Skip to main content
SpringerLink
Log in

Fast computation of 3D Tchebichef moments for higher orders

  • Original Research Paper
  • Published:
Journal of Real-Time Image Processing Aims and scope Submit manuscript

Abstract

This article proposes a new method for the fast and efficient calculation of 3D Tchebichef moments,which are an essential tool for the characterization and analysis of 3D objects. This method integrates the Kronecker tensor product to the computation of 3D Tchebichef moments for higher orders with the advantage of being parallelizable. The experimental results clearly show the benefits and efficacy of the proposed method compared to existing methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Liu, X., Han, G., Wu, J., Shao, Z., Coatrieux, G., Shu, H.: Fractional krawtchouk transform with an application to image watermarking. IEEE Trans. Signal Process. 65(7), 1894–1908 (2017)

    Article  MathSciNet  Google Scholar 

  2. Rivera-López, J., Bello, C.C.: Efficient encryption of image data in video sequences using discrete orthogonal moments. In: Applications of Digital Image Processing XL, vol. 10396, p. 103962Z. International Society for Optics and Photonics, Bellingham (2017)

  3. Yamni, M., Daoui, A., Karmouni, H., Sayyouri, M., Qjidaa, H., Flusser, J., et al.: Fractional Charlier moments for image reconstruction and image watermarking. Signal Process. 171, 107509 (2020)

    Article  Google Scholar 

  4. Ernawan, F., Abu, N.A., Suryana, N.: An optimal tchebichef moment quantization using psychovisual threshold for image compression. Adv. Sci. Lett. 20(1), 70–74 (2014)

    Article  Google Scholar 

  5. Ernawan, F., Kabir, N., Zamli, K.Z.: An efficient image compression technique using tchebichef bit allocation. Optik 148, 106–119 (2017)

    Article  Google Scholar 

  6. Senapati, R.K., Pati, U.C., Mahapatra, K.K.: Reduced memory, low complexity embedded image compression algorithm using hierarchical listless discrete tchebichef transform. IET Image Proc. 8(4), 213–238 (2014)

    Article  Google Scholar 

  7. Pee, C.-Y., Ong, S., Raveendran, P.: Numerically efficient algorithms for anisotropic scale and translation tchebichef moment invariants. Pattern Recogn. Lett. 92, 68–74 (2017)

    Article  Google Scholar 

  8. El Mallahi, M., Zouhri, A., El-Mekkaoui, J., Qjidaa, H.: Three dimensional radial tchebichef moment invariants for volumetric image recognition. Pattern Recogn. Image Anal. 27(4), 810–824 (2017)

    Article  Google Scholar 

  9. Ramalakshmi, K., SrinivasaRaghavan, V.: Soft computing-based edge-enhanced dominant peak and discrete tchebichef extraction for image segmentation and classification using dcml-ic. Soft Comput. 25, 1–12 (2020)

    Google Scholar 

  10. Elshoura, S., Megherbi, D.: Analysis of noise sensitivity of tchebichef and zernike moments with application to image watermarking. J. Vis. Commun. Image Represent. 24(5), 567–578 (2013)

    Article  Google Scholar 

  11. Kumar, A., Paramesran, R., Lim, C.-L., Dass, S.C.: Tchebichef moment based restoration of gaussian blurred images. Appl. Opt. 55(32), 9006–9016 (2016)

    Article  Google Scholar 

  12. Rahman, S.M., Howlader, T., Hatzinakos, D.: On the selection of 2d krawtchouk moments for face recognition. Pattern Recogn. 54, 83–93 (2016)

    Article  Google Scholar 

  13. Tang, L., Qian, J., Li, L., Hu, J., Wu, X.: Multimodal medical image fusion based on discrete t chebichef moments and pulse coupled neural network. Int. J. Imaging Syst. Technol. 27(1), 57–65 (2017)

    Article  Google Scholar 

  14. Benouini, R., Batioua, I., Zenkouar, K., Najah, S., Qjidaa, H.: Efficient 3d object classification by using direct krawtchouk moment invariants. Multimed. Tools Appl. 77(20), 27517–27542 (2018)

    Article  Google Scholar 

  15. Lakhili, Z., El Alami, A., Mesbah, A., Berrahou, A., Qjidaa, H.: Deformable 3d shape classification using 3d racah moments and deep neural networks. Proc. Comput. Sci. 148, 12–20 (2019)

    Article  Google Scholar 

  16. Di Ruberto, C., Putzu, L., Rodriguez, G.: Fast and accurate computation of orthogonal moments for texture analysis. Pattern Recogn. 83, 498–510 (2018)

    Article  Google Scholar 

  17. Batioua, I., Benouini, R., Zenkouar, K., Zahi, A., et al.: 3d image analysis by separable discrete orthogonal moments based on krawtchouk and tchebichef polynomials. Pattern Recogn. 71, 264–277 (2017)

    Article  Google Scholar 

  18. El Mallahi, M., Mesbah, A., El Fadili, H., Zenkouar, K., Qjidaa, H.: Image analysis by discrete orthogonal tchebichef moments for 3d object representation. WSEAS Trans. Comput. 14, 513–525 (2015)

    Google Scholar 

  19. Hosny, K.M., 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 Proc. 16(6), 2027–2041 (2019)

    Article  Google Scholar 

  20. Mesbah, A., Berrahou, A., El Mallahi, M., Qjidaa, H.: Fast and efficient computation of three-dimensional hahn moments. J. Electron. Imaging 25(6), 061621 (2016)

    Article  Google Scholar 

  21. Mesbah, A., ElMallahi, M., Lakhili, Z., Qjidaa, H., Berrahou, A.: Fast and accurate algorithm for 3d local object reconstruction using krawtchouk moments. In: 2016 5th International Conference on Multimedia Computing and Systems (ICMCS), pp. 1–6, IEEE, 2016

