Skip to main content
SpringerLink
Log in

2D and 3D image localization, compression and reconstruction using new hybrid moments

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

A Correction to this article was published on 02 March 2022

This article has been updated

Abstract

In this article, we will present a new set of hybrid polynomials and their corresponding moments, with a view to using them for the localization, compression and reconstruction of 2D and 3D images. These polynomials are formed from the Hahn and Krawtchouk polynomials. The process of calculating these is successfully stabilized using the modified recurrence relations with respect to the n order, the variable x and the symmetry property. The hybrid polynomial generation process is carried out in two forms: the first form contains the separable discrete orthogonal polynomials of Krawtchouk–Hahn (DKHP) and Hahn–Krawtchouk (DHKP). The latter are generated as the product of the discrete orthogonal Hahn and Krawtchouk polynomials, while the second form is the square equivalent of the first form, it consists of discrete squared Krawtchouk–Hahn polynomials (SKHP) and discrete polynomials of Hahn–Krawtchouk squared (SHKP). The experimental results clearly show the efficiency of hybrid moments based on hybrid polynomials in terms of localization property and computation time of 2D and 3D images compared to other types of moments; on the other hand, encouraging results have also been shown in terms of reconstruction quality and compression despite the superiority of classical polynomials.

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
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig.13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

Change history

References

  • Abdulhussain, S. H., Al-Haddad, S. A. R., Saripan, M. I., Mahmmod, B. M., & Hussien, A. (2020). Fast temporal video segmentation based on Krawtchouk-Tchebichef moments. IEEE Access, 8, 72347–72359.

    Article  Google Scholar 

  • Abdulhussain, S. H., Mahmmod, B. M., Saripan, M. I., Al-Haddad, S. A. R., & Jassim, W. A. (2019). A new hybrid form of Krawtchouk and Tchebichef polynomials: Design and application. Journal of Mathematical Imaging and Vision, 61(4), 555–570.

    Article  MathSciNet  Google Scholar 

  • Abdulhussain, S. H., Ramli, A. R., Al-Haddad, S. A. R., Mahmmod, B. M., & Jassim, W. A. (2017). On computational aspects of Tchebichef polynomials for higher polynomial order. IEEE Access, 5(1), 2470–2478.

    Article  Google Scholar 

  • Abdulhussain, S. H., Ramli, A. R., Al-Haddad, S. A. R., Mahmmod, B. M., & Jassim, W. A. (2018). Fast recursive computation of Krawtchouk polynomials. Journal of Mathematical Imaging and Vision, 60(3), 285–303.

    Article  MathSciNet  Google Scholar 

  • Batioua, I., Benouini, R., Zenkouar, K., et al. (2017). 3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials. Pattern Recognition, 71, 264–277.

    Article  Google Scholar 

  • Camacho-Bello, C., Padilla-Vivanco, A., Toxqui-Quitl, C., & Báez-Rojas, J.J. (2016). Reconstruction of color biomedical images by means of quatern-ion generic Jacobi–Fourier moments in the framework of polar pixels. Journal of Medicine Imaging, 3(1), 014004.

  • Camacho-Bello, C., & Rivera-Lopez, J. S. (2018). Some computational aspects of Tchebichef moments for higher orders. Pattern Recognition Letters, 112, 332–339.

    Article  Google Scholar 

  • Chen, B., Qi, X., Sun, X., & Shi, Y. Q. (2017). Quaternion pseudo-Zernike moments combining both of RGB information and depth information for color image splicing detection. Journal of Visual Communication and Image Representation, 49, 283–290.

    Article  Google Scholar 

  • Deng, A. W., & Gwo, C. Y. (2018). Fast and stable algorithms for high-order Pseudo Zernike moments and image reconstruction. Applied Mathematics and Computation, 334, 239–253.

    Article  MathSciNet  Google Scholar 

  • Deng, A. W., Wei, C. H., & Gwo, C. Y. (2016). Stable, fast computation of high-order Zernike moments using a recursive method. Pattern Recognition, 56, 16–25.

