Theory of texture discrimination of based on higher-order perturbations in individual texture samples

This analysis addresses the issue that texture properties are defined on ensembles of possible textures, while psychophysical judgments of texture properties must be made on individual texture samples, or regions of uniform texture within a larger texture field. Since the basic discrimination task requires comparison of two sample images (or regions) specified by different ensemble rules, the viewer is thus required to compare the estimates of their ensemble statistics of single textures. This paper develops a theory of texture discrimination incorporating a roving local sampling window that allows the visual system to derive an estimate of the ensemble statistics over the window from any particular texture image, without the need to present multiple samples for evaluation. This approach to texture explains how we can have a clear sense that two patterns derive from different statistical generation rules even though we see only one example of each type. In providing the theoretical basis for texture discrimination of individual samples, this analysis goes beyond previous work to account for our intuitive sense that we can estimate the generation rule underlying particular textures. It also analyzes the decision process for discriminating texture boundaries in extended images, defining a novel "Gregorian attractor" that replaces and extends standard Bayesian decision rules.