A CODE model bridging crowding in sparse and dense displays

Visual crowding is arguably the strongest limitation imposed on extrafoveal vision, and is a relatively well-understood phenomenon. However, most investigations and theories are based on sparse displays consisting of a target and at most a handful of flanker objects. Recent findings suggest that the laws thought to govern crowding may not hold for densely cluttered displays, and that grouping and nearest neighbour effects may be more important. Here we present a computational model that accounts for crowding effects in both sparse and dense displays. The model is an adaptation and extension of an earlier model that has previously successfully accounted for spatial clustering, numerosity and object-based attention phenomena. Our model combines grouping by proximity and similarity with a nearest neighbour rule, and defines crowding as the extent to which target and flankers fail to segment. We show that when the model is optimized for explaining crowding phenomena in classic, sparse displays, it also does a good job in capturing novel crowding patterns in dense displays, in both existing and new data sets. The model thus ties together different principles governing crowding, specifically Bouma's law, grouping, and nearest neighbour similarity effects.