Skip to main content
SpringerLink
Log in
Book cover

International Conference on Computer Analysis of Images and Patterns

CAIP 2003: Computer Analysis of Images and Patterns pp 41–48Cite as

Construction of Complete and Independent Systems of Rotation Moment Invariants

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2756))

Abstract

The problem of independence and completeness of rotation moment invariants is addressed in this paper. General method for constructing invariants of arbitrary orders by means of complex moments is described. It is shown that for any set of invariants there exists relatively small basis by means of which all other invariants can be generated. The method how to construct such a basis is presented. Moreover, it is proved that all moments involved can be recovered from this basis. The basis of the 3rd order moment invariants is constructed explicitly and its relationship to Hu’s invariants is studied. Based on this study, Hu’s invariants are shown to be dependent and incomplete.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hu, M.K.: Visual pattern recognition by moment invariants. IRE Trans. Information Theory 8, 179–187 (1962)

    Google Scholar 

  2. Li, Y.: Reforming the theory of invariant moments for pattern recognition. Pattern Recognition 25, 723–730 (1992)

    Article  Google Scholar 

  3. Wong, W.H., Siu, W.C., Lam, K.M.: Generation of moment invariants and their uses for character recognition. Pattern Recognition Letters 16, 115–123 (1995)

    Article  Google Scholar 

  4. Flusser, J.: On the independence of rotation moment invariants. Pattern Recognition 33, 1405–1410 (2000)

    Article  Google Scholar 

  5. Teague, M.R.: Image analysis via the general theory of moments. J. Optical Soc. of America 70, 920–930 (1980)

    Article  MathSciNet  Google Scholar 

  6. Abu-Mostafa, Y.S., Psaltis, D.: Recognitive aspects of moment invariants. IEEE Trans. Pattern Analysis and Machine Intelligence 6, 698–706 (1984)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 4, 182 08, Prague 8, Czech Republic

    Jan Flusser & Tomáš Suk

Authors
  1. Jan Flusser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tomáš Suk
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computing Science, University of Groningen, P.O.Box 800, 9700 AV, Groningen, The Netherlands

    Nicolai Petkov

  2. Institute of Mathematics and Computing Science, University of Groningen, Blauwborgje 3, 9747 AC, Groningen, The Netherlands

    Michel A. Westenberg

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Flusser, J., Suk, T. (2003). Construction of Complete and Independent Systems of Rotation Moment Invariants. In: Petkov, N., Westenberg, M.A. (eds) Computer Analysis of Images and Patterns. CAIP 2003. Lecture Notes in Computer Science, vol 2756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45179-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45179-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40730-0

  • Online ISBN: 978-3-540-45179-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation