Feature Extraction of Color Images Using Quaternion Moments

  • Khalid M. Hosny
  • Mohamed M. Darwish
Part of the Studies in Computational Intelligence book series (SCI, volume 804)


Color images play an essential role in computer vision systems where colors are useful information. Extraction of color images features is the backbone of many pattern recognition and image processing applications such classification of color images, color image retrieval, color image watermarking and template matching. Moments and moment invariants are widely used as global and local features for gray images. Quaternion moments are used in representation of color images. In this chapter, an overview of quaternion moments and their rotation, scaling and translation invariants is given. A series of numerical experiments are performed using different parameters to assess the performance of extracted features using different quaternion moments.


  1. 1.
    Papakostas, G.A.: Over 50 years of image moments and moment invariants. Sci. Gate Publ. 1, 332 (2014)Google Scholar
  2. 2.
    Upneja, R., Pawlak, M., Sahanb, A.M.: An accurate approach for the computation of polar harmonic transforms. Optik 158, 623–633 (2018)CrossRefGoogle Scholar
  3. 3.
    Hu, M.K.: Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory 8(2), 179–187 (1962)CrossRefzbMATHGoogle Scholar
  4. 4.
    Teague, M.R.: Image analysis via the general theory of moments. J. Opt. Soc. Am. A 70(8), 920–930 (1980)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Flusser, J., Suk, T., Zitov, B.: 2D and 3D image analysis by moments. Wiley Ltd (2017)Google Scholar
  6. 6.
    Wang, X., Xiao, B., Ma, J.F., Bi, X.L.: Scaling and rotation invariant analysis approach to object recognition based on Radon and Fourier Mellin transforms. Pattern Recogn. 40, 3503–3508 (2007)CrossRefzbMATHGoogle Scholar
  7. 7.
    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
  8. 8.
    Hosny, K.M.: Image representation using accurate orthogonal Gegenbauer moments. Pattern Recogn. Lett. 32(6), 795–804 (2011)CrossRefGoogle Scholar
  9. 9.
    Flusser, J.: Pattern recognition by affine moment invariants. Pattern Recogn. 26, 167–174 (1993)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kan, C., Srinath, M.D.: Invariant character recognition with Zernike and orthogonal Fourier-Mellin moments. Pattern Recogn. 35, 143–154 (2002)CrossRefzbMATHGoogle Scholar
  11. 11.
    Sheng, Y.L., Shen, L.X.: Orthogonal Fourier-Mellin moments for invariant pattern recognition. J. Opt. Soc. Am. A 11(6), 1748–1757 (1994)CrossRefGoogle Scholar
  12. 12.
    Pang, Y.H., Teoh, A.B.J., Ngo, D.C.L.: A discriminant pseudo-Zernike moments in face recognition. J. Res. Pract. Inf. Technol. 38(2), 197–211 (2006)Google Scholar
  13. 13.
    Choi, M., Kim, W.: A novel two stage template matching method for rotation and illumination invariance. Pattern Recogn. 35, 119–129 (2002)CrossRefzbMATHGoogle Scholar
  14. 14.
    Hosny, K.M.: Robust template matching using orthogonal legendre moment invariants. J. Comput. Sci. 6(10), 1054–1058 (2010)CrossRefGoogle Scholar
  15. 15.
    Kumar, Y., Aggarwal, A., Tiwari, S., Singh, K.: An efficient and robust approach for biomedical image retrieval using Zernike moments. Biomed. Sig. Process. Control 39, 459–473 (2018)CrossRefGoogle Scholar
  16. 16.
    Ismail, I.A., Shuman, M.A., Hosny, K.M., Abdel Salam, H.M.: Invariant image watermarking using accurate Zernike moments. J. Comput. Sci. 6(1), 52–59 (2010)CrossRefGoogle Scholar
  17. 17.
    Tsougenis, E.D., Papakostas, G.A., Koulouriotis, D.E., Tourassis, V.D.: Towards Adaptivity of image watermarking in polar harmonic transforms domain. Opt. Laser Technol. 54, 84–97 (2013)CrossRefGoogle Scholar
  18. 18.
    Hosny, K.M., Darwish, M.M.: Invariant image watermarking using accurate Polar Harmonic transforms. Comput. Electr. Eng. 62, 429–447 (2017)CrossRefGoogle Scholar
  19. 19.
    Mindru, F., Tuytelaars, T., Van Gool, L., Moons, T.: Moment invariants for recognition under changing view point and illumination. Comput. Vis. Image Underst. 94, 3–27 (2004)CrossRefGoogle Scholar
