two-dimensional fractional Brownian motion
total measurement error
rating estimation system
In the paper the questions of fractal dimension measurement with different methods and comparative analysis of methods with respect to estimation accuracy and time complexity, depending on observation window size, given fractal dimension and simulating algorithms of fractal surface, are considered.
Twelve most common estimation methods to measure fractal dimension are used: Box counting, Triangular prism, Variogram, Isorithm, Power spectrum, Walking divider, Probability, Blanket, Pentland’s, Directional dimension, Information dimension and Correlation dimension.
Comparative analysis of methods is based on a stochastic fractal reflected surface model – the two-dimensional fractional Brownian motion. Realizations of the model are obtained using the following simulation algorithms: sequential random addi-tion algorithm, midpoint displacement algorithm and fractal Fourier-filtering algorithm.
Statistical estimates of mean, variance, standard deviation, and total fractal dimension measurement error of methods de-pending upon observation window size, given fractal dimension and simulating algorithms of fractal surface are calculated. Comparative analysis of discussed methods based on suggested rating estimation system is carried out. The best of considered methods is found – directional fractal dimension method.