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Fast 3D image reconstruction by cuboids and 3D Charlier’s moments

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Abstract

In this article, we propose a novel approach to accelerate the processing of 3D images by the discrete orthogonal moments of Charlier. The proposed approach is based on two fundamental notions: The first is the acceleration of the computing time of Charlier discrete orthogonal polynomials and moments in the case of the 3D image using digital filters. The second is the description of the 3D image by a set of cuboids of fixed size instead of individual voxels by decomposing the image by cuboids of small sizes to ensure numerical stability. By applying this method, the 3D Charlier moments are calculated from the cuboids instead of the whole image, as the image processing will be locally in each cuboid. This method allows us to speed up the computation time of the moments and to avoid the problem of propagation of digital errors encountered as well when using of digital filters for 3D images of large sizes. The simulation results show the effectiveness of the proposed method in terms of the computation time of the 3D moments of Charlier and in terms of quality of 3D image.

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References

  1. Ghosal, S., Mehrotra, R.: Orthogonal moment operators for subpixel edge detection. Pattern Recognit., 26(2):295-306, 1993

    Article  Google Scholar 

  2. Hmimid, M., Sayyouri, Qjidaa, H.: Image classification using separable invariant moments of Charlier-Meixner and support vector machine. Multimed. Tools Appl., 2018, p. 1–25

  3. Hmimid, M., Sayyouri, Qjidaa, H.: Image classification using a new set of separable two-dimensional discrete orthogonal invariant moments. J. Electron. Imaging 23(1), 013026 (2014)

    Article  Google Scholar 

  4. Tuceryan, M.: Moment-based texture segmentation. Pattern Recognit. Lett., 15(7):659-668, 1994

    Article  Google Scholar 

  5. Bharathi, V.S., Ganesan, L.: Orthogonal moments based texture analysis of CT liver images. Pattern Recognit. Lett., 29(13):1868-1872, 2008

    Article  Google Scholar 

  6. Marcos, J.V., Cristobal, G.: Texture classification using discrete Tchebichef moments. J. Opt. Soc. Am. A, 30(8):1580-1591, 2013

    Article  Google Scholar 

  7. Hickman, M.S.: Geometric moments and their invariants. J. Math. Imaging Vision, 44(3):223-235, 2012

    Article  MathSciNet  Google Scholar 

  8. Honarvar, R., Paramesran, Lim, C.L.: Image reconstruction from a complete set of geometric and complex moments. Signal Process., 98:224_232, 2014

  9. Hmimid, M., Sayyouri, H., Qjidaa: Fast computation of separable two-dimensional discrete invariant moments for image classification. Pattern Recogn. 48, 509–521 (2015)

    Article  Google Scholar 

  10. Martin, J.A., Santos, H.M., and J. de Lope. Orthogonal variant moments features in image analysis. Inf. Sci., 180(6): 846-860, 2010

    Article  MathSciNet  Google Scholar 

  11. Wu, H., Coatrieux, J.L., Shu, H.: New algorithm for constructing and computing scale invariants of 3D Tchebichef moments. Math. Probl. Eng. 2013: 8, (Article ID 813606) (2013)

    MathSciNet  Google Scholar 

  12. Hosny, K.M.: Fast and low-complexity method for exact computation of 3D Legendre moments. Pattern Recognit. Lett., 32(9):1305-1314, 2011

    Article  Google Scholar 

  13. Hu, M.K.: Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory IT -8: 179–187 (1962)

    MATH  Google Scholar 

  14. Hosny, M.K.: Exact and fast computation of geometric moments for gray level images. Appl. Math. Comput. 189, 1214–1222 (2007)

    MathSciNet  MATH  Google Scholar 

  15. Hosny, M.K.: Image representation using accurate orthogonal Gegenbauer moments. Pattern Recogn. Lett. 32, 79s5–7804 (2011)

    Article  Google Scholar 

  16. Teague, M.R.: Image analysis via the general theory of moments. J. Opt. Soc. Am. 70(8), 920–930 (1980)

    Article  MathSciNet  Google Scholar 

  17. Mukundan, R., Ong, S.H., Lee, P.A.: Image analysis by Tchebichef moments. IEEE Trans. Image Process. 10(9), 1357–1364 (2000)

    Article  MathSciNet  Google Scholar 

  18. Shu, H.Z., Zhang, H., Chen, B.J., Haigron, P., Luo, L.M.: Fast computation of Tchebichef moments for binary and gray-scale images. IEEE Trans. Image Process. 19(12), 3171–3180 (2010)

    Article  MathSciNet  Google Scholar 

  19. Yap, P.T., Paramesran, R., Ong, S.H.: Image analysis by Krawtchouk moments. IEEE Trans. Image Process. 12(11), 1367–1377 (2003)

    Article  MathSciNet  Google Scholar 

  20. Sayyouri, M., Hmimid, A., Qjidaa, H.: Improving the performance of image classification by Hahn moment invariants. J. Opt. Soc. Am. A 30, 2381–2394 (2013)

    Article  Google Scholar 

  21. Sayyouri, M., Hmimid, A., Qjidaa, H.: A fast computation of Hahn moments for binary and gray-scale images. In: 2012 IEEE International Conference on Complex Systems (ICCS), pp. 1–6 (2012)

