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On the Imaging of Fractal Surfaces
September 1988 (vol. 10 no. 5)
pp. 704-707

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.

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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
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
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