Multifractal Texture Analysis using a Dilation-based Hölder Exponent

Joao Batista Florindo, Odemir Martinez Bruno, Gabriel Landini


We present an approach to extract descriptors for the analysis of grey-level textures in images. Similarly to the classical multifractal analysis, the method subdivides the texture into regions according to a local Hölder exponent and computes the fractal dimension of each subset. However, instead of estimating such exponents (by means of the mass-radius relation, wavelet leaders, etc.) we propose using a local version of Bouligand-Minkowski dimension. At each pixel in the image, this approach provides a scaling relation which fits better to what is expected from a multifractal model than the direct use of the density function. The performance of the classification power of the descriptors obtained with this method was tested on the Brodatz image database and compared to other previously published methods used for texture classification. Our method outperforms other approaches confirming its potential for texture analysis.


  1. Ardizzone, E., Bruno, A., and Mazzola, G. (2013). Scale detection via keypoint density maps in regular or near-regular textures. Pattern Recognition Letters, 34(16):2071 - 2078.
  2. Backes, A. R., Casanova, D., and Bruno, O. M. (2009). Plant leaf identification based on volumetric fractal dimension. International Journal of Pattern Recognition and Artificial Intelligence, 23(6):1145-1160.
  3. Bedford, T. (1989). Hölder exponents and box dimension for self-affine fractal functions. Constructive Approximation, 5(1):33-48.
  4. Brodatz, P. (1966). Textures: A Photographic Album for Artists and Designers. Dover Publications, New York.
  5. Chhabra, A., Meneveau, C., Jensen, R., and Sreenivasan, K. R. (1989). Direct determination of the f (a) singularity spectrum and its application to fully developed turbulence. Physical Review A, 40(9):5284-5294.
  6. Duda, R. O. and Hart, P. E. (1973). Pattern Classification and Scene Analysis. Wiley, New York.
  7. Falconer, K. (2003). Fractal Geometry: Mathematical Foundations and Applications. Wiley, Chichester,UK.
  8. Farinella, G. M., Allegra, D., and Stanco, F. (2014). A benchmark dataset to study the representation of food images. In International Workshop on Assistive Computer Vision and Robotics (ACVR).
  9. Florindo, J. B. and Bruno, O. M. (2013). Texture analysis by multi-resolution fractal descriptors. Expert Systems with Applications, 40(10):4022-4028.
  10. Gonzalez, R. C. and Woods, R. E. (2002). Digital Image Processing (2nd Edition). Prentice Hall, Upper Saddle River.
  11. Haralick, R. M. (1979). Statistical and structural approaches to texture. Proceedings of the IEEE, 67(5):786-804.
  12. Julesz, B. (1981). Textons, the elements of texture perception, and their interactions. Nature, 290(5802):91-97.
  13. Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. Freeman.
  14. Materka, A. and Strzelecki, M. (1998). Texture analysis methods - a review. Technical report, Institute of Electronics, Technical University of Lodz.
  15. Meakin, P. (1987). Random walks on multifractal lattices. Journal of Physics A: Mathematical and General, 20(12):L771.
  16. Ojala, T., Pietikäinen, M., and Harwood, D. (1996). A comparative study of texture measures with classification based on featured distributions. Pattern Recognition, 29(1):51-59.
  17. Todorovic, S. and Ahuja, N. (2009). Texel-based texture segmentation. In ICCV, pages 841-848. IEEE.
  18. Varma, M. and Zisserman, A. (2009). A statistical approach to material classification using image patch exemplars. IEEE Transactions on Pattern Analysis and Machine Intelligence, 31(11):2032-2047.
  19. Xu, Y., Ji, H., and Fermüller, C. (2009). Viewpoint invariant texture description using fractal analysis. International Journal of Computer Vision, 83(1):85-100.
  20. Zhang, J. and Tan, T. (2002). Brief review of invariant texture analysis methods. Pattern Recognition, 35(3):735 - 747.

Paper Citation

in Harvard Style

Florindo J., Bruno O. and Landini G. (2015). Multifractal Texture Analysis using a Dilation-based Hölder Exponent . In Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2015) ISBN 978-989-758-089-5, pages 505-511. DOI: 10.5220/0005302305050511

in Bibtex Style

author={Joao Batista Florindo and Odemir Martinez Bruno and Gabriel Landini},
title={Multifractal Texture Analysis using a Dilation-based Hölder Exponent},
booktitle={Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2015)},

in EndNote Style

JO - Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2015)
TI - Multifractal Texture Analysis using a Dilation-based Hölder Exponent
SN - 978-989-758-089-5
AU - Florindo J.
AU - Bruno O.
AU - Landini G.
PY - 2015
SP - 505
EP - 511
DO - 10.5220/0005302305050511