loading...
 This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
On the Imaging of Fractal Surfaces
September 1988 (vol. 10 no. 5)
pp. 704-707
ASCII Text
x 
 
P. Kube, A. Pentland, "On the Imaging of Fractal Surfaces," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 5, pp. 704-707, September, 1988.
 
 
BibTex
x
 
@article{ 10.1109/34.6779,
author = {P. Kube and A. Pentland},
title = {On the Imaging of Fractal Surfaces},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {10},
number = {5},
issn = {0162-8828},
year = {1988},
pages = {704-707},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.6779},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - On the Imaging of Fractal Surfaces
IS - 5
SN - 0162-8828
SP704
EP707
EPD - 704-707
A1 - P. Kube,
A1 - A. Pentland,
PY - 1988
KW - surface imaging; computerised picture processing; fractal Brownian elevation functions; Lambertian reflectance; Fourier power spectrum; fractional dimension value; computerised picture processing; Fourier transform spectra; fractals
VL - 10
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

An analysis is presented of the imaging of surfaces modeled by fractal Brownian elevation functions of the sort used in computer graphics. It is shown that, if Lambertian reflectance modest surface slopes and the absence of occlusions and self shadowing are assumed, a fractal surface with Fourier power spectrum proportional to f/sup beta / produces an image with power spectrum proportional to f/sup 2- beta /; here, f is the spatial frequency and beta is related to the fractional dimension value. This allows one to use the spectral falloff of the images to predict the fractal dimension of the surface.

[1] A. P. Pentland, "Fractal-based description of natural scenes,"IEEE Trans. Pattern Anal. Machine Intell., vol. 6, no. 6, pp. 661-674, 1984.
[2] R. F. Voss, "Random fractal forgeries," inFundamental Algorithms for Computer Graphics, R. A. Earnshaw, Ed. Berlin: Springer-Verlag, 1985.
[3] A. P. Pentland, "On describing complex surfaces,"Image and Vision Comput., vol. 3, no. 4, pp. 153-162, 1986.
[4] A. Fournier, D. Fussell, and L. Carpenter, "Computer rendering of stochastic models,"Commun. ACM, vol. 25, pp. 371-384, June 1982.
[5] B. B. Mandelbrot and J. W. Van Ness, "Fractional Brownian motions, fractional noises and applications,"SIAM Rev., vol. 10, no. 4, pp. 422-437, 1968.
[6] B. B. Mandelbrot,The Fractal Geometry of Nature. San Francisco, CA: Freeman, 1982.

Index Terms:
surface imaging; computerised picture processing; fractal Brownian elevation functions; Lambertian reflectance; Fourier power spectrum; fractional dimension value; computerised picture processing; Fourier transform spectra; fractals
Citation:
P. Kube, A. Pentland, "On the Imaging of Fractal Surfaces," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 5, pp. 704-707, Sept. 1988, doi:10.1109/34.6779
Usage of this product signifies your acceptance of the Terms of Use.