Fast Zernike moments

Abstract

Zernike moments are important digital image descriptors used in various applications starting from image watermarking to image recognition. Lots of fast algorithms have been proposed to speedup the computation of Zernike moments. This work provides computational complexity analysis of methods for the computation of Zernike moments, as well as a thorough study and simplification to the methods of finding Zernike moments from geometric moments. A new formula that relates Zernike moments to moments of digital filters is introduced that is very efficient and accurate. Comparisons are performed using Zernike moment via geometric moments method, the Q-recursive method, the coefficient method, and the symmetry method. Using a well defined performance metric, this work finds out that Zernike moments from geometric moments of digital filters is nearly 70 times faster than the best method known as the symmetry method.

Fast computation of pseudo Zernike moments

“…Even if PZRPs are efficiently generated using recursive or coefficient methods, there is still a huge computation overhead of the amount O N 2 n þ 1 ð Þ 2 : It is possible to further reduce the computation by considering the symmetry of a point in the first octant [18]. To do this, (1) can be rewritten as…”

Two-Dimensional Polar Harmonic Transforms for Invariant Image Representation

“…Recurrence equations [19] are often used in place of these direct formulas, but although recurrence formulas do help to push the maximal order of computable moment higher, they eventually will suffer from numerical instability. See [19], [20] for some ZM-computation-related issues. A summary of comparison of the various moment kernels and that of PHTs is given in Table 1.…”

Digital Filter Implementation of Orthogonal Moments

“…However, the plurality of large bit-width adders in the digital filter structure presents a major challenge to chip synthesis, placement and the routing process. Taking a different tack, Al-Rawi [23] generalized the relationship between the moments and the digital filter outputs using a recurrence formula.…”