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Paper

W-PnP Method: Optimal Solution for the Weak-Perspective n-Point Problem and Its Application to Structure from MotionTopics: Device Calibration, Characterization and Modeling; Stereo Vision and Structure from Motion

Keyword(s):Weak-perspective Projection, Calibration, PnP, Structure from Motion.

Related
Ontology
Subjects/Areas/Topics:Computer Vision, Visualization and Computer Graphics
;
Device Calibration, Characterization and Modeling
;
Image Formation and Preprocessing
;
Motion, Tracking and Stereo Vision
;
Stereo Vision and Structure from Motion

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.(More)

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.

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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

@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}, }

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