Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Enhancement of the Box-Counting Algorithm for Fractal Dimension Estimation

프랙탈 차원 추정을 위한 박스 계수법의 개선

  • So, Hye-Rim (OST Graduate School, Korea Maritime and Ocean University) ;
  • So, Gun-Baek (OST Graduate School, Korea Maritime and Ocean University) ;
  • Jin, Gang-Gyoo (Division of IT, Korea Maritime and Ocean University)
  • 소혜림 (한국해양대학교 OST 대학원) ;
  • 소건백 (한국해양대학교 OST 대학원) ;
  • 진강규 (한국해양대학교 IT공학부)
  • Received : 2016.03.03
  • Accepted : 2016.07.11
  • Published : 2016.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

Due to its simplicity and high reliability, the box-counting(BC) method is one of the most frequently used techniques to estimate the fractal dimensions of a binary image with a self-similarity property. The fractal calculation requires data sampling that determines the size of boxes to be sampled from the given image and directly affects the accuracy of the fractal dimension estimation. There are three non-overlapping regular grid methods: geometric-step method, arithmetic-step method and divisor-step method. These methods have some drawbacks when the image size M becomes large. This paper presents a BC algorithm for enhancing the accuracy of the fractal dimension estimation based on a new sampling method. Instead of using the geometric-step method, the new sampling method, called the coverage ratio-step method, selects the number of steps according to the coverage ratio. A set of experiments using well-known fractal images showed that the proposed method outperforms the existing BC method and the triangular BC method.

Keywords

References

  1. B. Mandelbrot, "How long is the coast of britain? statistical self-similarity and fractional dimension," Science, vol. 156, no. 3775, pp. 636-638, 1967. https://doi.org/10.1126/science.156.3775.636
  2. A. Pentland, "Fractal-based description of natural scenes," IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 661-674, 1984.
  3. K. C. Clarke, "Computation of the fractal dimension of topographic surfaces using the triangular prism surface area method," Computers & Geosciences, vol. 12, no. 5, pp. 713-722, 1986. https://doi.org/10.1016/0098-3004(86)90047-6
  4. D. Saupe, The Science of Fractal Images, Springer-Verlag, New York, 1988.
  5. R. Lopes and N. Betrouni, "Fractal and multifractal analysis: A review," Medical Image Analysis, vol. 13, pp. 634-649, 2009. https://doi.org/10.1016/j.media.2009.05.003
  6. A. Napolitano, S. Ungania, and V. Cannata, "Fractal dimension estimation methods for biomedical images," In MATLAB-A Fundamental Tool for Scientific Computing and Engineering Applications, V. N. Katsikis (Editor), vol. 3, pp. 161-178, 2012.
  7. D. Russel, J. Hanson, and E. Ott, "Dimension of strange attractors," Physical Review Letters, vol. 45, no. 14, pp. 1175-1178, 1980. https://doi.org/10.1103/PhysRevLett.45.1175
  8. N. Sarkar and B. B. Chaudhuri, "An efficient differential box-counting approach to compute fractal dimension of image," IEEE Transactions on Systems, Man and Cybernetics, vol. 24, no. 1, pp. 115-120, 1994. https://doi.org/10.1109/21.259692
  9. X. C. Jin, S. H. Ong, and Jayasooriah, "A practical method for estimating fractal dimension," Pattern Recognition Letters, vol. 16, no. 5, pp. 457-464, 1995. https://doi.org/10.1016/0167-8655(94)00119-N
  10. 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. https://doi.org/10.1016/j.patcog.2009.03.001
  11. K. Foroutan-pour, P Dutilleul, and D. L Smith, "Advances in the implementation of the box-counting method of fractal dimension estimation," Applied Mathematics and Computation, vol. 105, no. 2-3, pp. 195-210, 1999. https://doi.org/10.1016/S0096-3003(98)10096-6
  12. Y. Kaewaramsri and K. Woraratpanya, "Improved triangle box-counting method for fractal dimension estimation," Recent Advances in Information and Communication Technology 2015, vol. 361, pp. 53-61, 2015.
  13. S. Buczkowski, S. Kyriacos, F. Nekka, and L. Cartilier, "The modified box-counting method: Analysis of some characteristic parameters," Pattern Recognition, vol. 31, no. 4, pp. 411-418, 1998. https://doi.org/10.1016/S0031-3203(97)00054-X
  14. W. Ju and N. S.-N. Lam, "An improved algorithm for computing local fractal dimension using the triangular prism method," Computers and Geosciences, vol. 35, pp. 1224-1233, 2009. https://doi.org/10.1016/j.cageo.2008.09.008
  15. Scan type, https://en.wikipedia.org/wiki/Box_counting.