    Article  Google Scholar 

  • Ernawan, F., Kabir, N., & Zamli, K. Z. (2017). An efficient image compression technique using Tchebichef bit allocation. Optik, 148, 106–119. https://doi.org/10.1016/j.ijleo.2017.08.007

    Article  Google Scholar 

  • Flusser, J., Suk, T., Zitova, B. (2016). 2D and 3D image analysis by moments. Wiley.

  • Gishkori, S., & Mulgrew, B. (2018). Pseudo-zernike moments based sparse representations for SAR image classification. IEEE Transactions on Aerospace and Electronic Systems, 55(2), 1037–1044.

    Article  Google Scholar 

  • Hmimid, A., Sayyouri, M., & Qjidaa, H. (2018). Image classification using separable invariant moments of Charlier-Meixner and support vector machine. Multimedia Tools and Applications, pp. 1–25.

  • Hmimid, A., Sayyouri, M., & Qjidaa, H. (2015). Fast computation of separable two dimensional discrete invariant moments for image classification. Pattern Recognition, 48, 509–521. https://doi.org/10.1016/j.patcog.2014.08.020

    Article  MATH  Google Scholar 

  • Hmimid, A., Sayyouri, M., & Qjidaa, H. (2018a). Image classification using separable invariant moments of Charlier-Meixner and support vector machine. Multimedia Tools and Application, 77, 23607–32363.

    Article  Google Scholar 

  • Honarvar, B., Paramesran, R., & Lim, C. L. (2014). Image reconstruction from a complete set of geometric and complex moments. Signal Processing, 98, 224–232.

    Article  Google Scholar 

  • Hosny, K. M., Darwish, M. M., & Eltoukhy, M. M. (2020). New fractional-order shifted Gegenbauer moments for image analysis and recognition. Journal of Advanced Research.

  • Hosny, K. M., & Darwish, M. M. (2018). New set of quaternion moments for color images representation and recognition. Journal of Mathematical Imaging and Vision, 60(5), 717–736.

    Article  MathSciNet  Google Scholar 

  • Jahid, T., Hmimid, A., Karmouni, H., Sayyouri, M., Qjidaa, H., & Rezzouk, A. (2017). Image analysis by Meixner moments and a digital filter. Multimedia Tools and Applications, pp. 1–21.

  • Jahid, T., Karmouni, H., Sayyouri, M. et al. (2018). Fast algorithm of 3D discrete image orthogonal moments computation based on 3D cuboid. Journal of Mathematical Imaging and Vision, pp. 1–21.

  • Jassim, W. A., Raveendran, P., & Mukundan, R. (2012). New orthogonal polynomials for speech signal and image processing. IET Signal Processing, 6(8), 713–723.

    Article  MathSciNet  Google Scholar 

  • Karmouni, H., Jahid, T., El affar, I., Sayyouri, M., Hmimid, A., Qjidaa, H., & Rezzouk, A. (2017). Image analysis using separable Krawtchouk–Tchebichef’s moments. In International conference on advanced technologies for signal and image processing (Atsip'2017), May 22–24 2017, Fez - Morocco.

  • Karmouni, H., Jahid, T., Sayyouri, M., Hmimid, A., El affar, A., & Qjidaa, H. (2018). Image analysis by hahn moments and a digital filter. In Ezziyyani M. (Eds.), Advanced intelligent systems for sustainable development (AI2SD’2018). AI2SD 2018. Advances in intelligent systems and computing, vol 915. Springer, Cham.

  • Karmouni, H., Jahid, T., Sayyouri, M., El Alami, R., & Qjidaa, H. (2019a). Fast 3D image reconstruction by cuboids and 3D Charlier’s moments. Journal of Real-Time Image Processing, p. 1–17.

  • Karmouni, H., Jahid, T., Hmimid, A., Sayyouri, M., & Qjidaa, H. (2019). Fast computation of inverse Meixner moments transform using Clenshaw's formula. Multimedia Tools and Applications, pp. 1–21. https://doi.org/10.1007/s11042-019-07961-y

  • Karmouni, H., Jahid, T., Sayyouri, M. et al. (2019). Fast reconstruction of 3D images using Charlier discrete orthogonal moments. Circuits, Systems, and Signal Processing, pp. 1–28.

