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Complete and Incomplete Sets of Invariants


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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  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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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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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).

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