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Omnidirectional vision and conformal geometric algebra for visual landmark identification

Published online by Cambridge University Press:  01 September 2008

C. López-Franco
Affiliation:
CINVESTAV Unidad Guadalajara, Guadalajara, Jalisco 44270, México
E. Bayro-Corrochano*
Affiliation:
CINVESTAV Unidad Guadalajara, Guadalajara, Jalisco 44270, México
*
*Corresponding author. E-mail: edb@gdl.cinvestav.mx

Summary

The automatic landmark identification is very important in autonomous robot navigation tasks. In this paper, we use a monocular omnidirectional vision system to extract the image features and the conformal geometric algebra to compute the projective invariants from such features. We show how these features can be used to compute projective and permutation p2-invariants from any kind of omnidirectional vision system. The p2-invariants represent scene sublandmarks, and a set of them characterize a landmark. The advantage of this representation is that the landmarks are more robust than the single cross-ratio.

Type
Article
Copyright
Copyright © Cambridge University Press 2007

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References

1.Baker, S. and Nayar, S., “A theory of single-viewpoint catadioptric image formation,” Int. J. Comput. Vis. 35, 122 (1999).CrossRefGoogle Scholar
2.Barnett, V., “The ordering of multivariate data,” J. Roy. Statist. Soc. A 3, 318343 (1976).CrossRefGoogle Scholar
3.Bayro-Corrochano, E., “Robot Perception and Action Using Conformal Geometry,” In: Bayro-Corrochano, E. (ed.): Handbook of Geometric Computing. Applications in Pattern Recognition, Computer Vision, Neurocomputing and Robotics (Bayro-Carrochano, E., ed) (Springer-Verlag, Berlin, Heidelberg) pp. 405–458.CrossRefGoogle Scholar
4.Bayro-Corrochano, E. and López-Franco, C., “Omnidirectional Vision: Unified Model Using Conformal Geometry,” Proceeding of the European Conference on Computer Vision (2004) pp. 536–548.Google Scholar
5.Benosman, and Kang, , Panoramic Vision (Springer-Verlag, New York, 2006).Google Scholar
6.Biglieri, E. and Yao, K., “Some Properties of Singular Value Decomposition and Their Application to Digital Signal Processing,” Signal Process. 18, 277289 (2000).CrossRefGoogle Scholar
7.Brannan, D., Esplen, M. and Gray, J., Geometry (Cambridge Univ. Press, Cambridge, U.K.).Google Scholar
8.Colios, C. and Trahanias, P. E., “A framework for visual landmark identification based on projective and point-permutation invariant vectors,” Robot. Autonom. Syst. J. 35, 3751 (2001).CrossRefGoogle Scholar
9.Geyer, C. and Daniilidis, K., “A Unifying Theory for Central Panoramic Systems and Practical Implications,” Proceeding of the European Conference on Computer Vision (2000) pp. 445–461.Google Scholar
10.Golub, G. H. and Loan, van C. F., Matrix Computations (Johns Hopkins Univ. Press, Baltimore, MD).Google Scholar
11.Hartley, R., “Cheirality Invariants,” DARPA Image Understanding Workshop (1993) pp. 745–753.Google Scholar
12.Hestenes, D., Li, H. and Rockwood, A., “New Algebraic Tools for Classical Geometry,” In: Geometric Computing with Clifford Algebra (Sommer, G., ed.) (Springer-Verlag, Berlin, Heidelberg, 2001) pp. 326.CrossRefGoogle Scholar
13.Li, H. and Hestenes, D., “Generalized Homogeneous Coordinates for Computational Geometry,” In: Geometric Computing with Clifford Algebra (Sommer, G., ed.) (Springer-Verlag, Berlin, Heidelberg, 2001) pp. 2760.CrossRefGoogle Scholar
14.Meer, P., Lenz, R. and Ramakrishna, S., “Efficient invariant representation,” Int. J. Comput. Vision, 26, 137152 (1998).CrossRefGoogle Scholar
15.Lasenby, J. and Bayro-Corrochano, E., “Analysis and computation of projective invariants from multiple views in the geometric algebra framework,” Int. J. Patt. Recog. Art. Intel., 13, 11051121 (1999).CrossRefGoogle Scholar