A new fast algorithm to compute moment 3D invariants of generalized Laguerre modified by fractional-order for pattern re
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A new fast algorithm to compute moment 3D invariants of generalized Laguerre modified by fractional-order for pattern recognition O. El ogri1 · H. Karmouni2
· M. Yamni1 · A. Daoui1 · M. Sayyouri2 · H. Qjidaa1
Received: 24 January 2020 / Revised: 14 August 2020 / Accepted: 23 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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. Keywords Fractional-order modified generalized Laguerre polynomials · Fractional-order moment Invariants · Fast algorithm · Accurate computation · 3D image classification · Pattern recognition
Abbreviations CGLM FMGLPs FGLM
B
Classical generalized Laguerre moments Fractional-order modified generalized Laguerre polynomials Fractional-order modified generalized Laguerre moments
H. Karmouni [email protected]
Extended author information available on the last page of the article
123
Multidimensional Systems and Signal Processing
FGGMI FMGLMI RST ICR FDE GMI CMI GegMI JMI GHMI FC-FMGLMI-ICR
Fractional-order generalized geometric moment invariants Fractional-order modified generalized Laguerre moment invariants Rotation, scaling and translation Images cuboid representation Fractional differential equations Geometric moment invariants Chebychev moment invariants Gegenbauer moment invariants Jacobi moment invariants Gauss–Hermite moment invariants Fast computation of the fractional-order modified generalized Laguerre moment invariants by images cuboid representation
1 Introduction Image moments in the field of image processing are essentially weighted digital measurements of the intensity of the
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