Our perceptual systems have evolved to operate in the natural environment, and thus if we are to understand the design of our perceptual systems it is crucial to measure the statistical properties of natural stimuli. A major thrust of the research in my lab is concerned with measuring the statistical properties of natural images. For example, one project has been concerned with measuring the statistics of natural images that are relevant for contour grouping (Geisler, Perry, Super & Gallogly, 2001). To do this we first extract edge elements from natural images using image-processing techniques consistent with response properties of neurons in primary visual cortex. From these extracted elements we measure the probability of each possible geometrical relationship between edge elements (d,φ,θ) where d is the distance between the elements, φ is the direction of one element relative to the other, and θ is the orientation of one element relative to the other. We measure these probabilities for elements that belong to the same physical contour, p(d,φ,θ | C), and for elements that belong to different physical contours, p(d,φ,θ | ~C). Taking the ratio of these two conditional distributions gives the likelihood ratio distribution shown in the figure below. The center horizontal line segment in this plot represents one edge element (the reference) and every other line segment in the plot (there are 7776) represents a second edge element in one of the possible geometrical relationships with the reference. The distance of an element from the center of the diagram represents the distance between the element and the reference, the location of an element around the circle represents the direction of the element from the reference, and the orientation of an element at a given location indicates the orientation of the element with respect to the reference. The color of an element indicates the likelihood ratio that the element and the reference element belong to the physical contour (i.e., arise from the same physical source in the environment). The greater is the likelihood ratio the greater is the probability that the two elements belong to the same physical contour. As can be seen, edge elements that are co-circular (consistent with a smooth continuous contour) are more likely to have arisen from the same physical contour. These results show that the Gestalt principle of “good continuation” has a general basis in the statistics of the natural world.