Abstract

In this paper, a general class of fractional random fields, ℬα, 0≤α<2, is defined. The members of ℬα can be used to model natural scenes and textures. It is shown that the fractal dimension of random fields in ℬα is a linear nonincreasing function of a for 0≤α<α0 and a linear nondecreasing function of α for α0<α<2. The number α0 corresponds to the Hausdorff-Besicovitch dimension of the random field. These linear relationships are significant for texture comparison and classification.

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