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Scene Flow Estimation from Light Fields via the Preconditioned Primal-Dual Algorithm Read chapter Read first chapter

2014 | OriginalPaper | Chapter

On the Second Order Statistics of Essential Matrix Elements

Authors : M. Hossein Mirabdollah, Bärbel Mertsching

Published in: Pattern Recognition

Publisher: Springer International Publishing

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Abstract

In this paper, we investigate the second order statistics of essential matrix elements. Using the Taylor expansion for a rotation matrix up to second order terms and considering relatively high uncertainties for the rotation angles and translation parameters, a covariance matrix is obtained which includes the second order statistics of essential matrix elements. The covariance matrix is utilized along with the coplanarity equations and acts as a regularization term. Using the regularization term brings considerable improvements in the recovery of camera motion which will be proven based on simulation and different real image sequences.

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previous chapter Detection of Clustered Objects in Sparse Point Clouds Through 2D Classification and Quadric Filtering
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Literature
1.
2.
3.
Dellaert, F., Kaess, M.: Square root SAM: simultaneous localization and mapping via square root information smoothing. Int. J. Rob. Res. 25(12), 1181–1203 (2006)CrossRefMATH
4.
Faugeras, O.: Three-Dimensional Computer Vision: A Geometric Viewpoint. MIT Press, Cambridge (1993)
5.
Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24(6), 381–395 (1981)MathSciNetCrossRef
6.
Geiger, A., Lenz, P., Urtasun, R.: Are we ready for autonomous driving? the kitti vision benchmark suite. In: Conference on Computer Vision and Pattern Recognition (2012)
7.
Geiger, A., Ziegler, J., Stiller, C.: StereoScan: dense 3D reconstruction in real-time. In: Intelligent Vehicles Symposium, pp. 963–968 (2011)
8.
Hartley, R.I.: Estimation of relative camera positions for uncalibrated cameras. In: Sandini, G. (ed.) ECCV 1992. LNCS, vol. 588, pp. 579–587. Springer, Heidelberg (1992)CrossRef
9.
Hartley, R.I.: In defense of the eight-point algorithm. IEEE Trans. Pattern Anal. Mach. Intell. 19(6), 580–593 (1997)CrossRef
10.
Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2004). ISBN: 0521540518CrossRefMATH
11.
Li, H., Hartley, R.I.: Five-point motion estimation made easy. In: 18th International Conference on Pattern Recognition, pp. 630–633 (2006)
12.
Longuet-Higgins, H.C.: A computer algorithm for reconstructing a scene from two projections. Nature 293, 133–135 (1981)CrossRef
13.
Luong, Q., Deriche, R., Faugeras, O., Papadopoulo, T.: On determining the fundamental matrix: analysis of different methods and experimental results. Technical report 1894, INRIA (1993)
14.
Mirabdollah, M.H., Mertsching, B.: Single camera motion estimation: modification of the 8-point method. In: Lee, J., Lee, M.C., Liu, H., Ryu, J.-H. (eds.) ICIRA 2013, Part I. LNCS, vol. 8102, pp. 117–128. Springer, Heidelberg (2013)CrossRef
15.
Nistér, D.: An efficient solution to the five-point relative pose problem. IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 756–777 (2004)CrossRef
16.
Strasdat, H., Montiel, J.M.M., Davison, A.J.: Scale drift-aware large scale monocular SLAM. In: Proceedings of Robotics: Science and Systems (2010)
17.
Tsai, R.Y., Huang, T.S.: Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces. IEEE Trans. Pattern Anal. Mach. Intell 6(1), 13–27 (1984)MathSciNetCrossRef
18.
Yamaguchi, K., McAllester, D., Urtasun, R.: Robust monocular epipolar flow estimation. In: CVPR, pp. 1862–1869 (2013)
19.
Zhao, L., Huang, S., Yan, L., Dissanayake, G.: Parallax angle parametrization for monocular SLAM. In: IEEE International Conference on Robotics and Automation, pp. 3117–3124 (2011)
Metadata
Title
On the Second Order Statistics of Essential Matrix Elements
Authors
M. Hossein Mirabdollah
Bärbel Mertsching
Copyright Year
2014
Book
Pattern Recognition

Print ISBN: 978-3-319-11751-5

Electronic ISBN: 978-3-319-11752-2

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-11752-2_45

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