  20. 20.
    Suk T, Flusser J. Affine moment invariants of color images. In: International Conference on Computer Analysis of Images and Patterns, CAIP 2009, vol. 5702, pp. 334–341 (2009)CrossRefGoogle Scholar
  21. 21.
    Hamilton, W.R.: Elements of Quaternions. Longmans Green, London, United Kingdom (1866)Google Scholar
  22. 22.
    Ell, T.A., Sangwine, S.J.: Hypercomplex Fourier transforms of color images. IEEE Trans. Image Process. 16, 22–35 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Guo, L., Zhu, M.: Quaternion Fourier-Mellin moments for color images. Pattern Recogn. 44(2), 187–195 (2011)CrossRefzbMATHGoogle Scholar
  24. 24.
    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. Sig. Process. 92(2), 308–318 (2012)CrossRefGoogle Scholar
  25. 25.
    Chen, B.J., Xingming, S., Wang, D., Zhao, X.: Color face recognition using quaternion representation of color image. Acta Autom. Sinica 38(11), 1815–1823 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Wang, X., Li, W., Yang, H., Niu, P., Li, Y.: Invariant quaternion radial harmonic Fourier moments for color image retrieval. Opt. Laser Technol. 66, 78–88 (2015)CrossRefGoogle Scholar
  27. 27.
    Li, Y.N.: Quaternion polar harmonic transforms for color images. IEEE Sig. Process. Lett. 20(8), 803–806 (2013)CrossRefGoogle Scholar
  28. 28.
    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)MathSciNetzbMATHGoogle Scholar
  29. 29.
    Yang, H., Lian, L., Li, Y., Wang, X.: Quaternion exponent moments and their invariants for color image. Fundam. Inf. 145, 189–205 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Camacho-Bello, C., Bez-Rojas, J.J., Toxqui-Quitl, C., Padilla-Vivanco, A.: Color image reconstruction using quaternion Legendre-Fourier moments in polar pixels. In: International Conference on Mechatronics, Electronics and Automotive Engineering (2014)Google Scholar
  31. 31.
    Hosny, K.M., Darwish, M.M.: Robust color image watermarking using invariant quaternion Legendre-Fourier moments. Multimed. Tools Appl. 1–15 (2018)Google Scholar
  32. 32.
    Hosny, K.M., Darwish, M.M.: New set of quaternion moments for color images representation and recognition. J. Math. Imaging Vis. 1–19 (2018)Google Scholar
  33. 33.
    Karakasis, E., Papakostas, G., Koulouriotis, D., Tourassis, V.: A unified methodology for computing accurate quaternion color moments and moment invariants. IEEE Trans. Image Process. 23, 596–611 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Hosny, K.M., Darwish, M.M.: Accurate computation of quaternion polar complex exponential transform for color images in different coordinate systems. J. Electr. Imaging 26(2), 023021 (2017)CrossRefGoogle Scholar
  35. 35.
    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)CrossRefGoogle Scholar
  36. 36.
    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
  37. 37.
    Hosny, K.M.: Accurate orthogonal circular moment invariants of gray-level images. J. Comput. Sci. 7(5), 715–722 (2011)CrossRefGoogle Scholar
  38. 38.
    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(2), 73–80 (2011)CrossRefGoogle Scholar
  39. 39.
    Hosny, K.M., Darwish, M.M.: A kernel-based method for Fast and accurate computation of PHT in polar coordinates. J. Real-Time Image Process. 1–13 (2016)Google Scholar
  40. 40.
    Harris, J.W., Stocker, H.: Handbook of Mathematics and Computational Sciences. Springer, NewYork (1998)CrossRefzbMATHGoogle Scholar
  41. 41.
    Nene, S.A., Nayar, S.K., Murase, H.: Columbia object image library (COIL-100). Technical Report CUCS-006-96 (1996)Google Scholar
  42. 42.
    Nilsback, M., Zisserman, A.: Delving deeper into the whorl of flower segmentation. Image Vis. Comput. 28(6), 1049–1062 (2010)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Information TechnologyFaculty of Computers and Informatics Zagazig UniversityZagazigEgypt
  2. 2.Mathematics DepartmentFaculty of Science Assiut UniversityAssiutEgypt

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