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

Thai V. Hoang (1) , Salvatore Tabbone (2)

1 ORPAILLEUR - Knowledge representation, reasonning
2 QGAR - Querying Graphics through Analysis and Recognition

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, vol. 40, no. 4, pp. 1245--1254, 2007] 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.

Mots clés: Jacobi polynomials; Legendre polynomials; Chebyshev polynomials; Zernike moments; pseudo-Zernike moments; orthogonal Fourier--Mellin moments; Chebyshev--Fourier moments; pseudo-Jacobi--Fourier moments

Domaines: Traitement des images [eess.IV]

Thai V. Hoang, Salvatore Tabbone. Errata and comments on "Generic orthogonal moments: Jacobi--Fourier moments for invariant image description". Pattern Recognition, 2013, 46 (11), pp.3148-3155. ⟨10.1016/j.patcog.2013.04.011⟩. ⟨hal-00820279⟩