Comparison of human performance with algorithms for estimating fractal dimension of fractional Brownian statistics

Abstract

Five standard methods for estimating fractal dimension were compared by means of one-dimensional fractional Brownian series generated by four different algorithms yielding series with different statistics. The same one-dimensional series were also displayed as jagged lines and as one-dimensional luminance patterns for judgments by human observers. Only the algorithm implementing the maximum-likelihood method, which required that the generation statistic for the fractal series be known, gave better performance than human observers in estimating fractal dimension. However, when the method of generation is not known, one of the four other standard methods for estimating fractal dimension must be used, and these performed significantly worse than human observers.