The Earth’s topography generally obeys fractal statistics; after either one- or two-dimensional Fourier transforms the amplitudes have a power-law dependence on wave number. The slope gives the fractal dimension, and the unit wave-number amplitude is a measure of the roughness. In this study, digitized topography for the state of Oregon (~7 points/km) has been used to obtain maps of fractal dimension and roughness amplitude. The roughness amplitude correlates well with variations in relief and is a promising parameter for the quantitative classification of landforms. The spatial variations in fractal dimension are low and show no clear correlation with different tectonic settings. For Oregon the mean fractal dimension from a two-dimensional spectral analysis is D = 2.586, and for a one-dimensional spectral analysis the mean fractal dimension is D = 1.487, which is close to the Brown noise value D = 1.5. Synthetic two-dimensional images have also been generated for a range of values. For D = 2.6, the synthetic image has a mean one-dimensional spectral fractal dimension D = 1.58, which is consistent with our results for Oregon. This approach can be easily applied to any digitized image that obeys fractal statistics.
© 1990 Optical Society of America
Jie Huang and Donald L. Turcotte, "Fractal image analysis: application to the topography of Oregon and synthetic images," J. Opt. Soc. Am. A 7, 1124-1130 (1990)