (P3P) BY DETERMINING THE SUPPORT PLANE** . In *Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2011)* ISBN 978-989-8425-47-8, pages 119-124. DOI: 10.5220/0003320301190124

#### in Bibtex Style

@conference{visapp11,

author={Zhaozheng Hu and Takashi Matsuyama},

title={PERSPECTIVE-THREE-POINT (P3P) BY DETERMINING THE SUPPORT PLANE},

booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2011)},

year={2011},

pages={119-124},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003320301190124},

isbn={978-989-8425-47-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2011)

TI - PERSPECTIVE-THREE-POINT (P3P) BY DETERMINING THE SUPPORT PLANE

SN - 978-989-8425-47-8

AU - Hu Z.

AU - Matsuyama T.

PY - 2011

SP - 119

EP - 124

DO - 10.5220/0003320301190124