Skip to main content
Springer Nature Link
Log in

New Set of Quaternion Moments for Color Images Representation and Recognition

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

In this paper, a new set of quaternion radial-substituted Chebyshev moments (QRSCMs) is proposed for color image representation and recognition. These new moments are circular moments defined over a unit disk by using a new set of orthogonal basis functions called radial-substituted Chebyshev functions. A new hybrid method is proposed for highly accurate computation of QRSCMs in polar coordinates. In this method, the angular kernel is exactly computed by analytical integration of Fourier function over circular pixels. The radial kernel is computed using a recurrence relation which completely eliminates the coefficient matrix associated with the radial-substituted Chebyshev functions. Rotation, scaling, and translation (RST) invariances for QRSCMs are proved. Numerical experiments were conducted where the results of these experiments show better performance of QRSCMs over existing quaternion moments in terms of image reconstruction capabilities, RST invariances, robust to different noises, and CPU elapsed times.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Flusser, J., Zitova, B., Suk, T.: Moments and Moment Invariants in Pattern Recognition. Wiley, New York (2009). (ISBN: 978-0-470-69987-4)

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Bailey, R., Srinath, M.: Orthogonal moment features for use with parametric and non-parametric classifiers. IEEE Trans. Pattern Anal. Mach. Intell. 18(4), 389–399 (1996)

    Article  Google Scholar 

  4. Sheng, Y., Shen, L.: Orthogonal Fourier–Mellin moments for invariant pattern recognition. J. Opt. Soc. Am. A 11(6), 1748–1757 (1994)

    Article  Google Scholar 

  5. Ping, Z.L., Wu, R., Sheng, Y.L.: Image description with Chebyshev–Fourier moments. J. Opt. Soc. Am. A 19(9), 1748–1754 (2002)

    Article  MathSciNet  Google Scholar 

  6. Ren, H.P., Ping, Z.L., Wurigen, Y.L., Sheng, Y.: Multi-distorted invariant Image recognition with radial-harmonic-Fourier moments. J. Opt. Soc. Am. A 20(4), 631–637 (2003)

    Article  Google Scholar 

  7. Ping, Z., Ren, H., Zou, J., Sheng, Y., Bo, W.: Generic orthogonal moments: Jacobi–Fourier moments for invariant image description. Pattern Recogn. 40, 1245–1254 (2007)

    Article  MATH  Google Scholar 

  8. Yap, P., Jiang, X., Kot, A.C.: Two dimensional polar harmonic transforms for invariant image representation. IEEE Trans. Pattern Anal. Mach. Intell. 32(7), 1259–1270 (2010)

    Article  Google Scholar 

  9. Xiao, B., Wang, G., Li, W.: Radial shifted Legendre moments for image analysis and invariant image recognition. Image Vis. Comput. 32(12), 994–1006 (2014)

    Article  Google Scholar 

  10. Guo, F., Ye, S., Yang, T., Wang, X.: Robust circularly orthogonal moment based on Chebyshev rational function. Dig. Signal Proc. 62, 249–258 (2017)

    Article  Google Scholar 

  11. Chen, B.J., Shu, H.Z., Zhang, H., Chen, G., Toumoulin, C., Dillenseger, J.L., Luo, L.M.: Quaternion Zernike moments and their invariants for color image analysis and object recognition. Signal Process. 92(1), 308–318 (2012)

    Article  Google Scholar 

  12. Chen, B.J., Sun, X.M., Wang, D.C., Zhao, X.P.: Color face recognition using quaternion representation of color image. ACTA Autom. Sin. 38(11), 1815–1823 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Guo, L., Zhu, M.: Quaternion Fourier–Mellin moments for color images. Pattern Recogn. 44(2), 187–195 (2011)

    Article  MATH  Google Scholar 

  14. Wang, X.Y., Li, W.Y., Yang, H.Y., Niu, P.P., Li, Y.W.: Invariant quaternion radial harmonic Fourier moments for color image retrieval. Opt. Laser Technol. 66, 78–88 (2015)

