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Efficient Solution to the Epipolar Geometry for Radially Distorted Cameras

Zuzana Kukelova, Jan Heller, Martin Bujnak, Andrew Fitzgibbon, Tomas Pajdla
2015 2015 IEEE International Conference on Computer Vision (ICCV)  
The estimation of the epipolar geometry of two cameras from image matches is a fundamental problem of computer vision with many applications.  ...  The solutions to this equation are efficiently found using the Sturm sequences method.  ...  Acknowledgment The authors were supported by EC project FP7-SPACE-2012-312377 PRoViDE.  ... 
doi:10.1109/iccv.2015.266 dblp:conf/iccv/KukelovaHBFP15 fatcat:nnfgfdlizfdstpas3xshva7h2u

A ROBUST METHOD FOR FUNDAMENTAL MATRIX ESTIMATION WITH RADIAL DISTORTION

J.-S. Xue, X.-N. Chen, H. Yi
2018 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
Firstly, two-sided radial fundamental matrix is deduced to describe epipolar geometry relationship between two distorted images.  ...  Radial distortion makes the problem to be numerically challenging. We propose a novel robust method for radial fundamental matrix estimation.  ...  A numerically stable and efficient solution for the calibrateduncalibrated image registration problem with radial distortion was presented in (José H, 2012) .  ... 
doi:10.5194/isprs-archives-xlii-3-2029-2018 fatcat:2a7zoakg2jh6nhuijc6e6tpu5e

Two Minimal Problems for Cameras with Radial Distortion

Zuzana Kukelova, Tomas Pajdla
2007 2007 IEEE 11th International Conference on Computer Vision  
In this paper we formulate two new minimal problems for estimating epipolar geometry of cameras with radial distortion.  ...  Using the trace constraint which holds for the epipolar geometry of calibrated cameras to reduce the number of necessary points from eight to six.  ...  Conclusion In this paper we have presented two new minimal problems for simultaneous estimation of epipolar geometry and radial distortion.  ... 
doi:10.1109/iccv.2007.4409190 dblp:conf/iccv/KukelovaP07 fatcat:nhlqkzb4sbbmpdmnlvrz7si3ny

One-sided Radial-Fundamental Matrix Estimation

José Henrique Brito, Christopher Zach, Kevin Koeser, Manuel Ferreira, Marc Pollefeys
2012 Procedings of the British Machine Vision Conference 2012  
A commonly adopted strategy for determining epipolar geometry is based on feature matching and minimal solvers inside a RANSAC framework.  ...  We propose a simple and numerically stable two-step scheme to first estimate radial distortion parameters and subsequently the focal length using novel solvers.  ...  The Proposed Two-Step Approach In this section we derive our method to estimate the epipolar geometry between images taken by a fully calibrated camera and an uncalibrated one exhibiting radial lens distortion  ... 
doi:10.5244/c.26.96 dblp:conf/bmvc/BritoZKFP12 fatcat:qnotpxhom5g7vid27x2ghnyqze

Overconstrained Linear Estimation of Radial Distortion and Multi-view Geometry [chapter]

R. Matt Steele, Christopher Jaynes
2006 Lecture Notes in Computer Science  
The method is shown to contain significantly less bias on both controlled and real-world data and, in the case of a moving camera where additional views serve to constrain the number of solutions, an accurate  ...  This paper introduces a new method for simultaneous estimation of lens distortion and multi-view geometry using only point correspondences.  ...  Solutions may be found via efficient and globally convergent algorithms, yielding an estimate for both the distortion and the epipolar geometry.  ... 
doi:10.1007/11744023_20 fatcat:gxysosc2arfe7ibtrmaq4k3rai

Radial Distortion from Epipolar Constraint for Rectilinear Cameras

Ville Lehtola, Matti Kurkela, Petri Rönnholm
2017 Journal of Imaging  
Then, the camera network is loosely connected, i.e., it has weak geometry.  ...  In this paper, we set out to exploit the r-symmetry in determining a global estimate for the radial distortion and, in order to do so, also construct a global constraint for the center of distortion that  ...  Acknowledgments: The authors wish to thank the Academy of Finland for funding this research, Grant Nos. 257755, 272195, and 293389.  ... 
doi:10.3390/jimaging3010008 fatcat:mcxyrm6mujgg3gm46nauzj4ybe

Camera Models and Fundamental Concepts Used in Geometric Computer Vision

Peter Sturm
2010 Foundations and Trends in Computer Graphics and Vision  
The authors wish to thank Tomáš Pajdla for comments on the manuscript and Aseem Agarwala, Frédéric Devernay, Sujit Kuthirummal, Marc Pollefeys, Ryusuke Sagawa, and Steve Seitz for kindly allowing us to  ...  Sturm is grateful to the Alexander-von-Humboldt Foundation for a Research Fellowship supporting his sabbatical at TU Munich, during which the largest part of this manuscript was written.  ...  Zhang, in [566] , studied the epipolar geometry of two radially distorted images and showed that epipolar curves are cubic if only one radial distortion coefficient is considered.  ... 
doi:10.1561/0600000023 fatcat:i5puai3btrb4vfcvc5zgqgwz3u

