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

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.