A measure for spatial dependence in natural stochastic textures

Random textures differ from natural textures because they lack structure. Structure is a concept that is difficult to formalize, but we generally observe that it is associated with spatial dependence between adjacent pixels. Completely random textures, in fact, are characterized by independent pixels, while natural textures show some local dependence. In this paper, we propose a measure for such local dependence. The texture is scanned on a random walk path and the pixels values encountered are collected in form of a time-series. The statistical properties of the time-series are used to characterize the spatial dependence of the texture. We assume that the proposed measure can be used to help the model textures, to set the size of operating windows in texture synthesis algorithms, and to compute a simple indicator of texture scale. Moreover, we show how the measure can be linked to texture perception.