A Minimal Solution to Relative Pose with Unknown Focal Length and Radial Distortion [chapter]

Fangyuan Jiang, Yubin Kuang, Jan Erik Solem, Kalle Åström
2015 Lecture Notes in Computer Science  
This solver enables simultaneous auto-calibration of focal length and radial distortion for cameras. For experiments, the numerical stability of the solver is demonstrated on synthetic data.  ...  In this paper, we study the minimal problem of estimating the essential matrix between two cameras with constant but unknown focal length and radial distortion.  ...  The minimal problems, which are defined as using the minimal point correspondences to estimate the epipolar geometry as well as the camera calibration, e.g. focal length or radial distortion, plays an  ... 
doi:10.1007/978-3-319-16808-1_30 fatcat:prp4zn4ruvbkfkx5lqwjhycgve

A Clever Elimination Strategy for Efficient Minimal Solvers

Zuzana Kukelova, Joe Kileel, Bernd Sturmfels, Tomas Pajdla
2017 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion.  ...  We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns.  ...  calibrated camera and one camera with unknown focal length and unknown radial distortion, i.e. uncalibrated camera with radial distortion.  ... 
doi:10.1109/cvpr.2017.384 dblp:conf/cvpr/KukelovaKSP17 fatcat:dlzg5437nzffrpsjf4knnz5bom

A minimal solution to the autocalibration of radial distortion

Zuzana Kukelova, Tomas Pajdla
2007 2007 IEEE Conference on Computer Vision and Pattern Recognition  
In this paper we provide a solution to the problem of estimating radial distortion and epipolar geometry from eight correspondences in two images.  ...  Epipolar geometry and relative camera pose computation are examples of tasks which can be formulated as minimal problems and solved from a minimal number of image points.  ...  Conclusion We presented a robust and efficient solution to the minimal problem for the autocalibration of radial distortion.  ... 
doi:10.1109/cvpr.2007.383063 dblp:conf/cvpr/KukelovaP07 fatcat:ejyzoweezrhg7aqmg4qepxqkia

Unknown Radial Distortion Centers in Multiple View Geometry Problems [chapter]

José Henrique Brito, Roland Angst, Kevin Köser, Christopher Zach, Pedro Branco, Manuel João Ferreira, Marc Pollefeys
2013 Lecture Notes in Computer Science  
The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras.  ...  We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that -to the best of our knowledge -no other existing algorithm  ...  To the best of our knowledge, the approach presented in this paper is the only one designed to handle epipolar geometry problems with fully unknown radial distortion.  ... 
doi:10.1007/978-3-642-37447-0_11 fatcat:hwp5qos5srgf3dbroja4bzgn3y

A clever elimination strategy for efficient minimal solvers [article]

Zuzana Kukelova, Joe Kileel, Bernd Sturmfels, Tomas Pajdla
2017 arXiv   pre-print
We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion.  ...  We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns.  ...  calibrated camera and one camera with unknown focal length and unknown radial distortion, i.e. uncalibrated camera with radial distortion.  ... 
arXiv:1703.05289v1 fatcat:3hi5gczub5cu7cpuctky65foke

Evaluating performance of feature extraction methods for practical 3D imaging systems

Deepak Dwarakanath, Alexander Eichhorn, Pål Halvorsen, Carsten Griwodz
2012 Proceedings of the 27th Conference on Image and Vision Computing New Zealand - IVCNZ '12  
To achieve high quality, such applications are required to estimate accurate position and orientation of the cameras (called as camera calibration-pose estimation).  ...  The accuracy of autocalibration is sensitive to the accuracy of features extracted and matched between a stereo pair or multiple cameras.  ...  To explain this in detail, we bring in the concept of epipolar geometry.  ... 
doi:10.1145/2425836.2425887 dblp:conf/ivcnz/DwarakanathEHG12 fatcat:zsnd6h2gunbcxj6jcaygyj6qqu

Smartphones Based Mobile Mapping Systems

A. Al-Hamad, N. El-Sheimy
2014 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
The past 20 years have witnessed an explosive growth in the demand for geo-spatial data.  ...  extremely powerful computing power and very high resolution cameras.  ...  ACKNOWLEDGEMENTS This work was supported in part by research funds from TECTERRA Commercialization and Research Centre, the Canada Research Chairs Program, and the Natural Science and Engineering Research  ... 
doi:10.5194/isprsarchives-xl-5-29-2014 fatcat:3sgpwpfinvdtfgxdzirvdk4rg4

Multiperspective modeling, rendering, and imaging

Jingyi Yu, Leonard McMillan, Peter Sturm
2008 ACM SIGGRAPH ASIA 2008 courses on - SIGGRAPH Asia '08  
Furthermore, we show that many of these cameras satisfy the multiperspective stereo constraints and we demonstrate several multiperspective imaging systems for extracting 3D geometry for computer vision  ...  We demonstrate how to use these camera models for creating specific multiperspective rendering effects.  ...  For efficient automatic image matching, it is favorable to have an epipolar geometry where these loci are lines, as with perspective images.  ... 
doi:10.1145/1508044.1508094 fatcat:3vqlpa7msvhtfarwndyptuknwe
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