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Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments

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Abstract

This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments: a 3D substituted radial shifted Legendre moments (3DSRSLMs) and a 3D weighted radial one (3DWRSLMs). Both are centered on two types of polynomials. In the first case, a new 3D radial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendre moments (3DSRSLMs/3DWRSLMs) are introduced using a spherical representation of volumetric image. 3D invariants as derived from the suggested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three issues. To confirm the proposed approach, we have resolved three issues: rotation, scaling and translation invariants. The result of experiments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Simultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark (PSB) database for 3D image.

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Correspondence to Mostafa El Mallahi.

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Recommended by Guest Editor Zhi-Jie Xu

Mostafa El Mallahi received the B. Sc., M. Sc. and Ph. D. degrees in computer science from Faculty of Sciences, University Sidi Mohammed Ben Abdellah, Morocco in 2000, 2007 and 2017, respectively.

His research interests include image processing, pattern classification, orthogonal systems, neural networks, big data, data mining, data science, deep learning, genetic algorithms and special functions.

Jaouad El Mekkaoui received the B. Sc., M. Sc. and Ph. D. degrees in mathematics from Faculty of Sciences, Sidi Mohammed Ben Abdellah University, Morocco in 1999, 2002 and 2014, respectively. He is now a professor in Department of Mathematics and Computer Science, Polydisciplinaire Faculty, Morocco.

His research interests include mathematics, numerical analysis, classification, image processing, pattern recognition, orthogonal systems, neural networks, deep learning and data science, big data, genetic algorithms and special functions, image manuscripts recognition, cognitive science, human-machine interface, artificial intelligence and robotics.

Amal Zouhri received the B. Sc., M. Sc. and Ph. D. degrees in electrical engineering from Faculty of Sciences, Sidi Mohammed Ben Abdellah University, Morocco in 2008, 2011 and 2017, respectively.

Her research interests include embedded system, stability and stabilization of interconnected systems, decentralized systems, robust and H control, linear matrix inequalities, singular systems, time delay systems, computer science, image processing, pattern classification, orthogonal systems, neural networks, deep learning, genetic algorithms and special functions.

Hicham Amakdouf received the B. Sc., M. Sc. degrees in computer sciences from Faculty of Sciences, Sidi Mohammed Ben Abdellah University, Morocco in 2003 and 2007, respectively. He is presently a Ph. D. degree candidate in computer science at the Faculty of Sciences, Sidi Mohammed Ben Abdellah University, Morocco.

His research interests include image processing, computer graphics, artificial intelligence, geographic information systems.

Hassan Qjidaa received the M. Sc. and Ph. D. degrees in physics from Claud Bernard University of Lyon, France in 1983 and 1987, respectively. He is a full profossor of electrical engineering at the Faculty of Sciences, Sidi Mohammed Ben Abdellah University, Morocco 1999. He is now a professor in Sidi Mohammed Ben Abdellah University, Morocco.

His research interests include classification, image processing, pattern recognition, orthogonal systems, neural networks, deep learning and data science, big data, genetic algorithms and special functions.

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El Mallahi, M., El Mekkaoui, J., Zouhri, A. et al. Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments. Int. J. Autom. Comput. 15, 169–180 (2018). https://doi.org/10.1007/s11633-017-1105-8

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  • DOI: https://doi.org/10.1007/s11633-017-1105-8

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