  22. Zhu, H.Q., Shu, H.Z., Liang, J., Luo, L.M., Coatrieux, J.L.: Image analysis by discrete orthogonal Racah moments. Signal Process 87(4), 687–708 (2007)

    Article  Google Scholar 

  23. Zhu, H., Liu, M., Shu, H., Zhang, H., Luo, L.: General form for obtaining discrete orthogonal moments. IET Image Process. 4(5), 335–352 (2010)

    Article  MathSciNet  Google Scholar 

  24. Sayyouri, M., Hmimid, A., Qjidaa, H.: Image analysis using separable discrete moments of Charlier–Hahn. Multimed. Tools Appl. 75(1), 547–571 (2014)

    Article  Google Scholar 

  25. Sayyouri, M., Hmimid, A., Qjidaa, H.: A fast computation of novel set of Meixner invariant moments for image analysis. Circ. Syst. Signal Process. 2014, 1–26 (2014). https://doi.org/10.1007/s00034-014-9881-7

    Article  MATH  Google Scholar 

  26. Spiliotis, I.M., Mertzios, B.G.: Real-time computation of two-dimensional moments on binary images using image block representation. IEEE Trans. Image Process., 7(11):1609-1615, 1998

    Article  Google Scholar 

  27. Papakostas, G.A., Karakasis, E.G., Koulouriotis, D.E.: Efficient and accurate computation of geometric moments on gray-scale images. Pattern Recognit., 41(6):1895-1904, 2008

    Article  Google Scholar 

  28. Papakostas, G.A., Koulouriotis, D.E., Karakasis, E.G.: A unified methodology for the efficient computation of discrete orthogonal image moments. Inf. Sci., 179(20):3619_3633, 2009

  29. Papakostas, G.A., Karakasis, E.G., Koulouriotis, D.E.: Accurate and speedy computation of image Legendre moments for computer vision applications. Image Vision Comput., 28(3):414-423, 2010

    Article  Google Scholar 

  30. Hosny, M.K., Hafez, M.: An algorithm for fast computation of 3D zernike moments for volumetric images, Math. Probl. Eng., Volume 2012: 17, (Article ID 353406)

  31. Hosny, M.K., Salah, A., Saleh, H.I., Sayed, M.: Fast computation of 2D and 3D legendre moments using multi-core CPUs and GPU parallel architectures. J. Real Time Image Process (2017). https://doi.org/10.1007/s11554-017-0708-1

    Article  Google Scholar 

  32. Kumar, M.F., Hassan, P., Raveendran: Learning based restoration of Gaussian blurred images using weighted geometric moments and cascaded digital filters. Appl. Soft. Comput. 63, 124–138 (2018)

    Article  Google Scholar 

  33. Karmouni, H., Hmimid, A., Jahid, T., Sayyouri, M., Qjidaa, H., Rezzouk, A., Fast and stable computation of the Charlier moments and their inverses using digital filters and image block representation. Circuits Syst. Signal Process.: 1–19. (2018)

  34. Tarik Jahid, A., Hmimid, H., Karmouni, M., Sayyouri, H., Qjidaa, A., Rezzouk: Image analysis by Meixner moments and a digital filter. Multimed. Tools Appl. 77(15), 19811–19831 (2018)

    Article  Google Scholar 

  35. Nikiforov, A.F., Suslov, S.K., Uvarov, B.: Classical orthogonal polynomials of a discrete variable. Springer, New York (1991)

    Book  Google Scholar 

  36. http://www.cim.mcgill.ca/~shape/benchMark/airplane.html. (2017). Accessed 31 July 2017

  37. Benouini, R., Batioua, I., Zenkouar, K., Najah, S.: & H. Qjidaa. Efficient 3D object classification by using direct Krawtchouk moment invariants. Multimed. Tools Appl., 1–26, 2018

  38. Yap., P.T., Paramesran, R.: & S. H. Ong. Image analysis using Hahn moments. IEEE Trans. Pattern Anal. Mach. Intell., 29(11), 2007

  39. Hosny, M.K.: Fast computation of accurate zernike moments. J. Real Time Image Proc. 3(1–2), 97–107 (2008)

    Article  Google Scholar 

  40. Camacho-Bello, J.S., Rivera-Lopez: Some computational aspects of Tchebichef moments for higher orders. Pattern Recogn. Lett. 112, 332–339 (2018)

    Article  Google Scholar 

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Authors and Affiliations

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

    Hicham Karmouni, Tarik Jahid, Rachid El Alami & Hassan Qjidaa

  2. Laboratory of Sciences of the Engineer for the Energy, National school of applied sciences, Chouaib Doukkali University, d’El Jadida, EL Jadida Plateau, BP 1166, 24004, El Jadida, Morocco

    Mhamed Sayyouri

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  1. Hicham Karmouni
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  2. Tarik Jahid
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  3. Mhamed Sayyouri
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  4. Rachid El Alami
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  5. Hassan Qjidaa
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Correspondence to Hicham Karmouni.

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Karmouni, H., Jahid, T., Sayyouri, M. et al. Fast 3D image reconstruction by cuboids and 3D Charlier’s moments. J Real-Time Image Proc 17, 949–965 (2020). https://doi.org/10.1007/s11554-018-0846-0

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