# A Robust Least Squares Solution to the Relative Pose Problem on Calibrated Cameras with Two Known Orientation Angles

### Gaku Nakano, Jun Takada

#### Abstract

This paper proposes a robust least squares solution to the relative pose problem on calibrated cameras with two known orientation angles based on a physically meaningful optimization. The problem is expressed as a minimization problem of the smallest eigenvalue of a coefficient matrix, and is solved by using 3-point correspondences in the minimal case and more than 4-point correspondences in the least squares case. To obtain the minimum error, a new cost function based on the determinant of a matrix is proposed instead of solving the eigenvalue problem. The new cost function is not only physically meaningful, but also common in the minimal and the least squares case. Therefore, the proposed least squares solution is a true extension of the minimal case solution. Experimental results of synthetic data show that the proposed solution is identical to the conventional solutions in the minimal case and it is approximately 3 times more robust to noisy data than the conventional solution in the least squares case.

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#### Paper Citation

#### in Harvard Style

Nakano G. and Takada J. (2013). **A Robust Least Squares Solution to the Relative Pose Problem on Calibrated Cameras with Two Known Orientation Angles** . In *Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2013)* ISBN 978-989-8565-48-8, pages 147-154. DOI: 10.5220/0004277801470154

#### in Bibtex Style

@conference{visapp13,

author={Gaku Nakano and Jun Takada},

title={A Robust Least Squares Solution to the Relative Pose Problem on Calibrated Cameras with Two Known Orientation Angles},

booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2013)},

year={2013},

pages={147-154},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004277801470154},

isbn={978-989-8565-48-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP, (VISIGRAPP 2013)

TI - A Robust Least Squares Solution to the Relative Pose Problem on Calibrated Cameras with Two Known Orientation Angles

SN - 978-989-8565-48-8

AU - Nakano G.

AU - Takada J.

PY - 2013

SP - 147

EP - 154

DO - 10.5220/0004277801470154