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

  • Mostafa El Mallahi
  • Jaouad El Mekkaoui
  • Amal Zouhri
  • Hicham Amakdouf
  • Hassan Qjidaa
Research Article

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.

Keywords

3D 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 

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Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of SciencesSidi Mohamed Ben Abdellah UniversityFezMorocco
  2. 2.Department of Mathematics and Computer Science, Polydisciplinary FacultySultan Moulay Slimane UniversityBeni MellalMorocco

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