Analysis of algorithms for fast computation of pseudo Zernike moments and their numerical stability

This paper aims at analyzing the performance of various fast methods for the computation of pseudo Zernike moments (PZMs) with respect to their time complexity and numerical stability. Based on these different types of existing methods, four new methods are also proposed. A computational framework is provided which integrates the fast calculation of pseudo Zernike polynomials (PZPs), the angular functions and symmetry/anti-symmetry property of complex kernel functions. It is shown that the recursive methods that compute PZMs of all orders ⩽pmax for an image of resolution N×N pixels reduce the time complexity from to . Experimental analysis for numerical stability of various methods is provided which could be useful for the evaluation of these methods. It is observed that recursive methods are numerically stable for high orders of moments and their reconstruction error declines with increase in image size and moment order.