Comments on “fast computation of jacobi-Fourier moments for invariant image recognition”

• Published in: Pattern recognition 2017-07, Vol.67, p.16-22
• Main Author: Sáez-Landete, José
• Format: Article
• Language: English
• Subjects: Jacobi polynomials; Orthogonal moments; Rotation-invariant pattern recognition
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2017.01.025

•Computation procedure presented in “Fast computation of Jacobi–Fourier moments for invariant image recognition” has been analyzed and it has been demonstrated that the proposed domain of the kernel functions causes the loss of the orthogonality.•Some imprecisions in the determination of the particular cases of Jacobi–Fourier kernel, as well as some errata in the recursive computation of the polynomials have been corrected.•It has proposed the use of a polar pixel tiling scheme, which allows a more accurate moment computation.•It is demonstrated that the image reconstruction error is reduced, and this error continuously decreases as the number of considered moments increases. In the recent work: “Fast computation of Jacobi–Fourier moments for invariant image recognition, Pattern Recognition 48 (2015) 1836–1843”, the authors propose a new method for the recursive computation of Jacobi–Fourier moments. This method reduces the computational complexity in radial and angular kernel functions of the moments, improving the numerical stability of the computation procedure. However, they use a rectangular domain for the computation of the Jacobi–Fourier moments. In this work, we demonstrate that the use of this domain involves the loss of kernel orthogonality. Also, errata and inaccuracies which could lead to erroneous results have been corrected and clarified. Furthermore, we propose a more precise procedure of the moments computation by using a circular pixel tiling scheme, which is based on the image interpolation and an adaptive Simpson quadrature method for the numerical integration.