Rotation of 2D orthogonal polynomials

© 2017 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license: http://creativecommons.org/licenses/by-nc-nd/4.0/ This author accepted manuscript is made available following 24 month embargo from date of publication (Dec 2017) in accordance with the publisher’s archiving policyOrientation-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