Fast computation of Jacobi-Fourier moments for invariant image recognition

The Jacobi-Fourier moments (JFMs) provide a wide class of orthogonal rotation invariant moments (ORIMs) which are useful for many image processing, pattern recognition and computer vision applications. They, however, suffer from high time complexity and numerical instability at high orders of moment. In this paper, a fast method based on the recursive computation of radial kernel function of JFMs is proposed which not only reduces time complexity but also improves their numerical stability. Fast recursive method for the computation of Jacobi-Fourier moments is proposed.The proposed method not only reduces time complexity but also improves numerical stability of moments.Better image reconstruction is achieved with lower reconstruction error.Proposed method is useful for many image processing, pattern recognition and computer vision applications.

[1]  Chandan Singh,et al.  Algorithms for fast computation of Zernike moments and their numerical stability , 2011, Image Vis. Comput..

[2]  Ziliang Ping,et al.  Image description with Chebyshev-Fourier moments. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  Thai V. Hoang.  Image Representations for Pattern Recognition , 2011 .

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

[5]  Chandan Singh,et al.  On the fast computation of orthogonal Fourier–Mellin moments with improved numerical stability , 2010, Journal of Real-Time Image Processing.

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

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

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

[9]  Amandeep Kaur,et al.  Fast computation of polar harmonic transforms , 2012, Journal of Real-Time Image Processing.

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

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

[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]  Salvatore Tabbone,et al.  Errata and comments on "Generic orthogonal moments: Jacobi-Fourier moments for invariant image description" , 2013, Pattern Recognit..

[15]  Chandan Singh,et al.  Image adaptive and high-capacity watermarking system using accurate Zernike moments , 2014, IET Image Process..

[16]  Salvatore Tabbone,et al.  Fast Generic Polar Harmonic Transforms , 2014, IEEE Transactions on Image Processing.

[17]  Salvatore Tabbone,et al.  Generic polar harmonic transforms for invariant image representation , 2014, Image Vis. Comput..

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

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

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