Abstract
An algorithm for establishing the correspondence between two projectively transformed sets of coplanar points (or lines) is proposed and its performance analyzed. Five-tuples of features are represented by projective/permutation (p2) invariants which are insensitive to the order of the features in the computation. Matched five-tuples yield feature correspondence hypotheses accumulated in a contingency table. The final correspondence is extracted from the table by a greedy algorithm. Positional uncertainties of up to five pixels and the presence of outliers are tolerated.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Berger, M.: Geometry I, Springer, Berlin, 1987.
Grimson, W. E. L., Huttenlocher, D. P.: On the sensitivity of geometric hashing, Proceedings of the Third International Conference on Computer Vision, Osaka, Japan (December 1990) 334–338.
Grimson, W. E. L., Huttenlocher, D. P., Jacobs, D. W.: A study of affine matching with bounded sensor error, Computer Vision-ECCV '92, G. Sandini (Ed.), Springer, Berlin (1992) 292–306.
Forsyth, D., Mundy, J. L., Zisserman, A., Coelho, C., Heller, A.: Invariant descriptors for 3-D object recognition and pose, IEEE Trans. Pattern Anal. Mach. Intell., 13 (1991) 971–991.
Fulton, W., Harris, J.: Representation Theory, Graduate Texts in Mathematics (Vol. 129), Springer, Heidelberg, 1991.
Hartshorne, R.: Algebraic Geometry, Springer, New York, Corrected third printing, 1983.
Lamdan, Y., Schwartz, J. T., Wolfson, H. J.: Affine invariant model-based object recognition, IEEE Trans. Robot. Autom., 6 (1990) 578–589.
Lamdan, Y., Wolfson, H. J.: On the error analysis of ‘Geometric Hashing', Proceedings of the 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Lahaina, Maui, Hawaii (June 1991) 22–27.
Lenz, R., Meer, P.: Projection and permutation invariant object recognition, Proceedings of the 8th Scandinavian Conference on Image Analysis (May 1993) 389–396. Accepted for publication, Pattern Recognition.
Kanatani, K.: Computational projective geometry, CVGIP: Image Understanding, 54 (1991) 333–348.
Maybank, S. J.: The projection of two non-coplanar conics, 105–119 in [15].
Maybank, S. J.: Classification based on the cross ratio, Applications of Invariance in Computer Vision II. Proceedings of the Second European-US Workshop on Invariance, Ponta Delgada, Azores (October 1993) 113–132 (in this volume).
Meer, P., Weiss, I.: Point/line correspondence under 2D projective transformation, Proceedings of the 11th International Conference on Pattern Recognition: Computer Vision and Applications, The Hague, The Netherlands (September 1992) 399–402.
Morin, L.: Quelques contributions des invariants projectifs a la vision par ordinateur. PdD Thesis, Institut National Polytechnique de Grenoble, January 1993.
Mundy, J. L., Zisserman, A., editors: Geometric Invariance in Machine Vision, MIT Press, Cambridge, Mass, 1992.
Rothwell, C. A., Zisserman, A., Mundy, J. L., Forsyth, D. A.: Efficient model library access by projective invariant indexing functions, Proceedings of the 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Champaign, Illinois (June 1992) 109–114.
Shapiro, L. S., Brady, J. M.: Feature-based correspondence: an eigenvector approach, Image and Vision Computing, 10 (1992) 283–288.
Scott, G. L., Longuet-Higgins, H. C.: An algorithm for associating the features of two images, Proc. R. Soc. Lond. B, 244 (1991) 21–26.
Wayner, P. C.: Efficiently using invariant theory for model-based matching, Proceedings of the 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Lahaina, Maui, Hawaii (June 1991) 473–478.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Meer, P., Ramakrishna, S., Lenz, R. (1994). Correspondence of coplanar features through P2-invariant representations. In: Mundy, J.L., Zisserman, A., Forsyth, D. (eds) Applications of Invariance in Computer Vision. AICV 1993. Lecture Notes in Computer Science, vol 825. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58240-1_25
Download citation
DOI: https://doi.org/10.1007/3-540-58240-1_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58240-3
Online ISBN: 978-3-540-48583-4
eBook Packages: Springer Book Archive