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Construction of Complete and Independent Systems of Rotation Moment Invariants

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Computer Analysis of Images and Patterns (CAIP 2003)

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

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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.

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References

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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
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  2. Tomáš Suk
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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

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© 2003 Springer-Verlag Berlin Heidelberg

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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

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  • 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

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