Rotation of 2D orthogonal polynomials

Bo Yang, Jan Flusser, Jaroslav Kautsky

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Orientation-independent object recognition mostly relies on rotation invariants. Invariants from moments orthogonal on a square have favorable numerical properties but they are difficult to construct. The paper presents sufficient and necessary conditions, that must be fulfilled by 2D separable orthogonal polynomials, for being transformed under rotation in the same way as are the monomials. If these conditions have been met, the rotation property propagates from polynomials to moments and allows a straightforward derivation of rotation invariants. We show that only orthogonal polynomials belonging to a specific class exhibit this property. We call them Hermite-like polynomials.

Original languageEnglish
Pages (from-to)44-49
Number of pages6
JournalPattern Recognition Letters
Publication statusPublished - 15 Jan 2018


  • Hermite moments
  • Hermite-like polynomials
  • Orthogonal polynomials
  • Recurrent relation
  • Rotation invariants


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