    Article  Google Scholar 

  15. Wang, X., Li, W., Yang, H., Wang, P., Li, Y.: Quaternion polar complex exponential transform for invariant color image description. Appl. Math. Comput. 256, 951–967 (2015)

    MathSciNet  MATH  Google Scholar 

  16. Yang, H., Liang, L., Li, Y., Wang, X.: Quaternion exponent moments and their invariants for color image. Fund. Inf. 145, 189–205 (2016)

    MathSciNet  MATH  Google Scholar 

  17. Hamilton, W.R.: Elements of Quaternions. Longmans Green, London (1866)

    Google Scholar 

  18. Hosny, K.M., Shouman, M.A., Abdel-Salam, H.M.: Fast computation of orthogonal Fourier–Mellin moments in polar coordinates. J. Real-Time Image Process. 6(1), 73–80 (2011)

    Article  Google Scholar 

  19. Hosny, K.M.: Accurate orthogonal circular moment invariants of gray-level images. J. Comput. Sci. 7(5), 715–722 (2011)

    Article  MathSciNet  Google Scholar 

  20. Liu, C., Huang, X.-H., Wang, M.: Fast computation of Zernike moments in polar coordinates. IET Image Proc. 6(7), 996–1004 (2012)

    Article  MathSciNet  Google Scholar 

  21. Xin, Y., Pawlak, M., Liao, S.: Accurate computation of Zernike moments in polar coordinates. IEEE Trans. Image Process. 16(1), 581–587 (2007)

    Article  MathSciNet  Google Scholar 

  22. Harris, J.W., Stocker, H.: Handbook of Mathematics and Computational Science. Springer, New York (1998)

    Book  MATH  Google Scholar 

  23. Faires, J.D., Burden, R.L.: Numerical Methods, 3rd edn. Brooks Cole Publication, London (2002)

    MATH  Google Scholar 

  24. Camacho-Bello, C., et al.: High precision and fast computation of Jacobi–Fourier moments for image description. J. Opt. Soc. Am. A 31(1), 124–134 (2014)

    Article  Google Scholar 

  25. Camacho-Bello, C., et al.: Reconstruction of color biomedical images by means of quaternion generic Jacobi–Fourier moments in the framework of polar pixel. J. Med. Imaging 3(1), 014004 (2016)

    Article  Google Scholar 

  26. Hosny, K.M., Darwish, M.M.: Highly accurate and numerically stable higher order QPCET moments for color image representation. Pattern Recogn. Lett. 97, 29–36 (2017)

    Article  Google Scholar 

  27. http://www.cs.columbia.edu/CAVE/software/softlib/coil-100.php

  28. Suk, T., Flusser, J.: Affine moment invariants of color images. In: The 13th International Conference on Computer Analysis of Images and Patterns, Lecture Notes Computer Science, vol. 5702, pp. 334–341. Münste, Germany (2009)

  29. Lazebnik, S., Schmid, C., Ponce, J.: A maximum entropy framework for part-based texture and object recognition. Proc. IEEE Int. Conf. Comput. Vis. Beijing China 1, 832–838 (2005)

    Article  Google Scholar 

  30. Lazebnik, S., Schmid, C., Ponce, J.: Semi-local affine parts for object recognition. Proc. Br. Mach. Vis. Conf. 2, 959–968 (2004)

    Google Scholar 

  31. http://multibandtexture.recherche.usherbrooke.ca

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, Zagazig, 44519, Egypt

    Khalid M. Hosny

  2. Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71516, Egypt

    Mohamed M. Darwish

Authors
  1. Khalid M. Hosny
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Mohamed M. Darwish
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Khalid M. Hosny.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hosny, K.M., Darwish, M.M. New Set of Quaternion Moments for Color Images Representation and Recognition. J Math Imaging Vis 60, 717–736 (2018). https://doi.org/10.1007/s10851-018-0786-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-018-0786-0

Keywords