Cluster Computing

, Volume 22, Supplement 5, pp 12985–12996 | Cite as

Weighted spherical Bessel–Fourier image moments

  • Bing He
  • Jiangtao CuiEmail author


In order to improve the performance of image reconstruction and image recognition accuracy in classic image orthogonal moments, a new set of moments based on the weighted spherical Bessel polynomial of the first kind is proposed, named weighted spherical Bessel–Fourier moments (WSBFMs), which are orthogonal in polar coordinate domain and can be thought as generalized and orthogonal complex moments. Then, the set of proposed WSBFMs is derived from the weighted spherical Bessel polynomial and image rotation-invariant is easily to achieve. Compared with Zernike, orthogonal Fourier–Mellion and Bessel polynomials of the same degree, the weighted spherical Bessel orthogonal radial polynomials have more zeros value, and these zeros value are more uniformly distributed. It makes WSBFMs more suitable for geometric invariant recognition as a generalization of orthogonal complex moments. Finally, Theoretical and experimental results show the superiority of the new orthogonal moments in terms of image reconstruction capability and invariant object recognition accuracy under noise-free, noisy and smooth distortion condition.


Orthogonal moments Spherical Bessel polynomial Object recognition Image reconstruction Polar coordinate 



This work was supported by National Natural Science Foundation of China (Grant No. 61472298), Basic research project of Weinan science and Technology Bureau (Grant No. 2017JCYJ-2-6) and by project of Shaan xi Provincial supports discipline(mathematics). The authors would like to thank the anonymous referees for their valuable comments and suggestions.


  1. 1.
    Wang, X., Yang, T., Guo, F.: Image analysis by circularly semi-orthogonal moments. Pattern Recogn. 49(1), 226–236 (2016)Google Scholar
  2. 2.
    Honarvar, B., Paramesran, R., Lim, C.L.: Image reconstruction from a complete set of geometric and complex moments. Sig. Process. 98(5), 224–232 (2014)Google Scholar
  3. 3.
    Xiao, B., Lu, G., Zhang, Y., Li, W., Wang, G.: Lossless image compression based on integer discrete Tchebichef transform. Neurocomputing 214(1), 587–593 (2016)Google Scholar
  4. 4.
    Papakostas, G.A., Tsougenis, E.D., Koulouriotis, D.E.: Moment-based local image watermarking via genetic optimization. Appl. Math. Comput. 227(15), 222–236 (2014)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Rahman, S.M.M., Howlader, T., Hatzinakos, D.: On the selection of 2d krawtchouk moments for face recognition. Pattern Recogn. 54(6), 83–93 (2016)Google Scholar
  6. 6.
    Liao, S.X., Pawlak, M.: On image analysis by moments. IEEE Trans. Pattern Anal. Mach. Intell. 18(3), 254–266 (1996)Google Scholar
  7. 7.
    Shao, Z., Shu, H., Wu, J., Chen, B., Coatrieux, J.L.: Quaternion bessel-fourier moments and their invariant descriptors for object reconstruction and recognition. Pattern Recogn. 47(2), 603–611 (2014)zbMATHGoogle Scholar
  8. 8.
    Xiao, B., Wang, G.Y., Li, W.S.: Radial shifted Legendre moments for image analysis and invariant image recognition. Image Vis. Comput. 32(12), 994–1006 (2014)Google Scholar
  9. 9.
    Priyal, S.P., Bora, P.K.: A robust static hand gesture recognition system using geometry based normalizations and Krawtchouk moments. Pattern Recogn. 46(8), 2202–2219 (2013)zbMATHGoogle Scholar
  10. 10.
    Zhu, H., Yang, Y., Gui, Z., Zhu, Y., Chen, Z.: Image analysis by generalized chebyshev-fourier and generalized pseudo-jacobicfourier moments. Pattern Recogn. 51(1), 1–11 (2016)zbMATHGoogle Scholar
  11. 11.
    Papakostas, G.A., Karakasis, E.G., Koulouriotis, D.E.: Accurate and speedy computation of image Legendre moments for computer vision applications. Image Vis. Comput. 28(3), 414–423 (2010)Google Scholar
  12. 12.
    Singh, C., Walia, E., Upneja, R.: Accurate calculation of Zernike moments. Inf. Sci. 233(1), 255–275 (2013)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Singh, C., Walia, E., Upneja, R.: Accurate calculation of high order pseudo-Zernike moments and their numerical stability. Digit. Signal Proc. 27(4), 95–106 (2014)Google Scholar
  14. 14.
    Shao, Z.H., Shang, Y.Y., Zhang, Y., Liu, X.L., Guo, G.D.: Robust watermarking using orthogonal Fourier-Mellin moments and chaotic map for double images. Sig. Process. 120(3), 522–531 (2016)Google Scholar
  15. 15.
    Sheng, Y., Shen, L.: Orthogonal Fourier-Mellion moments for invariant pattern recognition. Opt. Soc. Am. 11(6), 1748–1757 (1994)Google Scholar
  16. 16.
    Zhang, H., Shu, H.Z., Haigron, P., Li, B.S., Luo, L.M.: Construction of a complete set of orthogonal Fourier-Mellin moment invariants for pattern recognition applications. Image Vis. Comput. 28(1), 38–44 (2010)Google Scholar
  17. 17.
    Chen, Y., Xu, X.H.: Supervised orthogonal discriminant subspace projects learning for face recognition. Neural Netw. 50(2), 33–46 (2014)zbMATHGoogle Scholar
  18. 18.
    Xiao, B., Ma, J.F., Wang, X.: Image analysis by Bessel-Fourier moments. Pattern Recogn. 43(8), 2620–2629 (2010)zbMATHGoogle Scholar
  19. 19.
    Mukundan, R., Ong, S.H., Lee, P.A.: Image analysis by Tchebichef moments. IEEE Trans. Image Process. 10(9), 1357–1364 (2001)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Barmak, H., Shakibaei, A., Flusser, J.: Fast computation of Krawtchouk moments. Inf. Sci. 28(12), 73–86 (2014)zbMATHGoogle Scholar
  21. 21.
    Karakasis, E.G., Papakostas, G.A., Koulouriotis, D.E., Tourassis, V.D.: Generalized dual Hahn moment invariants. Pattern Recogn. 46(7), 1998–2014 (2013)zbMATHGoogle Scholar
  22. 22.
    Batioua, I., Benouini, R., Zenkouar, K., Fadili, H.E.: Image analysis using new set of separable two-dimensional discrete orthogonal moments based on racah polynomials. Eurasip J. Image Video Process. 1, 20–36 (2017)Google Scholar
  23. 23.
    Zhu, H.Q., Shu, H.Z., Zhu, J., Luo, L.M., Coatrieux, G.: Image analysis by discrete Orthogonal dual Hahn moments. Pattern Recogn. Lett. 28(13), 1688–1704 (2007)Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyXidian UniversityXi’anChina
  2. 2.School of Mathematics and PhysicsWeinan Normal UniversityWeinanChina

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