The space of visual signals is high-dimensional and natural visual images have a highly complex statistical structure. While many studies suggest that only a limited number of image statistics are used for perceptual judgments, a full understanding of visual function requires analysis not only of the impact of individual image statistics, but also, how they interact. In natural images, these statistical elements (luminance distributions, correlations of low and high order, edges, occlusions, etc.) are intermixed, and their effects are difficult to disentangle. Thus, there is a need for construction of stimuli in which one or more statistical elements are introduced in a controlled fashion, so that their individual and joint contributions can be analyzed. With this as motivation, we present algorithms to construct synthetic images in which local image statistics—including luminance distributions, pair-wise correlations, and higher-order correlations—are explicitly specified and all other statistics are determined implicitly by maximum-entropy. We then apply this approach to measure the sensitivity of the human visual system to local image statistics and to sample their interactions.