Practical Fast Computation of Zernike Moments

The fast computation of Zernike moments from normalized geometric momentshas been developed in this paper. The computation is multiplicationfree and only additions are needed to generate Zernike moments.Geometric moments are generated using Hatamian's filter up tohigh orders by a very simple and straightforward computation scheme.Other kinds of moments (e.g., Legendre, pseudo Zernike) can becomputed using the same algorithm after giving the propertransformations that state their relations to geometric moments. Propernormalizations of geometric moments are necessary so that the method can beused in the efficient computation of Zernike moments. To ensure faircomparisons, recursive algorithms are used to generate Zernikepolynomials and other coefficients. The computational complexity modeland test programs show that the speed-up factor of the proposedalgorithm is superior with respect to other fast and/or directcomputations. It perhaps is the first time that Zernikemoments can be computed in real time rates, which encourages the use ofZernike moment features in different image retrieval systems thatsupport huge databases such as the XM experimental model stated for the MPEG-7experimental core. It is concluded that choosing direct computationwould be impractical.