Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion

Yubin Kuang; Jan Erik Solem; Fredrik Kahl; Karl Åström

doi:10.1109/CVPR.2014.12

Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion

Yubin Kuang, Jan Erik Solem, Fredrik Kahl, Karl Åström

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

Abstract

In this paper, we study the problems of estimating relative
pose between two cameras in the presence of radial distortion.
Specifically, we consider minimal problems where
one of the cameras has no or known radial distortion. There
are three useful cases for this setup with a single unknown
distortion: (i) fundamental matrix estimation where the two
cameras are uncalibrated, (ii) essential matrix estimation
for a partially calibrated camera pair, (iii) essential matrix
estimation for one calibrated camera and one camera
with unknown focal length. We study the parameterization
of these three problems and derive fast polynomial solvers
based on Gr¨obner basis methods. We demonstrate the numerical
stability of the solvers on synthetic data. The minimal
solvers have also been applied to real imagery with
convincing results.

Original language	English
Title of host publication	Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on
Publisher	IEEE - Institute of Electrical and Electronics Engineers Inc.
Pages	33-40
Number of pages	8
DOIs	https://doi.org/10.1109/CVPR.2014.12
Publication status	Published - 2014
Event	IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014), 2014 - Columbus, Ohio, United States Duration: 2014 Jun 24 → 2014 Jun 27

Publication series

Name
ISSN (Print)	1063-6919

Conference

Conference	IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014), 2014
Country/Territory	United States
City	Columbus, Ohio
Period	2014/06/24 → 2014/06/27

Subject classification (UKÄ)

Mathematics

Access to Document

10.1109/CVPR.2014.12

Cite this

@inproceedings{d2cf23e9e9b54ebc82b750929cca3c75,

title = "Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion",

abstract = "In this paper, we study the problems of estimating relative pose between two cameras in the presence of radial distortion. Specifically, we consider minimal problems where one of the cameras has no or known radial distortion. There are three useful cases for this setup with a single unknown distortion: (i) fundamental matrix estimation where the two cameras are uncalibrated, (ii) essential matrix estimation for a partially calibrated camera pair, (iii) essential matrix estimation for one calibrated camera and one camera with unknown focal length. We study the parameterization of these three problems and derive fast polynomial solvers based on Gr¨obner basis methods. We demonstrate the numerical stability of the solvers on synthetic data. The minimal solvers have also been applied to real imagery with convincing results.",

author = "Yubin Kuang and Solem, {Jan Erik} and Fredrik Kahl and Karl {\AA}str{\"o}m",

year = "2014",

doi = "10.1109/CVPR.2014.12",

language = "English",

publisher = "IEEE - Institute of Electrical and Electronics Engineers Inc.",

pages = "33--40",

booktitle = "Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on",

address = "United States",

note = "IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014), 2014 ; Conference date: 24-06-2014 Through 27-06-2014",

}

Kuang, Y, Solem, JE, Kahl, F & Åström, K 2014, Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion. in Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on. IEEE - Institute of Electrical and Electronics Engineers Inc., pp. 33-40, IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014), 2014, Columbus, Ohio, United States, 2014/06/24. https://doi.org/10.1109/CVPR.2014.12

Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion. / Kuang, Yubin; Solem, Jan Erik; Kahl, Fredrik et al.
Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on. IEEE - Institute of Electrical and Electronics Engineers Inc., 2014. p. 33-40.

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

TY - GEN

T1 - Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion

AU - Kuang, Yubin

AU - Solem, Jan Erik

AU - Kahl, Fredrik

AU - Åström, Karl

PY - 2014

Y1 - 2014

N2 - In this paper, we study the problems of estimating relative pose between two cameras in the presence of radial distortion. Specifically, we consider minimal problems where one of the cameras has no or known radial distortion. There are three useful cases for this setup with a single unknown distortion: (i) fundamental matrix estimation where the two cameras are uncalibrated, (ii) essential matrix estimation for a partially calibrated camera pair, (iii) essential matrix estimation for one calibrated camera and one camera with unknown focal length. We study the parameterization of these three problems and derive fast polynomial solvers based on Gr¨obner basis methods. We demonstrate the numerical stability of the solvers on synthetic data. The minimal solvers have also been applied to real imagery with convincing results.

AB - In this paper, we study the problems of estimating relative pose between two cameras in the presence of radial distortion. Specifically, we consider minimal problems where one of the cameras has no or known radial distortion. There are three useful cases for this setup with a single unknown distortion: (i) fundamental matrix estimation where the two cameras are uncalibrated, (ii) essential matrix estimation for a partially calibrated camera pair, (iii) essential matrix estimation for one calibrated camera and one camera with unknown focal length. We study the parameterization of these three problems and derive fast polynomial solvers based on Gr¨obner basis methods. We demonstrate the numerical stability of the solvers on synthetic data. The minimal solvers have also been applied to real imagery with convincing results.

U2 - 10.1109/CVPR.2014.12

DO - 10.1109/CVPR.2014.12

M3 - Paper in conference proceeding

SP - 33

EP - 40

BT - Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on

PB - IEEE - Institute of Electrical and Electronics Engineers Inc.

T2 - IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014), 2014

Y2 - 24 June 2014 through 27 June 2014

ER -

Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion

Abstract

Publication series

Conference

Subject classification (UKÄ)

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Cite this