Synthesis of Stochastic Images with Given Fractal Dimension

Synthesis methods based on spatial-frequency filtering have been developed for fractal images for which the structure functions are power laws over a wide range of increments which is about one-quarter of the image size. It is shown that, using theWeierstrass function, only stationary processes (images) can be simulated. An algorithm for modeling fractional Brownian images is proposed and studied. It is established that the integral characteristic of the spectrum of a Brownian image with the Hurst parameter alpha is well approximated by a power function with an exponent 2 is an element of (alpha + 1) for alpha is an element of(0, 1/2] and an exponent of 3 for ff 2 (1/2, 1). Using as an examples modifications of images of samples of amorphous alloys, it is shown that statistically self-similarity images little different from the original image can be simulated. This allows one to determine to what extent the structures visualized in the images exhibit fractal properties.