Faster Computation of Non-zero Invariants from Graph Based Method

  • Vazeerudeen Abdul Hameed
  • Siti Mariyam Shamsuddin
Part of the Communications in Computer and Information Science book series (CCIS, volume 304)


This paper presents a study of geometric moment invariants generated from graph based algorithms. One of the main problems addressed was that the algorithms produced too many graphs that resulted in zero moment invariants. Hence, we propose an algorithm to determine zero moment invariant generating graphs. Induction proof of the steps involved in the algorithm has also been presented with suitable example graphs. It has been found and illustrated with examples that the computational time for identifying non-zero invariants could be largely reduced with the help of our proposed algorithm.


computational complexity geometric moments image transforms orthogonal moments moment invariants 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dai, X.B., Zhang, H., Shu, H.Z., Luo, L.M.: Image Recognition by Combined Invariants of Legendre Moment. In: Proc. IEEE International Conference on Information and Automation, pp. 1793–1798 (2010)Google Scholar
  2. 2.
    Flusser, J., Suk, T., Zitová, B.: Moments and Moment Invariants in Pattern Recognition © 2009. John Wiley & Sons, Ltd (2009) ISBN: 978-0-470-69987-4Google Scholar
  3. 3.
    Mukundan, R., Ramakrishnan, K.R.: Moment Functions in Image Analysis: Theory and Applications, p. 9Google Scholar
  4. 4.
    Flusser, J., Suk, T., Saic, S.: Recognition of Blurred Images by the Method of Moments. IEEE Trans. Image Proc. 5, 87–92 (1996)CrossRefGoogle Scholar
  5. 5.
    Sivaramakrishna, R., Shashidhar, N.S.: Hu’s Moment Invariants: How Invariant are They under Skew and Perspective Transformations? In: Proc. WESCANEX 1997: Communications, Power and Computing Conference, Winnipeg, Man, Canada, pp. 292–295 (1997)Google Scholar
  6. 6.
    Suk, T., Flusser, J.: On the Independence of Rotation Moment Invariants. Pattern Recognition 33, 1405–1410 (2000)CrossRefGoogle Scholar
  7. 7.
    Flusser, J., Suk, T.: Rotation Moment Invariants for Recognition of Symmetric Objects. IEEE Trans. Image Proc. 15, 3784–3790 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Suk, T., Flusser, J.: Affine Moment Invariants Generated by Automated Solution of the Equations. In: 19th International Conference on Pattern Recognition, ICPR 2008, pp. 1–4 (2008), doi: 10.1109/ICPR.2008.4761221Google Scholar
  9. 9.
    Shamsuddin, S.M., Sulaiman, M.N., Darus, M.: Invarianceness of Higher Order Centralised Scaled-invariants Undergo Basic Transformations. International Journal of Computer Mathematics 79, 39–48 (2002)zbMATHCrossRefGoogle Scholar
  10. 10.
    Suk, T., Flusser, J.: Affine Moment Invariants Generated by Graph Method. Pattern Recognition 44(9), 2047–2056 (2010)CrossRefGoogle Scholar
  11. 11.
    Mu, H.B., Qi, D.W.: Pattern Recognition of Wood Defects Types Based on Hu Invariant Moments. In: 2nd International Congress on Image and Signal Processing, CISP 2009, Tianjin, pp. 1–5 (2009)Google Scholar
  12. 12.
    Zunic, J., Hirota, K., Rosin, P.L.: A Hu Moment Invariant as a Shape Circularitymeasure. Pattern Recognition, 47–57 (2010)Google Scholar
  13. 13.
    Sheela, S.V., Vijaya, P.A.: Non-linear Classification for Iris patterns. In: Proc. Multimedia Computing and Systems (ICMCS), 2011 International Conference Ouarzazate, Morocco, pp. 1–5 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vazeerudeen Abdul Hameed
    • 1
  • Siti Mariyam Shamsuddin
    • 1
  1. 1.Soft Computing Research Group, Faculty of Computer Science and Research GroupUniversiti Teknologi MalaysiaSkudaiMalaysia

Personalised recommendations