  • Karmouni, H., Yamni, M., Elogri, O., Daoui, A., Sayyouri, M., Qjidaa, H. (2020). Fast computation of 3D Meixner’s invariant moments using 3D image cuboid representation for 3D image classification.

  • Lang, W. S., Abu, N. A., Rahmalan, H. (2009). Fast 4x4 Tchebichef moment image compression. In 2009 International Conference on Soft Computing Pattern Recognition, IEEE, pp. 295–300.

  • Mahmmod, B. M., Abdulhussain, S. H., Al-Haddad, S. A. R., & Jassim, W. A. (2017). Signal compression and enhancement using a new orthogonal-polynomial-based discrete transform. IET Signal Processing, 12(1), 129–142.

    Article  Google Scholar 

  • Meena, K. B., & Tyagi, V. (2019). A copy-move image forgery detection technique based on Gaussian-Hermite moments. Multimedia Tools and Applications, 78(23), 33505–33526.

    Article  Google Scholar 

  • Mejjaoli, H., & Trimèche, K. (2020). k-Hankel two-wavelet theory and localization operators. Integral Transforms and Special Functions, pp. 1–25.

  • Noori Hashimi, A., & Noaman Kadhim, B. (2020). Face recognition based on fusion of SVD and Legendre moment. Journal of Physics Conference Series, p. 012120.

  • Rahman, S. M., Howlader, T., & Hatzinakos, D. (2016). On the selection of 2D Krawtchouk moments for face recognition. Pattern Recognition, 54, 83–93.

    Article  Google Scholar 

  • Sayyouri, M., Hmimid, A., & Qjidaa, H. (2015). A fast computation of novel set of meixner invariant moments for image analysis. Circuits Systems and Signal Processing, 34, 875–900. https://doi.org/10.1007/s00034-014-9881-7

    Article  MATH  Google Scholar 

  • Sayyouri, M., Hmimid, A., & Qjidaa, H. (2016). Image analysis using separable discrete moments of Charlier-Hahn. Multimedia Tools and Applications, 75(1), 547–571.

    Article  Google Scholar 

  • Siddiqi, K., Zhang, J., Macrini, D., Shokoufandeh, A., Bouix, S., & Dickinson, S. (2008). Retrieving articulated 3-D models using medial surfaces. Machine Vision and Applications, 19, 261–275.

    Article  Google Scholar 

  • Spiliotis, I. M., Karampasis, N. D., & Boutalis, Y. S. (2020). Fast computation of Hahn moments on gray images using block representation. Journal of Electronic Imaging, 29(1), 013020.

  • Spiliotis, I. M., Bekakos, M. P., & Boutalis, Y. S. (2020). Parallel implementation of the image block representation using OpenMP. Journal of Parallel and Distributed Computing, 137, 134–147.

    Article  Google Scholar 

  • Suk, T., Flusser, J., & Boldyš, J. (2015). 3D rotation invariants by complex moments. Pattern Recognition, 48(11), 3516–3526.

    Article  Google Scholar 

  • Upneja, R., & Singh, C. (2015). Fast computation of Jacobi-Fourier moments for invariant image recognition. Pattern Recognition, 48(5), 1836–1843.

    Article  Google Scholar 

  • Wang, C., Wang, X., Xia, Z., Ma, B., & Shi, Y. Q. (2019). Image description with polar harmonic Fourier moments. IEEE Transactions on Circuits and Systems for Video Technology.

  • Wang, C., Wang, X., Xia, Z., & Zhang, C. (2019a). Ternary radial harmonic Fourier moments based robust stereo image zero-watermarking algorithm. Information Sciences, 470, 109–120.

    Article  Google Scholar 

  • Wang, M., & Shang, X. (2020). A fast image fusion with discrete cosine transform. IEEE Signal Processing Letters, 27, 990–994.

    Article  Google Scholar 

  • Wee, C. Y., & Paramesran, R. (2007). Derivation of blur-invariant features using orthogonal Legendre moments. IET Computer Vision, 1(2), 66–77.

    Article  MathSciNet  Google Scholar 

  • Wu, G., & Xu, L. (2019). Shape description and recognition by implicit Chebyshev moments. Pattern Recognition Letters, 128, 137–145.

    Article  Google Scholar 

  • Wu, H., & Yan, S. (2016). Computing invariants of Tchebichef moments for shape-based image retrieval. Neurocomputing, 215, 110–117.

    Article  Google Scholar 

  • Xia, Z., Wang, X., Li, X., Wang, C., Unar, S., Wang, M., & Zhao, T. (2019). Efficient copyright protection for three CT images based on quaternion polar harmonic Fourier moments. Signal Processing, 164, 368–379.

    Article  Google Scholar 

  • Xiao, B., Cui, J.-T., Qin, H.-X., Li, W.-S., & Wang, G.-Y. (2015). Moments and moment invariants in the Radon space, Pattern Recognition, 48(9), 2772–2784.

  • Yamni, M., Daoui, A., Karmouni, H., Sayyouri, M., Qjidaa, H., & Flusser, J. (2020). Fractional Charlier moments for image reconstruction and image watermarking. Signal Processing, 171, 107509.

  • Yang, T., Ma, J., Miao, Y., Liu, X., Wang, X., Xiao, B., & Meng, Q. (2020). Privacy-preserving Krawtchouk moment feature extraction over encrypted image data. Information Sciences.

  • Yang, B., Kostková, J., Flusser, J., & Suk, T. (2017). Scale invariants from Gaussian-Hermite moments. Signal Processing, 132, 77–84.

    Article  Google Scholar 

  • Yang, B., Suk, T., Flusser, J., Shi, Z., & Chen, X. (2018). Rotation invariants from Gaussian-Hermite moments of color images. Signal Processing, 143, 282–291.

    Article  Google Scholar 

  • Yang, T., Ma, J., Wang, Q., Miao, Y., Wang, X., & Meng, Q. (2018). Image feature extraction in encrypted domain with privacy-preserving Hahn moments. IEEE Access, 6, 47521–47534.

    Article  Google Scholar 

  • Zhang, H., Shu, H., Han, G.-N., Coatrieux, G., Luo, L., & Coatrieux, J. L. (2010). Blurred image recognition by Legendre moment invariants. IEEE Transactions on Image Processing, 19(3), 596–611.

    Article  MathSciNet  Google Scholar 

  • Zhao, Z., Kuang, X., Zhu, Y., Liang, Y., & Xuan, Y. (2020). Combined kernel for fast GPU computation of Zernike moments. Journal of Real-Time Image Processing.

  • Zhi, R., Cao, L., & Cao, G. (2018). Translation and scale invariants of Krawtchouk moments. Information Processing Letters, 130, 30–35.

    Article  MathSciNet  Google Scholar 

  • Zhou, B., Duan, X. M., Wei, W., Ye, D. J., Woźniak, M., & Damaševičius, R. (2019). An adaptive local descriptor embedding zernike moments for image matching. IEEE Access, 7, 183971–183984.

    Article  Google Scholar 

  • Zhu, H., Shu, H., Liang, J., Luo, L., Coatrieux, J.-L. (2007). Image analysis by discrete orthogonal Racah moments. Signal Processing, 87, 687–708.

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

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors of this article would like to thank all the contributors to this work and all the reviewers who have examined this paper.

Author information

Authors and Affiliations

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

    Mohamed Amine Tahiri, Hicham Karmouni & Hassan Qjidaa

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

    Mhamed Sayyouri

Authors
  1. Mohamed Amine Tahiri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hicham Karmouni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mhamed Sayyouri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hassan Qjidaa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hicham Karmouni.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

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

The original online version of this article was revised: The author Mhamed Sayyouri affiliation has been corrected.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tahiri, M.A., Karmouni, H., Sayyouri, M. et al. 2D and 3D image localization, compression and reconstruction using new hybrid moments. Multidim Syst Sign Process 33, 769–806 (2022). https://doi.org/10.1007/s11045-021-00810-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-021-00810-y

Keywords

Search

Navigation