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International Journal of Automation and Computing 2018, Vol. 15 Issue (2) :169-180    DOI: 10.1007/s11633-017-1105-8
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Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments
Mostafa El Mallahi1, Jaouad El Mekkaoui2, Amal Zouhri1, Hicham Amakdouf1, Hassan Qjidaa1
1 Faculty of Sciences, Sidi Mohamed Ben Abdellah University, Fez, Morocco;
2 Department of Mathematics and Computer Science, Polydisciplinary Faculty, Sultan Moulay Slimane University, Beni Mellal, Morocco
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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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Keywords3D radial complex moments   3D radial shifted Legendre radial moments   radial shifted Legendre polynomials   3D image reconstruction   3D rotation scaling translation invariants   3D image recognition   computational complexities     
Received: 2017-01-10; Revised: 2017-09-28; published: 2017-09-28
Corresponding Authors: Mostafa El Mallahi     Email: mostafa.elmallahi@usmba.ac.ma
About author: 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.E-mail:mostafa.elmallahi@usmba.ac.ma;Jaouad El Mekkaoui received the B.Sc., M.Sc. and Ph.D. degrees in mathematics from Faculty of Sciences.E-mail:jawad.mekkaou@gmail.com;Amal Zouhri received the B.Sc., M.Sc. and Ph.D. degrees in electrical engineering from Faculty of Sciences.E-mail:amal.zouhri@usmba.ac.ma;Hicham Amakdouf received the B.Sc., M.Sc. degrees in computer sciences from Faculty of Sciences.E-mail:hicham.amakdouf@usmba.ac.ma;Hassan Qjidaa received the M.Sc. and Ph.D. degrees in physics from Claud Bernard University of Lyon, France in 1983 and 1987, respectively.E-mail:Hassan.qjidaa@usmba.ac.ma
Cite this article:   
Mostafa El Mallahi, Jaouad El Mekkaoui, Amal Zouhri, Hicham Amakdouf, Hassan Qjidaa. Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments[J]. International Journal of Automation and Computing , vol. 15, no. 2, pp. 169-180, 2018.
URL:  
http://www.ijac.net/EN/10.1007/s11633-017-1105-8      或     http://www.ijac.net/EN/Y2018/V15/I2/169
 
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