Numerical error analysis in Zernike moments computation

Algorithms for fast computation of Zernike moments and their numerical stability

“…During the course of the implementation of several algorithms, we observed that the q-recursive method [20] is quite stable and its stability increases with the size of image. Our observations are in line with the findings reported by [26,27]. For an image of the size 64 × 64 pixels it provides numerical stability for moment orders up to 180, and for 512 × 512 pixels image the stability is exhibited even for moment orders up to 450.…”

“…The non-recursive formulation of ZMs or the computation of ZMs through GMs suffers from numerical instability for high orders of moments(N45) and instability is reflected through the increasing trend of image reconstruction error starting from moment order 45. A detailed comparative study of numerical stability of recursive algorithms is performed by Papakostas et al [26,27]. Two types of error-overflow and finite precision errors-are taken into account while analyzing their effects on numerical behavior of radial polynomials and the coefficients associated with the recursive steps.…”

“…Although in [26,27] the numerical stability of various recursive methods including the q-recursive method, is analyzed and experimental results concerning to the values of radial polynomials are presented in details, the overall performance of recursive method on ZMs which is reflected in the image reconstruction error (∈ L ) is not given. Figs.…”

A new class of Zernike moments for computer vision applications

“…This need motivated many researchers [3][4][5][6]12,17,18,26], to develop of recursive algorithms, but some problems related to possible propagated quantization errors [24] that destroy the recursive algorithms, still exist.…”

“…Although, these recursive algorithms do not include any factorial terms, they involve the computation of intermediate moment orders and thus they need considerable memory resources, every time the calculation of a high order moment is requested. Additionally, the recursive algorithms have the disadvantage of carrying and propagating a possible numerical error that may appear in one step of the algorithm, to subsequent steps by making the final quantities unreliable [24].…”