Wednesday, March 21, 2007

Directional evaluation of fractal dimension using Power Spectrum Method

Power spectrum algorithm, based on J. Russ book [1] divided 2D power spectrum of an imput image into 'slices' which represent directions and frequencies as show below:
For example one can divide power spectrum i to 24 radial slices i.e. one slice is 15 degrees (24*15=360) and slice is divided to 30 frequencies (30 rings). The greater radius of the ring, the bigger frequency.
Apart from directional fractal dimension evaluation, algorithm performs overall fractal dimension analysis by 'averaging by circles'. In this case power spectrum is divided to 60 (2*30) rings:

In addition, vertical and horizontal direction are not considered in the computation as to avoid border effects.

[1]John C. Russ, Fractal Surfaces, 1994

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