Segmentation of textures with different roughness using the model of isotropic two-dimensional fractional Brownian motion

An attempt is made to apply a novel multidirectional resolution analysis to obtain boundaries between areas with different grades of ´roughness´. To this end, the image texture is parametrized with respect to direction, based on the model of isotropic 2-D fractional Brownian motion (2-D FBM). Some theoretical aspects of this model have not been clarified yet. The authors first provide some of the crucial missing links in the theory of 2-D FBM and present a concrete realization of this stochastic process. They then describe the segmentation procedure in detail. First, they present a suboptimal but fast estimation algorithm to obtain angle-dependent fractal parameter subimages, and compare its performance with the Cramer-Rao bound. They then apply matched edge-detection procedures to each subimage separately, and combine the angle-dependent boundary pixels to obtain the texture boundaries of the entire scene.<>