Accurate calculation of high order pseudo-Zernike moments and their numerical stability

The accuracy of pseudo-Zernike moments (PZMs) suffers from various errors, such as the geometric error, numerical integration error, and discretization error. Moreover, the high order moments are vulnerable to numerical instability. In this paper, we present a method for the accurate calculation of PZMs which not only removes the geometric error and numerical integration error, but also provides numerical stability to PZMs of high orders. The geometric error is removed by taking the square-grids and arc-grids, the ensembles of which maps exactly the circular domain of PZMs calculation. The Gaussian numerical integration is used to eliminate the numerical integration error. The recursive methods for the calculation of pseudo-Zernike polynomials not only reduce the computation complexity, but also provide numerical stability to high order moments. A simple computational framework to implement the proposed approach is also discussed. Detailed experimental results are presented which prove the accuracy and numerical stability of PZMs.

[1]  Karim Faez,et al.  Study on the performance of moments as invariant descriptors for practical face recognition systems , 2010 .

[2]  Karim Faez,et al.  An Efficient Feature Extraction Method with Pseudo-Zernike Moment in RBF Neural Network-Based Human Face Recognition System , 2003, EURASIP J. Adv. Signal Process..

[3]  Miroslaw Pawlak,et al.  On the Accuracy of Zernike Moments for Image Analysis , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Chee-Way Chong,et al.  The scale invariants of pseudo-Zernike moments , 2003, Pattern Analysis & Applications.

[5]  Chee-Way Chong,et al.  A comparative analysis of algorithms for fast computation of Zernike moments , 2003, Pattern Recognit..

[6]  Chandan Singh,et al.  Fast and numerically stable methods for the computation of Zernike moments , 2010, Pattern Recognit..

[7]  Chee-Way Chong,et al.  An Efficient Algorithm for Fast Computation of Pseudo-Zernike Moments , 2003, Int. J. Pattern Recognit. Artif. Intell..

[8]  Roland T. Chin,et al.  On Image Analysis by the Methods of Moments , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Mohammed Al-Rawi Fast computation of pseudo Zernike moments , 2009, Journal of Real-Time Image Processing.

[10]  Xiangyang Wang,et al.  A new robust digital image watermarking based on Pseudo-Zernike moments , 2010, Multidimens. Syst. Signal Process..

[11]  Miroslaw Pawlak,et al.  Circularly orthogonal moments for geometrically robust image watermarking , 2007, Pattern Recognit..

[12]  Xiangyang Wang,et al.  An effective image retrieval scheme using color, texture and shape features , 2011, Comput. Stand. Interfaces.

[13]  Run-sheng Li,et al.  Map Matching Algorithm According to Pseudo-Zernike Moments , 2010, 2010 Second World Congress on Software Engineering.

[14]  Chandan Singh,et al.  Accurate calculation of Zernike moments , 2013, Inf. Sci..

[15]  Amandeep Kaur,et al.  Sub-Pixel Edge Detection Using Pseudo Zernike Moment , 2011 .

[16]  C. Singh,et al.  On image reconstruction, numerical stability, and invariance of orthogonal radial moments and radial harmonic transforms , 2011, Pattern Recognition and Image Analysis.

[17]  Mandyam D. Srinath,et al.  Orthogonal Moment Features for Use With Parametric and Non-Parametric Classifiers , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Andrew Beng Jin Teoh,et al.  A Discriminant Pseudo Zernike Moments in Face Recognition , 2006, J. Res. Pract. Inf. Technol..

[19]  Yongqing Xin,et al.  Geometrically robust image watermarking via pseudo-Zernike moments , 2004, Canadian Conference on Electrical and Computer Engineering 2004 (IEEE Cat. No.04CH37513).

[20]  Chandan Singh,et al.  Error Analysis in the Computation of Orthogonal Rotation Invariant Moments , 2013, Journal of Mathematical Imaging and Vision.

[21]  Chandan Singh,et al.  Analysis of algorithms for fast computation of pseudo Zernike moments and their numerical stability , 2012, Digit. Signal Process..

[22]  Miroslaw Pawlak,et al.  Accurate Computation of Zernike Moments in Polar Coordinates , 2007, IEEE Transactions on Image Processing.

[23]  Tianxiao Ma,et al.  A pseudo-Zernike moment based audio watermarking scheme robust against desynchronization attacks , 2011, Comput. Electr. Eng..

[24]  Raveendran Paramesran,et al.  On the computational aspects of Zernike moments , 2007, Image Vis. Comput..

[25]  H. Shu,et al.  Image description with generalized pseudo-Zernike moments. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[26]  A. Bhatia,et al.  On the circle polynomials of Zernike and related orthogonal sets , 1954, Mathematical Proceedings of the Cambridge Philosophical Society.

[27]  Basil G. Mertzios,et al.  Efficient computation of Zernike and Pseudo-Zernike moments for pattern classification applications , 2010, Pattern Recognition and Image Analysis.