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Results

Generated and estimated fractal dimensions are compared in fig. 1, and the corresponding correlation coefficients are given in table 1.

Figure 1: A comparison of 8 methods (a-h) for the estimation of fractal dimension (D). Each plot compares the estimated D with generated D where a given method has been applied to 101 samples of 25x25 textures generated with fractal dimensions 2.00, 2.01, 2.02 ... 3.00.

r r r p
Sparial Correlation 0.890 0.891
Fourier 0.980 0.982
Tapered Fourier 0.919 0.958
Ring Fourier 0.868 0.873
Box Count 0.837 0.835
Surface Area 0.860 0.858
Modified Blanket 0.834 0.836
Blanket 0.618 0.632

Table 1: Product-moment (r p ) and rank (r r ) correlation coefficients between estimated and generated fractal dimension for the 8 estimation methods

Similarly, the correlation coefficients for the self-similar estimation methods applied to the samples with re-scaled intensity range are shown in table 2.

r r r p
Box Count 0.000 0.000
Surface Area 0.860 0.858
Modified Blanket 0.755 0.769

Table 2: Product-moment (r p ) and rank (r r ) correlation coefficients between estimated and generated fractal dimension for the self-similar estimators when applied to intensity re-scaled textures



Next: Discussion Up: A Comparison of Fractal Previous: Experimental Methods