Fast computation of orthogonal polar harmonic transforms

This paper presents a method for the computation of polar harmonic transforms that is fast and efficient. The method is based on the inherent recurrence relations among harmonic functions that are used in the definitions of the radial and angular kernels of the transforms. The employment of these relations leads to recursive strategies for fast computation of harmonic function-based kernels. Polar harmonic transforms were recently proposed and have shown nice properties for image representation and pattern recognition. The proposed method is 10-time faster than direct computation and five-time faster than fast computation of Zernike moments.

[1]  J. Flusser,et al.  Moments and Moment Invariants in Pattern Recognition , 2009 .

[2]  Xudong Jiang,et al.  Two-Dimensional Polar Harmonic Transforms for Invariant Image Representation , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Alireza Khotanzad,et al.  Invariant Image Recognition by Zernike Moments , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Ziliang Ping,et al.  Multidistortion-invariant image recognition with radial harmonic Fourier moments. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  J. Borwein,et al.  On the complexity of familiar functions and numbers , 1988 .

[6]  Miroslaw Bober,et al.  MPEG-7 visual shape descriptors , 2001, IEEE Trans. Circuits Syst. Video Technol..

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

[8]  Demetri Psaltis,et al.  Recognitive Aspects of Moment Invariants , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  M. Teague.  Image analysis via the general theory of moments , 1980 .

[10]  Jian Zou,et al.  Generic orthogonal moments: Jacobi-Fourier moments for invariant image description , 2007, Pattern Recognit..

[11]  Salvatore Tabbone,et al.  Generic polar harmonic transforms for invariant image description , 2011, 2011 18th IEEE International Conference on Image Processing.

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

[13]  Y. Sheng,et al.  Orthogonal Fourier–Mellin moments for invariant pattern recognition , 1994 .

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

[15]  Whoi-Yul Kim,et al.  A novel approach to the fast computation of Zernike moments , 2006, Pattern Recognit..