Peter A. Freeborough
Dementia Research Group,
National Hospital for Neurology and Neurosurgery,
8-11 Queen Square, London WC1N 3BG, UK
paf@ic.ac.uk
Five methods and three variants for the estimation of texture fractal dimension were assessed according to the degree of correlation between known and estimated fractal dimension when applied to synthetically generated fractional Brownian motion textures. Fourier based estimation correlated significantly more closely with the true fractal dimension than box counting, surface, blanket and spatial correlation methods (p<0.01). Highest correlation (r=0.98) was obtained where tapering was not used and all Fourier coefficients were used equally in the estimation process. However, the results were inconsistent with spectral density of the form f -(b+1) where b=2H+1 and H is the Hurst coefficient; they instead suggested a spectrum of the form f -a where a=4H. Estimation methods based upon an assumption of self-similarity (box counting, surface and blanket methods) performed poorly. Fractal dimension estimation for texture discrimination may best be acheived by Fourier methods; this has implications for the development of more complete fractal texture descriptors.