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2016 | OriginalPaper | Chapter

3. Fundamental Matrix Computation

Authors : Kenichi Kanatani, Yasuyuki Sugaya, Yasushi Kanazawa

Published in: Guide to 3D Vision Computation

Publisher: Springer International Publishing

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Abstract

Two images of the same scene are related by what is called the epipolar equation. It is specified by a matrix called the fundamental matrix. By computing the fundamental matrix between two images, one can analyze the 3D structure of the scene, which we discuss in Chaps. 4 and 5. This chapter describes the principle and typical computational procedures for accurately computing the fundamental matrix by considering the statistical properties of the noise involved in correspondence detection. As in ellipse fitting, the methods are classified into algebraic and geometric approaches. However, the fundamental matrix has an additional property called the rank constraint: it is required to have determinant 0. Three approaches for enforcing it are introduced here: a posteriori rank correction, hidden variables, and extended FNS. We then describe the procedure of repeatedly using them to compute the geometric distance minimization solution. The RANSAC procedure for removing wrong correspondences is also described.

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previous chapter Ellipse Fitting
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Literature
1.
W. Chojnacki, M.J. Brooks, A. van den Hengel, D. Gawley, On the fitting of surfaces to data with covariances. IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1294–1303 (2000)CrossRef
2.
R. Hartley, In defense of the eight-point algorithm. IEEE Trans. Pattern Anal. Mach. Intell. 19(6), 580–593 (1997)CrossRef
3.
R. Hartley, A. Zisserman, Multiple View Geometry in Computer Vision, 2nd edn. (Cambridge University Press, Cambridge, U.K., 2003)MATH
4.
K. Kanatani, Geometric Computation for Machine Vision (Oxford University Press, Oxford, U.K., 1993)MATH
5.
K. Kanatani, Renormalization for unbiased estimation, in Proceedings of 4th International Conference on Computer Vision, Berlin, Germany, pp. 599–606 (1993)
6.
K. Kanatani, Statistical Optimization for Geometric Computation: Theory and Practice, Elsevier, Amsterdam, The Netherlands (1996) (Reprinted by Dover, New York, U.S., 2005)
7.
K. Kanatani, Statistical optimization for geometric fitting: theoretical accuracy bound and high order error analysis. Int. J. Comput. Vision 80(2), 167–188 (2008)MathSciNetCrossRef
8.
K. Kanatani, C. Matsunaga, Computing internally constrained motion of 3-D sensor data for motion interpretation. Pattern Recogn. 46(6), 1700–1709 (2013)CrossRefMATH
9.
K. Kanatani, N. Ohta, Comparing optimal three-dimensional reconstruction for finite motion and optical flow. J. Electron. Imaging 12(3), 478–488 (2003)CrossRef
10.
Y. Sugaya, K. Kanatani, High accuracy computation of rank-constrained fundamental matrix, in Proceedings of 18th British Machine Vision Conference, Coventry, U.K., vol. 1, pp. 282–291 (2007)
11.
K. Kanatani, Y. Sugaya, High accuracy fundamental matrix computation and its performance evaluation. IEICE Trans. Inf. Syst. E90-D(2), 579–585 (2007)
12.
K. Kanatani, Y. Sugaya, Performance evaluation of iterative geometric fitting algorithms. Comput. Stat. Data Anal. 52(2), 1208–1222 (2007)MathSciNetCrossRefMATH
13.
K. Kanatani, Y. Sugaya, Compact fundamental matrix computation. IPSJ Trans. Comput. Vision Appl. 2, 59–70 (2010)CrossRef
14.
K. Kanatani, Y. Sugaya, Unified computation of strict maximum likelihood for geometric fitting. J. Math. Imaging Vision 38(1), 1–13 (2010)MathSciNetCrossRef
15.
K. Kanatani, Y. Sugaya, Y. Kanazawa, Latest algorithms for 3-D reconstruction form two view, in Handbook of Pattern Recognition and Computer Vision, 4th edn., ed. by C.H. Chen (World Scientific Publishing, Singapore, 2009), pp. 201–234CrossRef
16.
Y. Sugaya, K. Kanatani, Highest accuracy fundamental matrix computation, in Proceedings of 8th Asian Conference on Computer Vision, Tokyo, Japan, vol. 2, pp. 311–321 (2007)
Metadata
Title
Fundamental Matrix Computation
Authors
Kenichi Kanatani
Yasuyuki Sugaya
Yasushi Kanazawa
Copyright Year
2016
Book
Guide to 3D Vision Computation

Print ISBN: 978-3-319-48492-1

Electronic ISBN: 978-3-319-48493-8

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-48493-8_3

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