Points and Endpoints: A Size/Spacing Constraint for Dot Grouping

Abstract

One-dimensional arrangements of dots immediately group into contours. It is reported that, when these contours participate in certain larger arrangements, there is an abrupt point at which the percept changes as a function of dot spacing (or density along the contour). Closely spaced arrangements give rise to subjective effects involving apparent brightness and depth, whereas sparsely spaced ones do not. The effects are most clear in configurations that involve endpoints and possible occlusions. For these configurations, densely dotted contours are perceptually equivalent to solid ones, but sparse ones are not. This change in percept occurs abruptly and consistently at a dot to space ratio of 1:5, when the dot density is normalized by dot size, and this point is called the size/spacing constraint. It holds only for dots of the order of 1 min visual angle in diameter when small to modest contrast values are used. The subjective effects are not present for dotted contours (or even for solid ones) that are smaller (<0.5 min), and differ for contours that are larger (> 10 min). To demonstrate the significance of size/spacing constraints for early vision, a framework for grouping consisting of processes at many different levels is outlined, and the requirements for the earliest one (orientation selection) are sketched in greater detail. The size/spacing constraint follows directly from one of these requirements—receptive field structure—and seems to indicate a switch from early orientation-selection processes to later ones.