Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

Generalized essential matrix

Published: 01 February 2015 Publication History

Abstract

When considering non-central imaging devices, the computation of the relative pose requires the estimation of the rotation and translation that transform the 3D lines from one coordinate system to the second. In most of the state-of-the-art methods, this transformation is estimated by the computing a 6í 6 matrix, known as the generalized essential matrix. To allow a better understanding of this matrix, we derive some properties associated with its singular value decomposition.

References

[1]
E. Kruppa, Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung, Sitzungsberichte der Mathematisch Naturwissenschaftlichen Kaiserlichen Akademie der Wissenschaften.
[2]
D. Nister, O. Naroditsky, J. Bergen, Visual Odometry, IEEE Proc. Computer Vision and Pattern Recognition (CVPR).
[3]
M. A. Fischler, R. C. Bolles, Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography, Comm. of the ACM.
[4]
} D. Nistér, Preemptive RANSAC for live structure and motion estimation, IEEE Proc. Int'l Conf. Computer Vision (ICCV)
[5]
Y. Ma, S. Soatto, J. Kosecka, S.S. Sastry, An Invitation to 3-D Vision: From Images to Geometric Models, Springer Science+Business Media, 2004.
[6]
T. S. Huang, O. D. Faugeras, Some properties of the E matrix in two-view motion estimation, IEEE Trans. on Pattern Analysis and Machine Intelligence (TPAMI).
[7]
O. D. Faugeras, S. Maybank, Motion from point matches: multiplicity of solutions, Int'l J. Computer Vision (IJCV).
[8]
J. Philip, A non-iterative algorithm for determining all essential matrices corresponding to five point pairs, Photogrammetric Record.
[9]
D. Nister, An efficient solution to the five-point relative pose problem, IEEE Trans. on Pattern Analysis and Machine Intelligence (TPAMI).
[10]
H. Stewenius, D. Nister, F. Kahl, F. Schaffalitzky, A minimal solution for relative pose with unknown focal length, Image and Vision Computing.
[11]
Z. Kukelova, M. Bujnak, T. Pajdla, Polynomial eigenvalue solutions to minimal problems in computer vision, IEEE Trans. on Pattern Analysis and Machine Intelligence (TPAMI).
[12]
R. Hartley, H. Li, An efficient hidden variable approach to minimal-case camera motion estimation, IEEE Trans. on Pattern Analysis and Machine Intelligence (TPAMI).
[13]
B. K. P. Horn, Relative orientation, Int'l J. Computer Vision (IJCV).
[14]
R. Pless, Using many cameras as one, IEEE Proc. Computer Vision and Pattern Recognition (CVPR).
[15]
D. Grossberg, S. Nayar, The raxel imaging model and ray based calibration, Int'l J. Computer Vision (IJCV).
[16]
H. Pottmann, J. Wallner, Computational Line Geometry, Springer-Verlag Berlin Heidelberg, 2001.
[17]
P. Sturm, Multi-view geometry for general camera models, IEEE Proc. Computer Vision and Pattern Recognition (CVPR).
[18]
H. Li, R. Hartley, J.-H. Kim, A linear approach to motion estimation using generalized camera models, IEEE Proc. Computer Vision and Pattern Recognition (CVPR).
[19]
J.-S. Kim, T. Kanade, Degeneracy of the linear seventeen-point algorithm for generalized essential matrix, J. Math. Imaging Vis. (JMIV).
[20]
M. Lhuillier, Effective and generic structure from motion using angular error, IEEE Proc. Int'l Conf. Pattern Recognition (ICPR).
[21]
G. Schweighofer, A. Pinz, Fast and globally convergent structure and motion estimation for general camera models, Proc. British Machine Vision Conf. (BMVC).
[22]
C.F. Van Loan, G.H. Golub, Matrix Computations, Johns Hopkins Studies in Mathematical Sciences, 1996.

Cited By

View all
  • (2020)On the Generalized Essential Matrix Correction: An Efficient Solution to the Problem and Its ApplicationsJournal of Mathematical Imaging and Vision10.1007/s10851-020-00961-w62:8(1107-1120)Online publication date: 1-Oct-2020

Recommendations

Comments

Information & Contributors

Information

Published In

cover image Image and Vision Computing
Image and Vision Computing  Volume 34, Issue C
February 2015
62 pages

Publisher

Butterworth-Heinemann

United States

Publication History

Published: 01 February 2015

Author Tags

  1. Generalized epipolar geometry
  2. Relative pose
  3. Rigid transformation of lines
  4. Singular value decomposition

Qualifiers

  • Research-article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 05 Jan 2025

Other Metrics

Citations

Cited By

View all
  • (2020)On the Generalized Essential Matrix Correction: An Efficient Solution to the Problem and Its ApplicationsJournal of Mathematical Imaging and Vision10.1007/s10851-020-00961-w62:8(1107-1120)Online publication date: 1-Oct-2020

View Options

View options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media