Texture Classification Using Fractal Dimension and Lacunarity (original) (raw)

Abstract

The fractal features including fractal dimension (FD) and lacunarity measures are often used as indicators of texture. Several FD and lacunarity estimation methods leading to different results have been proposed in the literature. This paper is devoted mainly to show the need to combine the lacunarity with fractal dimension for the discrimination between different textures and especially to check if this combination is valid with any FD estimation method. Keywordstexture analysis; fractal dimension; lacunarity; classification.

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References (27)

  1. M. Tuceryan, and A.K. Jain, " Texture analysis," Chapter 2.1, The Handbook of Pattern Recognition and Computer Vision ( 2 nd Edition), C. H. Chen, L. F. Pau, P. S. P. Wang, Eds. Word Scientific Publishing Co., 1998, pp. 207-248.
  2. M. Rani, and S. Aggarwal, " Fractal texture: a survey,". Advances in Computational Research, vol. 5, no. 1, pp. 149-152, 2013.
  3. B.B. Mandelbrot, The Fractal Geometry of Nature,W.H Freeman and company, 1982.
  4. M. Lehamel, and K. Hammouche, "Comparative Evaluation of Various Fractal Dimension Estimation Methods," 8th International Conference on Signal-Image Technology and Internet-Based Systems (SITIS 2012), 25-29, November 2012, Sorrento, Naples, Italy.
  5. G. Zhou, and N.S.N. Lam, "A comparison of fractal dimension estimators based on multiple surface generation algorithms," Computers and Geosciences, vol. 31, pp. 1260-1269, 2005.
  6. V.S. Pleshanov, A.A. Napryushkin, and V.V. Kibitkin, "Use of the Theory of Fractals in Image Analysis Tasks," vol. 46, no. 1, pp. 86-97, 2010.
  7. W. Sun, G. Xu, P. Gong, and S. Liang, "Fractal analysis of remotely sensed images: A review of methods and applications,". International Jourmal of Remote Sensing, vol. 27, no. 22, pp. 4963-4990, 2006.
  8. R, Lopes, and N. Betrouni, "Fractal and multifractal analysis," Medical Image Analysis, vol. 13, pp. 634-649, 2009.
  9. K.I. Kilic, and R.H. Abiyev, "Exploiting the synergy between fractal dimension and lacunarity for improved texture recognition," Signal Processing, vol. 91, pp. 2332-2344, 2011.
  10. C.Allain, and M.Cloitre, "Characterizing the lacunarity of random and deterministic fractal sets," Pysical Review A, vol.44, pp.3552-3558, 1991.
  11. D.A. Russel, J.D. Hanson, and E. Ott, "Dimension of strange attractors," Physical Review Letters, vol. 45, pp. 1175-1178, 1980.
  12. JJ. Gangepain, and C. Roques-Carmes, "Fractal approach to tow dimensional and three dimensional surface roughness," Wear, vol. 109, pp. 119-126, 1986.
  13. N. Sarkar, and B.B. Chaudhuri, "An efficient Differential Box- Counting approach to compute fractal dimension of textural images," Pattern. Recognition Letters, vol. 25, pp. 1035-1041, 1992.
  14. W.L. Lee, and K.S. Hsieh, "A robust algorithm for the fractal dimension of images and its applications to the classification of natural images and ultrasonic liver images," Signal Processing, vol. 90, pp. 1894-1904, 2010.
  15. J. Li, Q. Du, and C. Sun, "An improved box-counting method for image fractal dimension estimation," Pattern. Recognition, vol. 42, pp. 2460- 2469, 2009.
  16. S. Xu, and Y. Weng, "A new approach to estimate fractal dimensions of corrosion images," Pattern Recognition Letters, vol. 27, pp. 1942-1947, 2006.
  17. R.Voss, "Random fractals: characterization and measurement in scaling phenomena in disordered systems,". R. Pynn and Skjeltorop, Eds. Plenum, New York, 1986.
  18. K.C. Clarke, "Computation of the Fractal Dimension of Topographical Surfaces Using the Triangular Prism Surface Area Method," Computer. Geoscience, vol. 12, no. 5, pp. 713-722, 1986.
  19. S. Peleg, J. Naor, R. Hartley, and D. Avnir, "Multiple resolution texture analysis and classification," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.6, no.4, pp. 518-523, 1984.
  20. C.M. Wu, Y.C. Chen, and K.S. Hsieh, "Texture features for classification of ultrasonic liver images," IEEE Transactions Medical Imaging, vol. 11, no 2, pp. 52-141, 1992.
  21. E.L. Chen, P.C. Chung, C.L. Chen, H.M. Sai, and C.I. Chang, "An automatic diagnostic system for CT liver image classification," IEEE. Transactions. Biomed. Engineering, vol. 45 , no. 6, pp. 783-794, 1998.
  22. B. Dubuc, C.Roques-Carmes, C.Tricot ,and S.W. Zucker, "The Variation Method: A Technique to Estimate the Fractal Dimension of Surface," Proc. SPIE. Visual Commun. Image Processing, vol. 845, pp. 241-248, 1987.
  23. G. Du, and T.S. Yeo, "A novel lacunarity estimation method applied to SAR image segmentation", IEEE Trans. On Geosience and Remote Sensing. vol. 40, no. 12, pp. 2687-2691, 2001.
  24. C. R. Tolle, T. R. McJunkin, and D. J. Gorsich, "A efficient implementation of the gliding box lacunarity algorithm," Physica D237, pp. 306-315, 2008.
  25. Brodatz, P. (1956). Texture: A Photograph Album for Artists and Designs, Dover, New York.
  26. http://www-cvr.ai.uiuc.edu/ponce grp [27] G. Shakhnarovish, T. Darrell and P. Indyk, "Nearest-Neighbor Methods inLearning and Vision," MIT Press, 2005
  27. C.C. Chang, and C. J. Lin. LIBSVM: a library for support vector machines, 2007. http://www.csie.ntu.edu.tw/\~cjlin/libsvm.