W-PnP Method: Optimal Solution for the Weak-Perspective n-Point Problem and Its Application to Structure from Motion

Levente Hajder

2017

Abstract

Camera calibration is a key problem in 3D computer vision since the late 80's. Most of the calibration methods deal with the (perspective) pinhole camera model. This is not a simple goal: the problem is nonlinear due to the perspectivity. The strategy of these methods is to estimate the intrinsic camera parameters first; then the extrinsic ones are computed by the so-called PnP method. Finally, the accurate camera parameters are obtained by slow numerical optimization. In this paper, we show that the weak-perspective camera model can be optimally calibrated without numerical optimization if the $L_2$ norm is used. The solution is given by a closed-form formula, thus the estimation is very fast. We call this method as the Weak-Perspective n-Point (W-PnP) algorithm. Its advantage is that it simultaneously estimates the two intrinsic weak-perspective camera parameters and the extrinsic ones. We show that the proposed calibration method can be utilized as the solution for a subproblem of 3D reconstruction with missing data. An alternating least squares method is also defined that optimizes the camera motion using the proposed optimal calibration method.

Paper Citation

in Harvard Style

Hajder L. (2017). W-PnP Method: Optimal Solution for the Weak-Perspective n-Point Problem and Its Application to Structure from Motion . In Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 6: VISAPP, (VISIGRAPP 2017) ISBN 978-989-758-227-1, pages 265-276. DOI: 10.5220/0006158902650276

in Bibtex Style

@conference{visapp17,
author={Levente Hajder},
title={W-PnP Method: Optimal Solution for the Weak-Perspective n-Point Problem and Its Application to Structure from Motion},
booktitle={Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 6: VISAPP, (VISIGRAPP 2017)},
year={2017},
pages={265-276},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006158902650276},
isbn={978-989-758-227-1},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 6: VISAPP, (VISIGRAPP 2017)
TI - W-PnP Method: Optimal Solution for the Weak-Perspective n-Point Problem and Its Application to Structure from Motion
SN - 978-989-758-227-1
AU - Hajder L.
PY - 2017
SP - 265
EP - 276
DO - 10.5220/0006158902650276