A fast and accurate computation of 2D and 3D generalized Laguerre moments for images analysis
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A fast and accurate computation of 2D and 3D generalized Laguerre moments for images analysis Mhamed Sayyouri 1 Hassan Qjidaa 2
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& Hicham Karmouni & Abdeslam Hmimid & Ayoub Azzayani &
Received: 10 April 2020 / Revised: 9 August 2020 / Accepted: 16 September 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
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. Keywords Generalized Laguerre polynomials . Generalized Laguerre moments . Matrix multiplication . Fast computation . 2D and 3D image reconstruction
1 Introduction The theory of moments has seen a renewed interest in recent years in the field of image processing on everything for the applications of classification, pattern recognition and 2D/3D images analysis [27, 35, 37, 41–45]. This is due to their ability to describe the * Mhamed Sayyouri [email protected] Extended author information available on the last page of the article
Multimedia Tools and Applications
image completely by coding its content in a compact manner. The orthogonal moments are defined as the orthogonal projection of the information space (Signal/image) on an orthogonal basis. These can be classified into two main categories: continuous orthogonal moments such as: Legendre [35, 41], Chebyshev [36], Gegenbauer [15], GaussianHermite [17], Jacobi [34], Zernike [8, 13, 46] and pseudo-Zernike [39] and discrete orthogonal moments such as: Tchebichef [22, 38], Krawtchouk [1], Hahn [23, 30], Charlier [24] and Meixner [19, 31]. The orthogonal moments have important properties for reconstructing noisy images without information redundancy [17, 19, 22, 23]. However, the use of the continuous orthogonal moments as descriptors characteristic of the image is limited by two major problems: (i) the discretization error due to the numerical approximation of the integrals by finite sum
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