Modified Factorial-Free Direct Methods for Zernike and Pseudo-Zernike Moment Computation

Modified direct methods for the computation of Zernike and pseudo-Zernike moments are presented in this paper. The presence of many factorial terms in direct methods for computing Zernike-type moments makes their computation process a very time consuming task. Although the computational power of the modern computers is impressively increasing, the calculation of the factorial of a big number is still an inaccurate numerical procedure. The main concept of this paper is that, using Stirling's approximation for the factorial and applying some suitable mathematical properties, novel factorial-free direct methods can be developed. The resulting moments are not equal to those computed using the original direct methods, but they are a sufficiently accurate approximation of them. In addition, their variability does not affect their ability to uniquely describe and distinguish the objects that they represent. This is verified by appropriate pattern recognition experiments.