The random cuts method was used over a (25x25) image matrix with 10,000 iterations; displacement of each cut from the centre of the grid was taken from a uniform distribution over [-125,125]. A total of 101 texture samples with H = {0.00, 0.01, 0.02 .. 1.00} were generated. The fractal dimension was estimated for each sample using the 5 different methods and the 3 variants. Prior to estimation the pixel intensity of each sample was linearly scaled to the range 0 to 65535 for the self-affine estimation methods (i.e. spatial correlation and Fourier) and to the range 0 to 25 for the self-similar estimation methods (i.e. box counting, surface, blanket).
To assess the effect of intensity scaling on the self-similar estimations methods (i.e. box counting, surface and modified blanket estimators) the previous experiment was repeated for these estimators having scaled pixel intensity to the range 0 to 65535.
For all estimators the product-moment and rank correlation coefficients (r p and r r respectively) of generated and estimated fractal dimensions were calculated. Difference in correlation was tested for statistical significance on the basis that Z=0.5ln((1+r)/(1-r)) is normally distributed with variance 1/(n-3), where r is the correlation coefficient and n is the sample size.