New set of fractional-order generalized Laguerre moment invariants for pattern recognition

This article presents a new series of invariant moments, called Fractional-order Generalized Laguerre Moment Invariants (FGLMI), based on Fractional-order Generalized Laguerre polynomials (FGLPs). To begin, we provide the relations and the properties necessary to define the fractional-order generalized Laguerre moments. Then, we present the theoretical framework to derive invariants from fractional-order moments with respect to the change in orientation, size and position based on the algebraic relationships between FGLM and fractional-order geometric moments. In addition, a fast and precise algorithm has been proposed for the calculation of FGLM in order to speed up the calculation time and ensure the numerical stability of the invariant moments. Numerical experiments are carried out to demonstrate the efficiency of FGLM and their proposed invariants compared to existing methods, with regard to the reconstruction of 2D and 3D images, the computation time, the global entity extraction capacity and image localization, invariability property and 2D / 3D image classification performance on different 2D and 3D image databases. The theoretical and experimental results presented clearly show the efficiency of the descriptors proposed for the representation and classification of 2D and 3D images by other types of orthogonal moments.