A new fast algorithm to compute moment 3D invariants of generalized Laguerre modified by fractional-order for pattern recognition

Abstract

Orthogonal moments are the projections of image functions on particular functions of the kernel. They play an essential role in image extraction: rotation, scaling, translation invariance, object recognition, image classification, image noise robustness, and low information redundancy. These moments are derived from orthogonal polynomials that can be continuous or discrete. This paper focuses on the fractional-order modified generalized Laguerre moment invariants (FMGLMIs), which is a generalization of the traditional integer order one. In this research, we have developed a new algorithm to compute the 3D invariant moments of FMGLMIs based on the 3D image cuboid representation, our proposed calculation method can improve the efficiency of 3D invariant moment calculation to maintain numerical stability and significantly reduce calculation time with very satisfactory accuracy. To check this new algorithm, the calculation of 3D invariant moments gives very encouraging results for the invariability property of the proposed method with respect to different geometric transformations and noise degradations of 3D images, classification and recognition of 3D images and the calculation time of fractional-order invariants proposed. Finally, the experimental results show that the proposed method makes it possible to construct fractional-order modified generalized Laguerre invariant moments offering better performances for image analysis and pattern recognition.