Proximity model of perceived numerosity

Abstract

The occupancy model (OM) was proposed to explain how the spatial arrangement of dots in sparse random patterns affects their perceived numerosity. The model's central thesis maintained that each dot seemingly fills or occupies its surrounding area within a fixed radius r_o and the total area collectively occupied by all the dots determines their apparent number. Because the perceptual system is not adapted for the precise estimation of area, it looks likely that the OM is just a convenient computational algorithm that does not necessarily correspond to the processes that actually take place in the perceptual system. As an alternative, the proximity model (PM) was proposed, which instead relies on a binomial function with the probability β characterizing the perceptual salience with which each element can be registered by the perceptual system. It was also assumed that the magnitude of β is proportional to the distance between a dot and its nearest neighbor. A simulation experiment demonstrated that the occupancy area computed according to the OM can almost perfectly be replicated by the mean nearest neighbor distance. It was concluded that proximity between elements is a critical factor in determining their perceived numerosity, but the exact algorithm that is used for the measure of proximities is yet to be established.

Keywords: Nearest neighbor distance; Numerosity illusions; Perceived number; Spatial statistics; The occupancy model; Visual crowding.