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Complete and Incomplete Sets of Invariants

Journal of Mathematical Imaging and Vision volume 63, pages 917–922 (2021)Cite this article

Abstract

The paper shows that the moment invariants proposed recently in this journal by Hjouji et al. (J Math Imaging Vis 62:606–624, 2020) are incomplete, which leads to a limited discriminability. We prove this by means of circular projection of the image. In a broader context, we demonstrate that completeness of the invariants leads to a better recognition power.

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Notes

  1. This statement is known as Moment Uniqueness Theorem, see [1] for more details.

  2. For some images, certain moments may be constrained to be zero or non-zero, so the choice may not be totally free.

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Acknowledgements

This work has been supported by the Czech Science Foundation under the Grant No. GA21-03921S and by the Praemium Academiae.

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Authors and Affiliations

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

    Jan Flusser, Tomáš Suk & Barbara Zitová

Authors
  1. Jan Flusser
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  2. Tomáš Suk
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  3. Barbara Zitová
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Correspondence to Jan Flusser.

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Flusser, J., Suk, T. & Zitová, B. Complete and Incomplete Sets of Invariants. J Math Imaging Vis 63, 917–922 (2021). https://doi.org/10.1007/s10851-021-01039-x

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Keywords

  • Moment invariants
  • Complex moments
  • Completeness
  • Discriminability
  • Circular projection