On the lawfulness of grouping by proximity.

The visual system groups close things together. Previous studies of grouping by proximity have failed to measure grouping strength or to assess the effect of configuration. We do both. We reanalyze data from an experiment by Kubovy and Wagemans (1995) in which they briefly presented multi-stable dot patterns that can be perceptually organized into alternative collections of parallel strips of dots, and in which they parametrically varied the distances between dots and the angles between alternative organizations. Our analysis shows that relative strength of grouping into strips of dots of a particular orientation approximates a decreasing exponential function of the relative distance between dots in that orientation. The configural or wholistic properties that were varied--such as angular separations of the alternative organizations and the symmetry properties of the dot pattern--do not matter. Additionally, this grouping function is robust under transformations of scale in space (Experiment 1) and time (Experiment 2). Grouping of units which are themselves the result of grouping (i.e., pairs of dots; Experiment 3) also follows our nonconfigural rule.