Errata and comments on "Generic orthogonal moments: Jacobi-Fourier moments for invariant image description"

Abstract Ping et al. [Z. Ping, H. Ren, J. Zou, Y. Sheng, and W. Bo, Generic orthogonal moments: Jacobi–Fourier moments for invariant image description, Pattern Recognition 40 (4) (2007) 1245–1254] made a landmark contribution to the theory of two-dimensional orthogonal moments confined to the unit disk by unifying the radial kernels of existing polynomial-based circular orthogonal moments under the roof of shifted Jacobi polynomials. However, the work contains some errata that result mainly from the confusion between the two slightly different definitions of shifted Jacobi polynomials in the literature. Taking into account the great importance and the high impact of the work in the pattern recognition community, this paper points out the confusing points, corrects the errors, and gives some other relevant comments. The corrections developed in this paper are illustrated by some experimental evidence.

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

[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]  Salvatore Tabbone,et al.  Fast computation of orthogonal polar harmonic transforms , 2012, Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012).

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

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

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

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

[8]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

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

[10]  Qing Wang,et al.  Rotational Invariance Based on Fourier Analysis in Polar and Spherical Coordinates , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[12]  von F. Zernike.  Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode , 1934 .

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

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

[15]  ZouJian,et al.  Generic orthogonal moments , 2007 .

[16]  Surong Hasi,et al.  Image analysis by pseudo-Jacobi (p = 4, q = 3)-Fourier moments. , 2004, Applied optics.

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