Abstract
Projective reconstruction recovers 3-D points in projective space P 3 from their several projections to 2-D images. Applications of projective reconstruction include algorithms for selecting point correspondences, algorithms for camera self-calibration, and algorithms for 3D shape recovery. We introduce a method for the projective reconstruction from n views. The method is based on concatenation of trifocal constraints and relies on linear estimates only. The method is not symmetrical with respect to input data. One of the captured images is selected as a reference image which plays a special role during the computation. The proposed algorithm requires that all the points involved be visible in the reference image. Accuracy and stability of the proposed algorithm with respect to pixel errors were tested. Experimental results are presented too.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
D. Bondyfalat, B. Mourrain, and V. Y. Pan. Controlled iterative methods for solving polynomials systems. Proceedings ISSAC98, pages 252–259. ACM Press, 1998.
O. Faugeras and T. Papadopoulo. Grassmann-Cayley algebra for modeling systems of cameras and the algebraic equations of the manifold of trifocal tensors. Technical Report 3225, INRIA, July 1997.
O. D. Faugeras. What can be seen in three dimensions with an uncalibrated stereo rig? In Proceedings ECCV-92, pages 563–578. Springer-Verlag, LNCS 588, 1992.
R. I. Hartley. Computation of the quadrifocal tensor. In Proceedings ECCV-98, volume I, pages 20–35. Springer Verlag, 1998.
R. I. Hartley. Lines and points in three views and the trifocal tensor. International Journal of Computer Vision, 22(2): 125–140, March 1997.
A. Heyden. A common framework for multiple view tensors. In Proceedings ECCV-98, volume I, pages 3–19. Springer Verlag, 1998.
A. Heyden. Reduced multilinear constraints — theory and experiments. International Journal of Computer Vision, 30:5–26, 1998.
M. Pollefeys, R. Koch, and L. VanGool. Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters. In Proceedings ICCV98, pages 90–95, 1998.
M. Urban, T. Pajdla, and V. Hlaváč. Projective reconstruction from multiple views. Technical Report CTU-CMP-1999–5, CMP, FEL ČVUT, Karlovo náměstí 13, Praha, Czech Republic, December 1999.
M. Urban. Uncalibrated 3D Vision: Contributions to Projective Reconstruction and Camera Self-Calibration. PhD thesis, Czech Technical University, Faculty of Electrical Engineering, Department of Cybernetics, Karlovo náměstí 13, Prague, Czech Republic, 1999.
Z. Zhang. Determining the epipolar geometry and its uncertainty: A review. International Journal of Computer Vision, 27(2): 161–195, 1998.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Urban, M., Pajdla, T., Hlaváč, V. (2000). Consistent Projective Reconstruction from Multiple Views. In: Leonardis, A., Solina, F., Bajcsy, R. (eds) Confluence of Computer Vision and Computer Graphics. NATO Science Series, vol 84. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4321-9_3
Download citation
DOI: https://doi.org/10.1007/978-94-011-4321-9_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6612-6
Online ISBN: 978-94-011-4321-9
eBook Packages: Springer Book Archive