  22. Jahid, T., Karmouni, H., Sayyouri, M., Hmimid, A., Qjidaa, H.: Fast algorithm of 3d discrete image orthogonal moments computation based on 3d cuboid. J. Math. Imaging Vis. 61(4), 534–554 (2019)

    Article  MathSciNet  Google Scholar 

  23. Karmouni, H., Jahid, T., Sayyouri, M., El Alami, R., Qjidaa, H.: Fast 3d image reconstruction by cuboids and 3d Charlier’s moments. J. Real-Time Image Process. 17, 1–17 (2019)

  24. Karmouni, H., Yamni, M., El Ogri, O., Daoui, A., Sayyouri, M., Qjidaa, H., Tahiri, A., Maaroufi, M., Alami, B.: Fast computation of 3d discrete invariant moments based on 3d cuboid for 3d image classification. Circuits Syst. Signal Process. 40, 1–31 (2021)

  25. Sayyouri, M., Karmouni, H., Hmimid, A., Azzayani, A., Qjidaa, H.: A fast and accurate computation of 2d and 3d generalized laguerre moments for images analysis. Multimed Tools Appl. 80(5), 1–24 (2020)

  26. Karmouni, H., Yamni, M., Daoui, A., Sayyouri, M., Qjidaa, H., et al.: Fast computation of 3d meixner’s invariant moments using 3d image cuboid representation for 3d image classification. Multimedia Tools and Applications 79(39), 29121–29144 (2020)

  27. Daoui, A., Yamni, M., El Ogri, O., Karmouni, H., Sayyouri, M., Qjidaa, H.: New algorithm for large-sized 2d and 3d image reconstruction using higher-order hahn moments. Circuits Syst. Signal Process. 39(9), 1–26 (2020)

  28. Daoui, A., Yamni, M., Karmouni, H., Sayyouri, M., Qjidaa, H., et al.: Stable computation of higher order charlier moments for signal and image reconstruction. Inf. Sci. 521, 251–276 (2020)

    Article  Google Scholar 

  29. Daoui, A., Sayyouri, M., Qjidaa, H.: Efficient computation of high-order meixner moments for large-size signals and images analysis Multimed. Tools Appl. 80(2), 1–30 (2020)

  30. El Mallahi, M., Mesbah, A., El Fadili, H., Zenkouar, K., Qjidaa, H.: Compact computation of tchebichef moments for 3d object representation. WSEAS Trans. Circuits Syst. 13, 368–380 (2014)

    Google Scholar 

  31. Mukundan, R.: Some computational aspects of discrete orthonormal moments. IEEE Trans. Image Process. 13(8), 1055–1059 (2004)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  34. Abdul-Hadi, A.M., Abdulhussain, S.H., Mahmmod, B.M.: On the computational aspects of charlier polynomials. Cogent Eng. 7(1), 1763553 (2020)

    Article  Google Scholar 

  35. Mahmmod, B.M., Abdul-Hadi, A.M., Abdulhussain, S.H., Hussien, A.: On computational aspects of krawtchouk polynomials for high orders. J. Imaging 6(8), 81 (2020)

    Article  Google Scholar 

  36. 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 

  37. Graham, A.: Kronecker Products and Matrix Calculus with Applications. Courier Dover Publications, New York (2018)

    MATH  Google Scholar 

  38. Atteya, M.J.: Kronecker product with applications. MJ J. Algebra Appl. 1, 1–4 (2016)

    Google Scholar 

  39. Benesty, J., Cohen, I., Chen, J.: Array Processing. Springer, New York (2019)

    Book  Google Scholar 

  40. Higham, N.J.: Exploiting fast matrix multiplication within the level 3 blas. ACM Trans. Math. Softw. (TOMS) 16(4), 352–368 (1990)

    Article  MathSciNet  Google Scholar 

  41. Nugteren, C.: Clblast: a tuned openCL blas library. In: Proceedings of the International Workshop on OpenCL, pp. 1–10 (2018)

  42. MCGill, S.: Mcgill 3d shape benchmark. http://www.cim.mcgill.ca/shape (2005)

  43. Song, H.S., Cho, N.I.: Stanford 3d scanning repository http://graphics.stanford.edu/data/3dscanrep. IEICE Trans. Inf. Syst. 91(5), 1512–1521 (2008)

  44. Nikolaos Ploskas, N.S.: GPU Programming in MATLAB, 1st edn. Morgan Kaufmann, Burlington (2016)

    MATH  Google Scholar 

Download references

Acknowledgements

We extend our gratitude to the reviewers for their valuable suggestions and Beatriz Flores Vargas for the comments on grammar and writing. Saul Rivera-Lopez thanks to Consejo Nacional de Ciencia y Tecnología (CONACyT) for the Ph.D. scholarship #714746.

Author information

Authors and Affiliations

  1. Universidad Politécnica de Tulancingo, Tulancingo, Hidalgo, Mexico

    J. Saúl Rivera-Lopez, César Camacho-Bello, Horlando Vargas-Vargas & Alicia Escamilla-Noriega

Authors
  1. J. Saúl Rivera-Lopez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. César Camacho-Bello
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Horlando Vargas-Vargas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alicia Escamilla-Noriega
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Saúl Rivera-Lopez.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rivera-Lopez, J.S., Camacho-Bello, C., Vargas-Vargas, H. et al. Fast computation of 3D Tchebichef moments for higher orders. J Real-Time Image Proc 19, 15–27 (2022). https://doi.org/10.1007/s11554-021-01152-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11554-021-01152-5

Keywords

Search

Navigation