Eigenvector Sign Correction for Spectral Correspondence Matching

  • Muhammad Haseeb
  • Edwin R. Hancock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8157)


In this paper we describe a method to correct the sign of eigenvectors of the proximity matrix for the problem of correspondence matching. The signs of the eigenvectors of a proximity matrix are not unique and play an important role in computing the correspondences between a set of feature points. We use the coefficients of the elementary symmetric polynomials to make the direction of the eigenvectors of the two proximity matrices consistent with each other for the problem correspondence matching. We compare our method to other methods presented in the literature. The empirical results show that using the coefficients of the elementary symmetric polynomials for eigenvectors sign correction is a better choice to solve the problem.


Eigenvector Direction Correction Symmetric Polynomials Correspondence Matching Point Pattern Matching 


  1. 1.
    Caelli, T., Kosinov, S.: An Eigenspace Projection Clustering Method for Inexact Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence 26, 515–519 (2004)CrossRefGoogle Scholar
  2. 2.
    Carcassoni, M., Hancock, E.R.: Spectral Correspondence for Point Pattern Matching. Pattern Recognition 36(1), 193–204 (2003)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chui, H., Rangarajan, A.: A New Algorithm for Non-Rigid Point Matching. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 44–51 (2000)Google Scholar
  4. 4.
    Ling, H., Jacobs, D.W.: Shape Classification using the Inner-Distance. IEEE Transactions on Pattern Analysis and Machine Intelligence 29, 286–299 (2007)CrossRefGoogle Scholar
  5. 5.
    Mateus, D., Horaud, R.P., Knossow, D., Cuzzolin, F., Boyer, E.: Articulated Shape Matching using Laplacian Eigenfunctions and Unsupervised Point Registration. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, CVPR (June 2008)Google Scholar
  6. 6.
    Park, S.H., Lee, K.M., Lee, S.U.: A Line Feature Matching Technique Based on an Eigenvector Approach. Computer Vision and Image Understanding 77(3), 263–283 (2000)CrossRefGoogle Scholar
  7. 7.
    Scott, G.L., Longuet-Higgins, H.C.: An Algorithm for Associating the Features of Two Images. Proceedings of the The Royal Society London B(224), 21–26 (1991)Google Scholar
  8. 8.
    Shapairo, L.S.: Towards a Vision-based Motion Framework. First Year Report, Department of Engineering Science, Oxford University (1991)Google Scholar
  9. 9.
    Shapairo, L.S., Brady, J.M.: Feature-based Correspondence: An Eigenvector Approach. Image and Vision Computing 10(5), 283–288 (1992)CrossRefGoogle Scholar
  10. 10.
    Sun, J., Ovsjanikov, M., Guibas, L.: A Concise and Provably Informative Multi-scale Signature Based on Heat Diffusion. In: Proceedings of the Symposium on Geometry Processing, SGP 2009, pp. 1383–1392. Eurographics Association, Aire-la-Ville (2009),
  11. 11.
    Umeyama, S.: An Eigendecomposition Approach to Weighted Graph Matching Problems. IEEE Transactions on Pattern Analysis and Machine Intelligence 10(5), 695–703 (1988), CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Muhammad Haseeb
    • 1
    • 2
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer ScienceUniversity of YorkUK
  2. 2.Department of Computer ScienceUniversity of PeshawarPakistan

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