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On Fractal Dimension Estimation Methods

S. Sukumaran, Dr. M. Punithavalli

Abstract


Fractals are complex geometric figures made up of small scale and large scale structures that resemble one another. Fractal dimension is an effective measure for complex objects. It is widely applied in the fields of image segmentation and shape recognition. There are number of methods to estimate the fractal dimension. This paper contributes the comparative study of fractal dimension methods in terms of effectiveness and accuracy. In this work, we have taken five main types of fractal dimension estimation methods and compared.


Keywords


Fractal, Fractal dimension, Box-counting, Mass method, Dividers method.

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References


Ajay Kumar Bisoi, Jibitesh Mishra, “On calculation of fractal dimension of images”, Pattern Recognition Letters, Volume 22, Issues 6, pp: 631- 637, May 2001.

Chen.S, M. Keller, and R. Crownover. “On the calculation of fractal features from images”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(10) pp:1087–1090, October 1993.

Creutzburg R. and E. Ivanov. “Fast algorithm for computing fractal dimensions of image segments”, Lecture Notes in Computer Science, 399:42–51, 1989.

Dubuc, B. "Evaluating the fractal dimension of profiles" Phys. Rev. A , pp:1500-1512, 1989.

Grassberger. P "Generalizations of the Hausdorff dimension of fractal measures," Phys. Lett. A pp:101-10, 1985.

Grossu, I.V., C. Besliu, M.V. Rusu, Al. Jipa, C.C. Bordeianu, D. Felea, “Visual tool for estimating the fractal dimension of images”, Computer Physics Communications, May 2009.

James Theiler, “Estimating fractal dimension”. Journal of Optical Society of America , Vol 7. No. 6 pp: 1055- 1072, 1999.

Jin, X. C. S. H. Ong, Jayasooriah, “A practical method for estimating fractal dimension”,Pattern Recognition Letters, Volume 16, Issue 5, pp:457-464, May 1995.

Kaye, B.H.,”A Random Walk Through Fractal Dimensions”, VCH, NY, 1989.

Mandelbrot B.B., “Fractal Geometry of Nature”, Freeman, New York, 1997.

Passamante T., AHediger, and M. Gollub, "Fractal dimension and local intrinsic dimension," Phys. Rev. A pp: 39, 3640 ,1989.

Peitgen “Fractals in the Classroom, Part 1”, Springer Verlag, 1991.

Peitgen, Dietmer Saupe, “The Science of Fractal Images”,Springer- Verlag, 1985.

Pentland, A. P. “Fractal based description of natural scenes”, IEEE Trans. Pattern Anal. Machine Intell. Vol. PAMI-6, pp.661-674, 1994.


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