Synergy in the multi-local statistics of gradient directions in images

Gestalt psychologists were able to establish a number of qualitative grouping rules which govern human visual perceptions. It is possible that natural image statistics underlie those grouping rules, specifically multi-local statistics. We define multi-local to mean local measurements made simultaneously at multiple locations. To assess whether multi- local interactions occur in natural images we have used information-theoretic methods, specifically interaction information. For example, we have measured triples of gradient directions, and computed the mutual information between a pair of gradient directions, and how the context of a third gradient direction affects that mutual information. If it increases, then measuring triples of gradient directions is synergetic. We find that triples of gradient directions show synergy for all of the following image classes: natural images, their phase randomized and whitened versions and Gaussian noise images. Further, we find that the mean power spectrum of image ensembles determines the dependencies between gradient directions.