About moment normalization and complex moment descriptors

  • A. Abo-Zaid
  • O. R. Hinton
  • E. Horne
Shone Analysis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 301)


A new normalization factor is given. Its application produces a normalized image with regard to intensity variations and scale changes. Further, in the same operation the dynamic range of the moment vector is reduced, such that higher order moments can be used without recourse to logarithmic representation.

The complex moments descriptors provides a complete set of invariants without any considerable calculation for rotational changes. This is achieved by using the phase of a reference component (C21, C32, ...) to cancel the effect of rotational angle variations by simple relation.

The simulation results presented demonstrate the efficiency of both the proposed normalization factor and the complex moment descriptor.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.R. TEAGUE, "Optical Calculation of Irradiance Moments", Applied Optics, vol. 19, No. 8, 1980, pp. 1353:1356.Google Scholar
  2. 2.
    M.R. TEAGUE, "Image Analysis via the General Theory of Moments", J. opt. Soc. Am., vol. 70, no. 8, 1980, pp.920:930.Google Scholar
  3. 3.
    Y.N. HSU, "Rotation Invariant Discrimination Between Almost Similar Objects", Applied Optics, vol. 22, No. 1, 1983, pp. 130:132.Google Scholar
  4. 4.
    P. REEVES, "Shape Analysis of Segmented Objects Using Moments", Proceeding IEEE Computer Society Conf. on Pattern Recognition and Image Processing, August 1981, pp. 171:176.Google Scholar
  5. 5.
    S.A. DUDANI & GHEE, "Aircraft Identification by Moment Invariant", IEEE, T. Computer, C-26, 1977, pp. 39:45.Google Scholar
  6. 6.
    S.S. REDDI, "Radial and Angular Moment Invariant for Image Identification", IEEE, PAMI-3, No. 2, 1981, pp. 240:242.Google Scholar
  7. 7.
    C. TEH, "On Digital Approximation of Moments Invariants", Computer Graphics and Image Processing, 33, 1986, pp. 318:326.Google Scholar
  8. 8.
    HOSSACK, "Moment Invariant for Pattern Recognition", Pattern Recognition Letters, 1, 1983, pp. 451:456.Google Scholar
  9. 9.
    N. DROVNYCHENKO, "Upsilon Invariants: A Uniform Set of Moment Invariants", SPIE, vol. 504, 1984, pp. 40:44.Google Scholar
  10. 10.
    ABO-MOSTFA, "Recognitive Aspects of Moments Invariants", IEEE, PAMI-6, No. 6, 1984, pp. 698:706.Google Scholar
  11. 11.
    S. MAITRA, "Moment Invariants", Proceeding of IEEE, vol. 67, No. 4, 1979, pp. 697:699.Google Scholar
  12. 12.
    ABO-MOSTFA, "Image Normalization by Complex Moments", IEEE, PAMI-7, No. 1, 1985, pp. 45:55.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • A. Abo-Zaid
    • 1
  • O. R. Hinton
    • 1
  • E. Horne
    • 1
  1. 1.Electronic Engineering Labs.University of KentCanterbury

Personalised recommendations