A New Approach to Estimate Fractal Dimension of Texture Images

  • André R. Backes
  • Odemir M. Bruno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5099)


One of the most important visual attributes for image analysis and pattern recognition is the texture. Its analysis allows to describe and identify different regions in the image through pixel organization, performing a better image description and classification. This paper presents a novel approach for texture analysis, based on calculation of the fractal dimension of binary images generated from a texture, using different threshold values. The proposed approach performs a complexity analysis as the threshold values changes, producing a texture signature which is able to characterize efficiently different texture classes. The paper illustrates the novel method performance on an experiment using Brodatz images.


Fractal Dimension Texture Analysis Complexity 


  1. 1.
    Ebert, D., Musgrave, K., Peachey, D., Perlin, K., Worley.: Texturing and Modeling: A Procedural Approach. Academic Press, London (1994)Google Scholar
  2. 2.
    Wang, L., Liu, J.: Texture classification using multiresolution markov random field models. Pattern Recognition Letters 20(2), 171–182 (1999)CrossRefGoogle Scholar
  3. 3.
    Unser, M.: Texture classification and segmentation using wavelet frames. IEEE Trans. Image Processing 4(11), 1549–1560 (1995)CrossRefGoogle Scholar
  4. 4.
    Emerson, C.W., Lam, N.N., Quattrochi, D.A.: Multi-scale fractal analysis of image texture and patterns. Photogrammetric Engineering and Remote Sensing 65(1), 51–62 (1999)Google Scholar
  5. 5.
    Chaudhuri, B.B., Sarkar, N.: Texture segmentation using fractal dimension. IEEE Trans. Pattern Anal. Mach. Intell 17(1), 72–77 (1995)CrossRefGoogle Scholar
  6. 6.
    Schroeder, M.: Fractals, Chaos, Power Laws: Minutes From an Infinite Paradise. W.H. Freeman, New York (1996)Google Scholar
  7. 7.
    Tricot, C.: Curves and Fractal Dimension. Springer, Heidelberg (1995)zbMATHGoogle Scholar
  8. 8.
    Lange, G.D., Marks, W.B.: Fractal methods and results in cellular morphology - dimensions, lacunarity and multifractals. Journal of Neuroscience Methods 69(2), 123–136 (1996)CrossRefGoogle Scholar
  9. 9.
    Coelho, R.C., Costa, L.F.: The box-counting fractal. dimension: Does it provide an accurate subsidy for experimental shape characterization? if so, how to use it? In: Anais do Sibgrapi, vol. 95, pp. 183–191 (1995)Google Scholar
  10. 10.
    Li, J., Sun, C., Du, Q.: A new box-counting method for estimation of image fractal dimension. In: International Conference on Image Processing, pp. 3029–3032 (2006)Google Scholar
  11. 11.
    Everitt, B.S., Dunn, G.: Applied Multivariate Analysis, 2nd edn. Arnold (2001)Google Scholar
  12. 12.
    Fukunaga, K.: Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press, London (1990)zbMATHGoogle Scholar
  13. 13.
    Falconer, K.J.: Fractal geometry: mathematical foundations and applications, 288 p. Wiley, Chichester (1990); CALL NUM: QA614.86 .F35 1990zbMATHGoogle Scholar
  14. 14.
    Brodatz, P.: A Photographic Album for Arts and Design, vol. 1. Dover Publishing Co., Toronto (1966)Google Scholar
  15. 15.
    Liao, P.S., Chen, T.S., Chung, P.C.: A fast algorithm for multilevel thresholding. J. Inf. Sci. Eng 17(5), 713–727 (2001)Google Scholar
  16. 16.
    Otsu, N.: A threshold selection method from gray level histograms. IEEE Trans. Systems, Man and Cybernetics 9, 62–66 (1979); minimize intra and inter class varianceCrossRefGoogle Scholar
  17. 17.
    Azencott, R., Wang, J.P., Younes, L.: Texture classification using windowed fourier filters. IEEE Trans. Pattern Anal. Mach. Intell. 19(2), 148–153 (1997)CrossRefGoogle Scholar
  18. 18.
    Haralick, R.M.: Statistical and structural approaches to texture. Proc. IEEE 67(5), 786–804 (1979)CrossRefGoogle Scholar
  19. 19.
    Jain, A.K., Farrokhnia, F.: Unsupervised texture segmentation using Gabor filters. Pattern Recognition 24(12), 1167–1186 (1991)CrossRefGoogle Scholar
  20. 20.
    Daugman, J., Downing, C.: Gabor wavelets for statistical pattern recognition. In: Arbib, M.A. (ed.) The Handbook of Brain Theory and Neural Networks, pp. 414–419. MIT Press, Cambridge (1995)Google Scholar
  21. 21.
    Idrissa, M., Acheroy, M.: Texture classification using gabor filters. Pattern Recognition Letters 23(9), 1095–1102 (2002)zbMATHCrossRefGoogle Scholar
  22. 22.
    Manjunath, B.S., Ma, W.Y.: Texture features for browsing and retrieval of image data. IEEE Trans. Pattern Anal. Mach. Intell 18(8), 837–842 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • André R. Backes
    • 1
  • Odemir M. Bruno
    • 1
  1. 1.Instituto de Ciências Matemáticas e de Computação (ICMC)Universidade de São Paulo (USP)São CarlosBrazil

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