On Image Analysis by the Methods of Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Invariant Image Recognition by Zernike Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient computation of radial moment functions using symmetrical property
Pattern Recognition
A novel approach to the fast computation of Zernike moments
Pattern Recognition
Fast Zernike wavelet moments for Farsi character recognition
Image and Vision Computing
A new class of Zernike moments for computer vision applications
Information Sciences: an International Journal
Circularly orthogonal moments for geometrically robust image watermarking
Pattern Recognition
Complex Zernike moments features for shape-based image retrieval
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special section: Best papers from the 2007 biometrics: Theory, applications, and systems (BTAS 07) conference
Geometric Invariance in image watermarking
IEEE Transactions on Image Processing
Fast and efficient method for computing ART
IEEE Transactions on Image Processing
Invariant image watermark using Zernike moments
IEEE Transactions on Circuits and Systems for Video Technology
Analysis of algorithms for fast computation of pseudo Zernike moments and their numerical stability
Digital Signal Processing
The fast recursive computation of Tchebichef moment and its inverse transform based on Z-transform
Digital Signal Processing
A high capacity image adaptive watermarking scheme with radial harmonic Fourier moments
Digital Signal Processing
Error Analysis in the Computation of Orthogonal Rotation Invariant Moments
Journal of Mathematical Imaging and Vision
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Zernike moments (ZMs) are used in many image processing applications due to their superior performance over other moments. However, they suffer from high computation cost and numerical instability at high order of moments. In the past many recursive methods have been developed to improve their speed performance and considerable success has been achieved. The analysis of numerical stability has also gained momentum as it affects the accuracy of moments and their invariance property. There are three recursive methods which are normally used in ZMs calculation-Prata's, Kintner's and q-recursive methods. The earlier studies have found the q-recursive method outperforming the two other methods. In this paper, we modify Prata's method and present a recursive relation which is proved to be faster than the q-recursive method. Numerical instability is observed at high orders of moments with the q-recursive method suffering from the underflow problem while the modified Prata's method suffering from finite precision error. The modified Kintner's method is the least susceptible to these errors. Keeping in view the better numerical stability, we further make the modified Kintner's method marginally faster than the q-recursive method. We recommend the modified Prata's method for low orders (@?90) and Kintner's fast method for high orders (90) of ZMs.