Local image statistics have a perceptual metric that is nearly Euclidean

Abstract

Natural scenes have an intricate statistical structure, including correlations of low and high orders that covary in a complex way. Thus, while the function of the visual system is best understood in the context of its natural inputs, it can be difficult to move from experiments that study responses to naturalistic inputs, to computational models that analyze how these responses arise. This motivated us to develop stimulus sets that abstract the statistics in natural scenes, and enable testing their effects individually and in combination. To reduce the dimensionality of the problem, we focus on binarized images. Following the findings of Tkacik et al. (2010), we restrict consideration to configurations of pixels in 2x2 neighborhoods, as this typifies the informative local image statistics. The 16 possible configurations within these neighborhoods are completely described by 10 image statistics, which thus form the coordinates of a perceptual space. We use a 4-AFC segmentation task to characterize human visual sensitivity to these 10 image statistics, alone and in combination. Results show that sensitivity to individual statistics is highly consistent across N=12 subjects (including naïve and experienced observers), as is sensitivity to pairwise interactions (N=6). In 4 subjects, we determined the perceptual metric in the entire 10-dimensional space. The metric is very close (~5% RMSE) to Euclidean. Moreover, the deviations from a Euclidean metric, though small, are conserved across subjects. These deviations are of two types: (i) an asymmetry between sensitivity to positive and negative variations of even-order statistics, and (ii) a unique interaction between specific pairwise statistics. (i) may reflect interactions across spatial scale, and (ii) may reflect a special role for corners. In sum, the informative statistics of natural images map out an orderly perceptual space, with simple, conserved rules for how individual statistics of low and high order combine. Meeting abstract presented at VSS 2012