A novel algorithm for fast computation of Zernike moments

Zernike moments (ZMs) have been successfully used in pattern recognition and image analysis due to their good properties of orthogonality and rotation invariance. However, their computation by a direct method is too expensive, which limits the application of ZMs. In this paper, we present a novel algorithm for fast computation of Zernike moments. By using the recursive property of Zernike polynomials, the inter-relationship of the Zernike moments can be established. As a result, the Zernike moment of order n with repetition m, Z(nm), can be expressed as a combination of Z(n-2.m) and Z(n-4.m). Based on this relationship, the Zernike moment Z(nm), for n > m, can be deduced from Z(mm). To reduce the computational complexity, we adopt an algorithm known as systolic array for computing these latter moments. Using such a strategy, the multiplication number required in the moment calculation of Z(mm) can be decreased significantly. Comparison with known methods shows that our algorithm is as accurate as the existing methods, but is more efficient. (C) 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.