Abstract
In this research, we have developed a new algorithm to compute the moments defined in a rectangular region. By applying the recurrent formulas, symmetry properties, and particularly the parallelized matrix operations, our proposed computational method can improve the efficiency of computing Legendre, Gegenbauer, and Jacobi moments extensively with highly satisfied accuracy. To verify this new computational algorithm, the image reconstructions from the higher orders of Legendre, Gegenbauer, and Jacobi moments are performed on a testing image sized at 1024 × 1024 with very encouraging results. It took only a few seconds to compute moments and conduct the image reconstructions from the 1000-th order of the Legendre, Gegenbauer, and Jacobi moments with the PSNR values up to 45. By utilizing our new algorithm, image analysis and recognition applications using the higher orders of moments defined in a rectangular region in the range of milliseconds will be possible.
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