Accurate and efficient computation of high order Zernike moments

Zernike Moments are useful tools in pattern recognition and image analysis due to their orthogonality and rotation invariance property. However, direct computation of these moments is very expensive, limiting their use especially at high orders. There have been some efforts to reduce the computational cost by employing quantized polar coordinate systems, which also reduce the accuracy of the moments. In this paper, we propose an efficient algorithm to accurately calculate Zernike moments at high orders. To preserve accuracy, we do not use any form of coordinate transformation and employ arbitrary precision arithmetic. The computational complexity is reduced by detecting the common terms in Zernike moments with different order and repetition. Experimental results show that our method is more accurate than other methods and it has comparable computational complexity especially in case of using large images and high order moments.