Structure Tensor of Colour Quaternion Image Representations for Invariant Feature Extraction

  • Jesús Angulo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5646)


Colour image representation using real quaternions has shown to be very useful for linear and morphological colour filtering. This paper deals with the extension of first derivatives-based structure tensor for various quaternionic colour image representations. Classical corner and edge features are obtained from eigenvalues of the quaternionic colour structure tensors. We study the properties of invariance of the quaternion colour spatial derivatives and their robustness for feature extraction on practical examples.


Colour Image Structure Tensor Scalar Part Reference Colour Real Quaternion 
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  1. 1.
    Angulo, J., Serra, J.: Modelling and Segmentation of Colour Images in Polar Representations. Image and Vision Computing 25(4), 475–495 (2007)CrossRefGoogle Scholar
  2. 2.
    Angulo, J.: Quaternion colour representations and derived total orderings for morphological operators. In: CGIV 2008, pp. 417–422 (2008)Google Scholar
  3. 3.
    Bigun, J., Granlund, G., Wiklund, J.: Multidimensional orientation estimation with applications to texture analysis and opitcal flow. IEEE Trans. Patt. Anal. and Mach. Intell. 13(8), 775–790 (1991)CrossRefGoogle Scholar
  4. 4.
    Bunyak, F., Palaniappan, K., Nath, S.K., Seetharaman, G.: Flux tensor constrained geodesic active contours with sensor fusion and persistent object tracking. Journal of Multimedia 2(4), 20–33 (2007)CrossRefGoogle Scholar
  5. 5.
    Cai, C., Mitra, S.K.: A normalized color difference edge detector based on quaternion representation. In: ICIP 2000 (2000)Google Scholar
  6. 6.
    Cumani, A.: Edge detection in multispectral images. CVGIP: Graphical Models and Image Processing 53(1) (1991)Google Scholar
  7. 7.
    Denis, P., Carré, P., Fernandez-Maloigne, C.: Spatial and spectral quaternionic approaches for colour images. Computer Vision and Image Understanding 107(2-3), 74–87 (2007)CrossRefGoogle Scholar
  8. 8.
    Di Zenzo, S.: A note on the gradient of a multi-image. Computer Vision, Graphics, and Image Processing 33(1), 116–125 (1986)CrossRefzbMATHGoogle Scholar
  9. 9.
    Ell, T.A., Sangwine, S.J.: Hypercomplex Wiener-Khintchine theorem with application to color image correlation. In: IEEE ICIP 2000, vol. II, pp. 792–795 (2000)Google Scholar
  10. 10.
    Ell, T.A., Sangwine, S.J.: Hypercomplex Fourier transform of color images. IEEE Transactions on Image Processing 16(1), 22–35 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Harris, C., Stephens, M.: A combined corner and edge detector. In: Proc. 4th Alvey Vision Conf., vol. 15, pp. 147–151 (1988)Google Scholar
  12. 12.
    Montesinos, P., Gouet, V., Deriche, R.: Differential invariants for color images. In: IAPR International Conference on Pattern Recognition (ICPR 1998), pp. 838–840 (1998)Google Scholar
  13. 13.
    Naik, S.K., Murthy, C.A.: Standardization of edge magnitude in color images. IEEE Trans. on Image Processing 15(9), 2588–2595 (2006)CrossRefGoogle Scholar
  14. 14.
    Noble, J.A.: Finding corners. Image and Vision Computing 6(2), 121–128 (1988)CrossRefGoogle Scholar
  15. 15.
    Ruzon, M.A., Tomasi, C.: Edge, junction, and corner detection using color distributions. IEEE Trans. Patt. Anal. and Mach. Intell. 23(11), 1281–1295 (2001)CrossRefGoogle Scholar
  16. 16.
    Sangwine, S.J., Ell, T.A.: Mathematical approaches to linear vector filtering of colour images. In: CGIV 2002, pp. 348–351 (2002)Google Scholar
  17. 17.
    Schmid, C., Mohr, R., Bauckhage, C.: Evaluation of interest point detectors. International Journal of Computer Vision 37(2), 151–172 (2000)CrossRefzbMATHGoogle Scholar
  18. 18.
    Shi, L., Funt, B.: Quaternion color texture segmentation. Computer Vision and Image Understanding 107(1-2), 88–96 (2007)CrossRefGoogle Scholar
  19. 19.
    Sochen, N., Kimmel, R., Malladi, R.: A general framework for low level vision. IEEE Transactions on Image Processing 7(3), 310–318 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Veit, T., Tarel, J.-P., Nicolle, P., Charbonnier, P.: Evaluation of Road Marking Feature Extraction. In: Proceedings of 11th IEEE Conference on Intelligent Transportation Systems (ITSC 2008), Beijing, China, October 12-15 (2008)Google Scholar
  21. 21.
    van de Weijer, J., Gevers, T., Geusebroek, J.M.: Edge and corner detection by photometric quasi-invariants. IEEE Trans. Patt. Anal. and Mach. Intell. 27(4) (2005)Google Scholar
  22. 22.
    van de Weijer, J., Gevers, T., Smeulders, A.W.M.: Robust Photometric Invariant Features From the Colour Tensor. IEEE Trans. on Image Processing 15(1), 118–127 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jesús Angulo
    • 1
  1. 1.CMM-Centre de Morphologie Mathématique, Mathématiques et SystèmesMINES ParistechFontainebleau CedexFrance

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