A fast and accurate computation of 2D and 3D generalized Laguerre moments for images analysis

Abstract

In this paper, we will present a new set of 2D and 3D continuous orthogonal moments based on generalized Laguerre orthogonal polynomials (GLPs) for 2D and 3D image analysis. However, the computation of the generalized Laguerre orthogonal moments (GLMs) is limited by the problems of discretization of the continuous space of the polynomials, approximation of the integrals by finite sums and of too high computation time. To remedy these problems, we will propose a new method for the fast and the precise computation of 2D and 3D GLMs. This method is based on the development of an exact calculation of the double and triple integrals which define the 2D and 3D GLMs, and on the matrix calculation to accelerate the processing time of the images instead of the direct calculation. In addition to the theoretical results obtained, several experiments are carried out to validate the efficiency of the 2D and 3D GLMs descriptors in terms of computation precision and accuracy and in terms of acceleration of computation time and 2D/3D image reconstruction. The experimental results clearly show the advantages and the effectiveness of GLMs compared to the continuous orthogonal moments of Legendre, Chebyshev, Gegenbauer and Gaussian-Hermite.