Synthesis of nonstationary fields with stationary increments

We show that general nonstationary fields with stationary increments can be useful in modeling a great variety of possibly anisotropic textures. The anisotropy in the images is introduced through the structure function, which characterizes the form of the correlation of the increments. It can be defined for any nonstationary field with stationary increments. We propose a method to generate anisotropic self-similar fields with stationary increments, which can be applied as well to other nonstationary fields with stationary increments. This method is a generalization of the incremental Fourier synthesis of the fBm, proposed by Kaplan and Kuo (see IEEE Trans. Image Proc., no.5, p.754-60, 1996). It is based on the use of the structure function to generate the increments, which are then added up to form the nonstationary process. The diversity of the textures generated using this method is connected to the admissible solutions for the structure function. In order to guide the choice of this function, we state some restrictive conditions that must be satisfied and, in the case of self-similar fields, we give its general form