Institute of Information Theory and Automation

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Publication details

Rotation of 2D orthogonal polynomials

Journal Article

Yang B., Flusser Jan, Kautský J.

serial: Pattern Recognition Letters vol.102, 1 (2018), p. 44-49

project(s): GA15-16928S, GA ČR

keywords: Rotation invariants, Orthogonal polynomials, Recurrent relation, Hermite-like polynomials, Hermite moments

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abstract (eng):

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 polynomi- als, 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.


bocek: 2012-12-21 16:10