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Pattern Recognition
Volume 33, Issue 2, February 2000, Pages 251-261
 
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doi:10.1016/S0031-3203(99)00049-7    How to Cite or Link Using DOI (Opens New Window)
Copyright © 1999 Pattern Recognition Society. Published by Elsevier Science B.V.

Point-based projective invariants

TomáImage SukCorresponding Author Contact Information, E-mail The Corresponding Author and Jan FlusserE-mail The Corresponding Author

Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou vImage Image í 4, 182 08 Praha 8, Czech Republic

Received 23 January 1998;
accepted 3 February 1999.
Available online 14 December 1999.

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Abstract

The paper deals with features of a 2-D point set which are invariant with respect to a projective transform. First, projective invariants for five-point sets, which are simultaneously invariant to the projective transform and to permutation of the points, are derived. They are expressed as functions of five-point cross-ratios. Then, the invariants for more than five points are derived. The algorithm for searching the correspondence between the points of two 2-D point sets is presented. The algorithm is based on the comparison of two projective and permutation invariants of five-tuples of the points. The best-matched five tuples are then used for the computation of the projective transformation and that with the maximum of corresponding points is used. Stability and discriminability of the features and behavior of the searching algorithm are demonstrated by numerical experiments.

Author Keywords: Projective transform; Point set matching; Point-based invariants; Projective invariants; Permutation invariants; Registration; Control points

Article Outline

1. Introduction
2. Five-point permutation invariants
2.1. The derivation of the invariants
2.2. The roots of the invariants
2.3. The normalization of the invariants
3. Invariants for more than five points
4. Point matching
4.1. Full search algorithm
4.2. Pairing algorithm by means of the projective and permutation invariants
5. Numerical experiments
6. Conclusion
7. Summary
Acknowledgements
Appendix A
Appendix B
References
Vitae










Pattern Recognition
Volume 33, Issue 2, February 2000, Pages 251-261
 
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