Discrimination of natural homogeneous textures based on fractal models

This paper describes and discusses fractal models and features closely related with the needs of practical applications, specially those implemented through low computational costs algorithms, Two kind of models will be described: one is based on the transformation by autocorrelation of fractional Brownian models: another kind relies on box counting measurements, The first one relates short range values of the image's autocorrelation function with local Hausdorff dimension thus allowing the estimation of the fractal dimension of microtextures; the second is based on density distribution probability of the image's pixels lying inside boxes of variable sizes, L, in order to equate the fractal dimension as a linear relationship between the logarithms of the number of boxes and of their sizes (-log L). A feature describing the fractal mass, the lacunarity, is defined and algorithms implemented to show their discrimination power, Experimental results were obtained by using training and test sets images captured from paper sheets and cork agglomerate. Texture was estimated by our fractal dimension and lacunarity methods. Results were discussed and assessed through the goodness-of-fitting between the predicted model and the observed data by using the K-S (Kolmogorov-Smirnov) test statistic.