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Fast Computation of 3D Discrete Invariant Moments Based on 3D Cuboid for 3D Image Classification

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Abstract

The use of 3D discrete orthogonal invariant moments as descriptors of images constitutes one of the hot topics in the field of 3D image analysis, especially in the recognition and classification of deformed objects, due to their high numerical precision and low computing complexity. The TSR (translation, scale and rotation) invariant functions of discrete orthogonal moments can be obtained by expressing them as a linear combination of the corresponding invariant of geometric moments. This classical method is very expensive in time due to the long time allocated to compute the polynomial coefficients when complex or large 3D images are used. This main drawback eliminates the use of these moments in the recognition and classification fields of 3D objects. In this article, we propose a fast and efficient method for calculating 3D discrete orthogonal invariant moments of Hahn, Tchebichef, Krawtchouk, Meixner and Charlier of 3D image. This proposed method is based on the extraction of the 3D discrete orthogonal invariant moments from the 3D geometric invariant moments of the entire 3D image, using the 3D image cuboid representation (ICR) strategy, where each cuboid is treated independently. The proposed method has the advantage of accelerating the process of extracting the 3D discrete invariant moments compared with the classical method. The performance of the proposed method is evaluated in terms of the calculation time and classification accuracy using a set of 3D images. Instead of some examples of using the discrete orthogonal invariant moments of Hahn, Tchebichef, Krawtchouk, Meixner and Charlier as pattern features for pattern classification are also provided.

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Availability of Data and Materials

The datasets generated in our experiments are available from McGill 3D Shape Benchmark images database, URL link: http://www.cim.mcgill.ca/~shape/benchMark/airplane.html. (2017). Accessed 12 February 2020. The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions.

Funding

No funding has been granted for this work.

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Authors and Affiliations

  1. Faculty of Science Dhar El Mahrez, Laboratory of Electronic Signals and Systems of Information LESSI, CED-ST, STIC, University Sidi Mohamed Ben Abdellah, Fez, Morocco

    Hicham Karmouni, Mohamed Yamni, Omar El Ogri & Hassan Qjidaa

  2. Engineering, Systems and Applications Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, BP 72, My Abdallah Avenue Km. 5 Imouzzer Road, Fez, Morocco

    Achraf Daoui & Mhamed Sayyouri

  3. Laboratory of Computer Science and Interdisciplinary Physics LIPI, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Ahmed Tahiri

  4. Faculty of Medicine and Pharmacy, Department of Biophysics and Clinical MRI Methods, Sidi Mohamed Ben Abdellah University, BP. 893, Km 2.200, Sidi Hrazem Road, 30000, Fez, Morocco

    Badreeddine Alami

  5. Faculty of Medicine and Pharmacy, Clinical Neuroscience Laboratory, Sidi Mohamed Ben Abdellah University, Fez, Morocco

    Mustapha Maaroufi & Badreeddine Alami

  6. Department of Radiology and Clinical Imaging, University Hospital of Fez, Fez, Morocco

    Mustapha Maaroufi & Badreeddine Alami

Authors
  1. Hicham Karmouni
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  2. Mohamed Yamni
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  3. Omar El Ogri
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  4. Achraf Daoui
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  6. Hassan Qjidaa
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  7. Ahmed Tahiri
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  8. Mustapha Maaroufi
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  9. Badreeddine Alami
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Contributions

Category 1 H. Karmouni, M. Yamni and O. El Ogri contributed to the conception and design of study. H. Karmouni, M. Yamni, O. El ogri, Mhamed Sayyouri and Hassan Qjidaa contributed to the acquisition of data. H. Karmouni, M. Sayyouri, H. Qjidaa, A. Tahiri, M. Maaroufi and B. Alami contributed to the analysis and/or interpretation of data. Category 2 H. Karmouni, M. Yamni and A. Daoui contributed to the drafling the manuscript. H. Karmouni, M. Sayyouri, H. Qjidaa, A. Tahiri and M. Maaroufi contributed to revising the manuscript critically for important intellectual content. Category 3 H. Karmouni, M. Yamni, O. El Ogri, A. Daoui, M. Sayyouri, H. Qjidaa, A. Tahiri, M. Maaroufi and B. Alami contributed to the approval of version of the manuscript to be published.

Corresponding author

Correspondence to Hicham Karmouni.

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Karmouni, H., Yamni, M., El Ogri, O. et al. Fast Computation of 3D Discrete Invariant Moments Based on 3D Cuboid for 3D Image Classification. Circuits Syst Signal Process 40, 3782–3812 (2021). https://doi.org/10.1007/s00034-020-01646-w

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