Abstract
The fundamental matrix combines the mutual relation of the corresponding points in the two images of an observed scene. This relation, known also as an epipolar geometry, allows for a further depth reconstruction, image rectification or camera calibration. Thus, computation of the fundamental matrix has been one of the most important problems of computer vision. Many linear and non-linear methods were already proposed to solve this problem. However, due to the nature of image processing there is no unique solution and each method exhibits some exclusive properties. In this paper a neural approach to the computation of the fundamental matrix is proposed. For this purpose, the special configuration of the back-propagation neural network was developed. Both, linear and non-linear versions are also discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chesi, G., Garulli, A., Vicino, A., Cipolla, R.: On the Estimation of the Fundamental Matrix: A Convex Approach to Constrained Least-Squares. In: Vernon, D. (ed.) ECCV 2000. LNCS, vol. 1842, pp. 236–250. Springer, Heidelberg (2000)
Cyganek, B.: Three Dimensional Image Processing. EXIT, Warsaw (2002) (in Polish)
Cyganek, B., Borgosz, J.: A Software Platform for Evaluation of Neural Algorithms for Stereo Image Processing. In: IEEE ICNNSC-2002, Poland, pp. 656–661 (2002)
Faugeras, O.D., Luong, Q.-T.: The Geometry of Multiple Images. MIT Press, Cambridge (2001)
Haykin, S.: Neural Networks. In: A Comprehensive Foundation, Prentice Hall, Englewood Cliffs (1999)
Hartley, R.I.: In Defense of the Eight-Point Algorithm. PAMI 19(6), 580–593 (1997)
Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision. CUP (2000)
Luong, Q.-T., Faugeras, O.D.: The Fundamental matrix: theory, algorithms, and stability analysis. INRIA (1995)
Luong, Q.-T., Deriche, R., Faugeras, O.D., Papadopoulo, T.: On Determining the Fundamental Matrix: INRIA Technical Report No. 1894 (1993)
Tadeusiewicz, R.: Neural Networks. RM Academic Publishing House, Warsaw (1993) (in Polish)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cyganek, B. (2004). Neural Computation of the Fundamental Matrix. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds) Artificial Intelligence and Soft Computing - ICAISC 2004. ICAISC 2004. Lecture Notes in Computer Science(), vol 3070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24844-6_110
Download citation
DOI: https://doi.org/10.1007/978-3-540-24844-6_110
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22123-4
Online ISBN: 978-3-540-24844-6
eBook Packages: Springer Book Archive