Advertisement

A novel unified method for the fast computation of discrete image moments on grayscale images

  • Xia HuaEmail author
  • Hanyu Hong
  • Jianguo Liu
  • Yu Shi
Original Research Paper
  • 33 Downloads

Abstract

We proposed a new method to compute the discrete image moments in this paper. By simple mathematical deduction, the discrete image moments can be transformed into first-order moments. Therefore, the fast algorithm for first-order moments’ calculation can be used to compute discrete image moments. We also design an efficient computation structure based on systolic array to implement this approach. Since our method does not use the moment kernel polynomials’ properties in the calculation process, the proposed method can be used to compute any discrete image moments in the same way. The presented algorithm has several advantages such as regular and simple computation structure, without multiplication, independent of the image’s intensity distribution, applicable to any discrete moment family. Various experiments demonstrate the effectiveness of the proposed algorithm in comparison with some state-of-the-art methods.

Keywords

Feature extraction Discrete image moments Moment calculation Fast algorithms 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 61433007, 61801337, 61671337, 61701353) and Hubei Education Department Science And Technology Research Project (No. Q20171510).

References

  1. 1.
    Hu, M.K.: Visual pattern recognition by moment invariants. IRE Trans. Inform. Theory. 8(2), 179–187 (1962)CrossRefzbMATHGoogle Scholar
  2. 2.
    Shu, H.Z., Zhou, J., Han, G.N., Luo, L.M., Coatrieux, J.L.: Image reconstruction from limited range projections using orthogonal moments. Pattern Recognit. 40(2), 670–680 (2007)CrossRefzbMATHGoogle Scholar
  3. 3.
    Dai, X.B., Shu, H.Z., Luo, L.M., Han, G.N., Coatrieux, J.L.: Reconstruction of tomographic images from limited range projections using discrete Radon transform and Tchebichef moments. Pattern Recognit. 43(3), 1152–1164 (2010)CrossRefzbMATHGoogle Scholar
  4. 4.
    Khalid, M.H., George A.P.: In: The proceedings of the IEEE 18th international conference of digital signal processing. Accurate reconstruction of noisy medical images using orthogonal moments. July 1–3, 2013, GreeceGoogle Scholar
  5. 5.
    Hosny, Khalid M., Darwish, Mohamed M.: Invariant image watermarking using accurate polar harmonic transforms. Comput. Electr. Eng. 62, 429–447 (2017)CrossRefGoogle Scholar
  6. 6.
    Hosny, Khalid M.: A new set of Gegenbauer moment invariants for pattern recognition application. Arab. J. Sci. Eng. 39, 7097–7107 (2014)CrossRefzbMATHGoogle Scholar
  7. 7.
    Flusser, J., Suk, T.: Pattern recognition by affine moment invariants. Pattern Recognit. 26(1), 167–174 (1993)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ke, L., Qian, W., Jian, X., Weiguo, P.: 3D model retrieval and classification by semi-supervised learning with content-based similarity. Inf. Sci. 281, 703–713 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Zhang, H., Shu, H., Han, G., Coatrieux, G., Luo, L., Coatrieux, J.: Blurred image recognition by Legendre moment invariants. IEEE Trans. Image Process. 19(3), 596–611 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Teague, M.R.: Image analysis via the general theory of moments. J. Opt. Soc. Am. 70(8), 920–930 (1980)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Xin, Y., Pawlak, M., Liao, S.: Accurate computation of Zernike moments in polar coordinates. IEEE Trans. Image Process. 16(2), 581–587 (2007)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lin, H., Si, J.: Orthogonal rotation-invariant moments for digital image processing. IEEE Trans. Image Process. 17(3), 272–282 (2008)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Yap, P.T., Paramesran, R., Ong, S.H.: Image analysis by Krawtchouk moments. IEEE Trans. Image Process. 12(11), 1367–1377 (2003)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Yap, P.T., Paramesran, R., Ong, S.H.: Image analysis using Hahn moments. IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 2057–2062 (2007)CrossRefGoogle Scholar
