Fast computation of Zernike moments from normalized geometric moments has been developed in this work. The computation is multiplications free and only additions are needed to generate Zernike moments. Geometric moments have been generated using Hatamian's filter up to high orders by a very simple and straightforward computation scheme. Other kinds of moments (i.e., Legendre, pseudo Zernike. etc.) can be computed using the same algorithm after giving the proper transformations that state their relation to geometric moments. Proper normalizations to geometric moments are necessary so that it can be used in the efficient computation of Zernike moments. To ensure fair comparisons, recursive algorithms are used to generate Zernike polynomials and any other coefficients. Computational complexity model and the test programs show that the speed up factor of the proposed algorithm is superior with respect to other fast and/or direct computations. To our knowledge, it is the first time that Zernike moments can be computed in real time rates which encourages the use of Zernike moments features in different image retrieval systems that supports huge database such as XM experimental model stated for MPEG-7 experimental core. It is concluded that choosing direct computation would be impractical.