Perceptual Completion Behind Occluders: The Role of Convexity

An important problem in perceptual organization is to determine whether two image regions belong to the same object. In this chapter, we consider the situation when two image regions potentially group into a single object behind a common occluder. We study the extent to which two image regions are grouped more strongly than two other image regions. Existing theories in both human and computer vision have mainly emphasized the role of good continuation. Namely, the shorter and smoother the completing contours are between two image regions, the stronger the grouping will be. In contrast, Jacobs [3] has proposed a theory that considers relative positions and orientations of two image regions. For instance, the theory predicts that two image regions that can be linked by convex completing contours are grouped more strongly than those that can only be linked by concave completing contours, even though the completing contours are identical in shape. We present, in addition to our previous work (Liu, Jacobs, and Basri, 1999), human psychophysical evidence that concurs with the predictions of this theory and suggests an important role of convexity in perceptual grouping.