  15. 15.
    Zhu, H., Shu, H., Liang, J., Luo, L., Coatrieux, J.L.: Image analysis by discrete orthogonal Racah moments. Signal Process. 87, 687–708 (2007)CrossRefzbMATHGoogle Scholar
  16. 16.
    Zhu, H., Shu, H., Zhou, J., Luo, L., Coatrieux, J.L.: Image analysis by discrete orthogonal dual Hahn moments. Pattern Recognit. Lett. 28(13), 1688–1704 (2007)CrossRefGoogle Scholar
  17. 17.
    Zhu, H., Shu, H., Xia, T., Luo, L., Coatrieux, J.L.: Translation and scale invariants of Tchebichef moments. Pattern Recognit. 40(9), 2530–2542 (2007)CrossRefzbMATHGoogle Scholar
  18. 18.
    Fu, B., Zhoua, J., Lia, Y., Zhang, G., Wang, C.: Image analysis by modified Legendre moments. Pattern Recognit. 40(2), 691–704 (2007)CrossRefGoogle Scholar
  19. 19.
    Lim, C., Honarvar, B., Thung, K.H., Paramesran, R.: Fast computation of exact Zernike moments using cascaded digital filters. Inf. Sci. 181(17), 3638–3651 (2011)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Papakostas, G.A., Koulouriotis, D.E., Karakasis, E.G.: Computation strategies of orthogonal image moments: A comparative study. Appl. Math. Comput. 216, 1–17 (2010)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Wang, G.B., Wang, S.G.: Recursive computation of Tchebichef moment and its inverse transform. Pattern Recognit. 39(1), 47–56 (2006)CrossRefGoogle Scholar
  22. 22.
    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)CrossRefzbMATHGoogle Scholar
  23. 23.
    Papakostas, G.A., Koulouriotis, D.E., Karakasis, E.G.: A unified methodology for the efficient computation of discrete orthogonal image moments. Inf. Sci. 179, 3619–3633 (2009)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Shu, H., Zhang, H., Chen, B., Haigron, P., Luo, L.: Fast computation of Tchebichef moments for binary and grayscale images. IEEE Trans. Image Process. 19(12), 3171–3180 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Asli, B.H.S., Paramesran, R., Lim, C.-L.: The fast recursive computation of Tchebichef moment and its inverse transform based on Z-transform. Digital Signal Process. 23(5), 1738–1746 (2013)CrossRefGoogle Scholar
  26. 26.
    Asli, B.H.S., Flusser, J.: Fast computation of Krawtchouk moments. Inf. Sci. 288, 73–86 (2014)CrossRefzbMATHGoogle Scholar
  27. 27.
    Jahid, T., Hmimid, A., Karmouni, H., Sayyouri, M., Qjidaa, H., Rezzouk, A.: Image analysis by Meixner moments and a digital filter. Multimed Tools Appl. 77, 19811–19831 (2018)CrossRefGoogle Scholar
  28. 28.
    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. 37, 4015–4033 (2018)CrossRefGoogle Scholar
  29. 29.
    Chan, F.H.Y., Lam, F.K., Li, H.F., Liu, J.G.: An all adder systolic structure for fast computation of moments. J. VLSI Signal Process. 12(2), 159–175 (1996)CrossRefGoogle Scholar
  30. 30.
    Hua, X., Liu, J.: A novel fast algorithm for the pseudo Winger–Ville distribution. J Commun. Technol. Electron. 60(11), 1238–1247 (2015)CrossRefGoogle Scholar
  31. 31.
    Liu, J.G., Pan, C., Liu, Z.B.: Novel convolutions using first-order moments. IEEE Trans. Comput. 61(7), 1050–1056 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Marimuthu, C.N., Thangaraj, P., Ramesan, A.: Low power shift and add multiplier design. Int. J. Comput. Sci. Inf. Technol. 2, 12–22 (2010)Google Scholar
  33. 33.
    Hosny, K.M.: Fast computation of accurate Zernike moments. J. Real-Time Image Process. 3(1–2), 97–107 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electrical and Information EngineeringWuhan Institute of TechnologyWuhanChina
  2. 2.School of AutomationHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations