A measure of closure

In images of real visual scenes, contours are often fragmented by occlusion, shadows and low reflectance contrast. In order to infer shape from contour, the human visual system must selectively integrate fragments projecting from a common object while keeping fragments from different objects separate. In a previous paper we showed that contour closure has a strong influence on the speed of this process. In this paper we employ a visual search method to evaluate potential measures for the perceptual closure of fragmented shapes. We show that while certain intuitive measures are psychophysically inconsistent, a measure based on a sum of squares of the lengths of contour gaps is appropriate for both polygonal and smooth shapes in that response time can be expressed as a function of this measure. This L2 measure is shown to emphasize large gaps relative to small, and to embody a principle of perceptual regularity.