This Article 
 Bibliographic References 
 Add to: 
On the Calculation of Fractal Features from Images
October 1993 (vol. 15 no. 10)
pp. 1087-1090

Fractal geometry is becoming increasingly more important in the study of image characteristics. There are numerous methods available to estimate parameters from images of fractal surfaces. A very general technique to calculate numerous fractal features involves the estimation of the mass density function by box counting. The authors analyze the box-counting method, establish a lower bound for the box size, and indicate how algorithms can be improved to give better estimates of fractal features of images. This provides a theoretical basis for a heuristic approach used by C.A. Pickover and A.L. Khorasani (1986).

[1] B. Mandelbrot,The Fractal Geometry of Nature. San Francisco, CA: Freeman, 1977.
[2] B. Mandelbrot, and J. W. Van Ness, "Fractional brownian motions, fractional noises and applications,"SIAM Rev., vol. 10, no. 4, pp. 422-437, 1968.
[3] A. Pentland, "Fractal-based description," inProc. Int. Joint Conf. Artificial Intell., 1983, pp. 973-981, 1983.
[4] A. Pentland, "Fractal-based description of natural scenes,"IEEE Trans. Patt. Anal. Machine Intell., vol. 6, pp. 661-674, 1984.
[5] P. Kube and A. Pentland, "On the imaging of fractal surfaces,"IEEE Trans. Patt. Anal. Machine Intell., vol. 10, no. 5, pp. 704-707, 1988.
[6] G. Medioni, and Y. Yasumoto, "A note on using the fractal dimension for segmentation," inProc. IEEE Comput. Vision Workshop(Annapolis, MD), 1984, pp. 25-30.
[7] S. Peleg, J. Naor, R. Hartley, and D. Avnir, "Multiple resolution texture analysis and classification,"IEEE Trans. Patt. Anal. Machine Intell., vol. 6, no. 4, pp. 518-523, 1984.
[8] T. Lundahlet. al., "Fractional brownian motion: A maximum likelihood estimator and its application to image texture,"IEEE Trans. Med. Imaging, vol. 5, no. 3, pp. 152-161, 1986.
[9] J. M. Keller, R. M. Crownover, and R. Y. Chen, "Characteristics of natural scenes related to the fractal dimension,"IEEE Trans. Patt. Anal. Machine Intell., vol. 9, no. 5, pp. 621-627, 1987.
[10] J. M. Keller, S. Chen, and R. M. Crownover, "Texture description through fractal geometry,"Comput. Vision Graphics Image Processing, vol. 45, pp. 150-166, 1989.
[11] S. Chen, J. Keller, and R. Crownover, "Shape from fractal geometry,"Artificial Intell., vol. 43, pp. 199-218, 1990.
[12] J. Keller and T. Downey, "Fuzzy segmentation using fractal features," inProc. SPIE Symp. Intell. Robots Comput. Vision(Cambridge, MA), 1988, pp. 369-376.
[13] R. F. Voss, "Random fractals: Characterization and measurement," inScaling Phenomena in Disordered Systems. New York: Plenum, 1985, pp. 1-11.
[14] K. Falconer,Fractal Geometry Mathematical Foundations and Applications. Chichester, UK: Wiley, 1990.
[15] C. A. Pickover and A. L. Khorasani, "Fractal characterization of speech waveform graphs,"Comput. Graphics, vol. 10, no. 1, pp. 51-61, 1986.

Index Terms:
fractal feature calculation; fractal geometry; box size lower bound; images; image characteristics; fractal surfaces; mass density function; box counting; heuristic approach; feature extraction; fractals; parameter estimation
S.S. Chen, J.M. Keller, R.M. Crownover, "On the Calculation of Fractal Features from Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 10, pp. 1087-1090, Oct. 1993, doi:10.1109/34.254066
Usage of this product signifies your acceptance of the Terms of Use.