Radial distortion triangulation
(2019) 32nd IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2019 p.9673-9681- Abstract
- This paper presents the first optimal, maximal likelihood, solution to the triangulation problem for radially distorted cameras. The proposed solution to the two-view triangulation problem minimizes the L2-norm of the reprojection error in the distorted image space. We cast the problem as the search for corrected distorted image points, and we use a Lagrange multiplier formulation to impose the epipolar constraint for undistorted points. For the one-parameter division model, this formulation leads to a system of five quartic polynomial equations in five unknowns, which can be exactly solved using the Groebner basis method. While the proposed Groebner basis solution is provably optimal; it is too slow for practical applications. Therefore,... (More)
- This paper presents the first optimal, maximal likelihood, solution to the triangulation problem for radially distorted cameras. The proposed solution to the two-view triangulation problem minimizes the L2-norm of the reprojection error in the distorted image space. We cast the problem as the search for corrected distorted image points, and we use a Lagrange multiplier formulation to impose the epipolar constraint for undistorted points. For the one-parameter division model, this formulation leads to a system of five quartic polynomial equations in five unknowns, which can be exactly solved using the Groebner basis method. While the proposed Groebner basis solution is provably optimal; it is too slow for practical applications. Therefore, we developed a fast iterative solver to this problem. Extensive empirical tests show that the iterative algorithm delivers the optimal solution virtually every time, thus making it an L2-optimal algorithm de facto. It is iterative in nature, yet in practice, it converges in no more than five iterations. We thoroughly evaluate the proposed method on both synthetic and real-world data, and we show the benefits of performing the triangulation in the distorted space in the presence of radial distortion. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f80a5e11-4e4c-4951-a3f6-c7dfa7d371e6
- author
- Kukelova, Zuzana and Larsson, Viktor LU
- publishing date
- 2019
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
- pages
- 9 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 32nd IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2019
- conference location
- Long Beach, United States
- conference dates
- 2019-06-16 - 2019-06-20
- external identifiers
-
- scopus:85078787573
- DOI
- 10.1109/CVPR.2019.00991
- language
- English
- LU publication?
- no
- id
- f80a5e11-4e4c-4951-a3f6-c7dfa7d371e6
- date added to LUP
- 2022-09-06 11:42:20
- date last changed
- 2022-09-23 18:38:51
@inproceedings{f80a5e11-4e4c-4951-a3f6-c7dfa7d371e6,
abstract = {{This paper presents the first optimal, maximal likelihood, solution to the triangulation problem for radially distorted cameras. The proposed solution to the two-view triangulation problem minimizes the L2-norm of the reprojection error in the distorted image space. We cast the problem as the search for corrected distorted image points, and we use a Lagrange multiplier formulation to impose the epipolar constraint for undistorted points. For the one-parameter division model, this formulation leads to a system of five quartic polynomial equations in five unknowns, which can be exactly solved using the Groebner basis method. While the proposed Groebner basis solution is provably optimal; it is too slow for practical applications. Therefore, we developed a fast iterative solver to this problem. Extensive empirical tests show that the iterative algorithm delivers the optimal solution virtually every time, thus making it an L2-optimal algorithm de facto. It is iterative in nature, yet in practice, it converges in no more than five iterations. We thoroughly evaluate the proposed method on both synthetic and real-world data, and we show the benefits of performing the triangulation in the distorted space in the presence of radial distortion.}},
author = {{Kukelova, Zuzana and Larsson, Viktor}},
booktitle = {{2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}},
language = {{eng}},
pages = {{9673--9681}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
title = {{Radial distortion triangulation}},
url = {{http://dx.doi.org/10.1109/CVPR.2019.00991}},
doi = {{10.1109/CVPR.2019.00991}},
year = {{2019}},
}