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Robust Reconstruction and Generalized Dual Hahn Moments Invariants Extraction for 3D Images

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3D Research

Abstract

In this paper, we introduce a new set of 3D weighed dual Hahn moments which are orthogonal on a non-uniform lattice and their polynomials are numerically stable to scale, consequent, producing a set of weighted orthonormal polynomials. The dual Hahn is the general case of Tchebichef and Krawtchouk, and the orthogonality of dual Hahn moments eliminates the numerical approximations. The computational aspects and symmetry property of 3D weighed dual Hahn moments are discussed in details. To solve their inability to invariability of large 3D images, which cause to overflow issues, a generalized version of these moments noted 3D generalized weighed dual Hahn moment invariants are presented where whose as linear combination of regular geometric moments. For 3D pattern recognition, a generalized expression of 3D weighted dual Hahn moment invariants, under translation, scaling and rotation transformations, have been proposed where a new set of 3D-GWDHMIs have been provided. In experimental studies, the local and global capability of free and noisy 3D image reconstruction of the 3D-WDHMs has been compared with other orthogonal moments such as 3D Tchebichef and 3D Krawtchouk moments using Princeton Shape Benchmark database. On pattern recognition using the 3D-GWDHMIs like 3D object descriptors, the experimental results confirm that the proposed algorithm is more robust than other orthogonal moments for pattern classification of 3D images with and without noise.

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Authors and Affiliations

  1. LESSI, CED-ST Center of Doctoral Studies in Sciences and Technologies, Faculty of Sciences Dhar el Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Abderrahim Mesbah, Amal Zouhri, Mostafa El Mallahi, Khalid Zenkouar & Hassan Qjidaa

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  1. Abderrahim Mesbah
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  2. Amal Zouhri
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  3. Mostafa El Mallahi
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  4. Khalid Zenkouar
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  5. Hassan Qjidaa
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Correspondence to Mostafa El Mallahi.

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Mesbah, A., Zouhri, A., El Mallahi, M. et al. Robust Reconstruction and Generalized Dual Hahn Moments Invariants Extraction for 3D Images. 3D Res 8, 7 (2017). https://doi.org/10.1007/s13319-016-0113-8

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  • DOI: https://doi.org/10.1007/s13319-016-0113-8

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