The whole is equal to the sum of its parts: a probabilistic model of grouping by proximity and similarity in regular patterns

The authors investigated whether the gestalt grouping principles can be quantified and whether the conjoint effects of two grouping principles operating at the same time on the same stimuli differ from the sum of their individual effects. After reviewing earlier attempts to discover how grouping principles interact, they developed a probabilistic model of grouping by proximity, which allows measurement of strength on a ratio scale. Then, in 3 experiments using dot lattices, they showed that the strength of the conjoint effect of 2 grouping principles--grouping by proximity and grouping by similarity--is equal to the sum of their separate effects. They propose a physiologically plausible model of this law.