Perceived numerosity of spatiotemporal events.

Numerosity discrimination was examined when items were varied in space-time position rather than in space only. Observers were instructed to indicate which of two adjacent streams of visual events contained more items. The precision of numerosity discrimination of dynamic events was not remarkably different from that of static patterns. Two basic numerosity biases previously found for static dot patterns--inhibitory overestimation and satellite underestimation--were demonstrated for items distributed randomly over a spatiotemporal interval. It was also demonstrated that two streams, equated in the number and luminous energy of items, are not judged equal in their visible number if items in one of these two streams have longer duration than items in the second stream. These findings can be accounted for by the occupancy model of perceived numerosity (Allik & Tuulmets, 1991a) if it is supposed that the impact that each element has on its neighborhood is spread along both spatial and temporal coordinates. Perceived numerosity decreases with both spatial and temporal proximity between the visual items. Space and time have interchangeable effects on perceived numerosity: the amount of numerosity bias caused by the spatial proximity of items can also be produced by the properly chosen temporal proximity of items.

Occupancy model of perceived numerosity.

Observers saw 234 different pairs of stochastically organized dot patterns and indicated which of the two patterns appeared to be more numerous. All of the data can be accounted for by supposing that the choice of the more numerous pattern is based on the determination of the occupancy indices of both patterns. Each dot is posited to have an impact upon its neighborhood in a constant occupancy radius R. The area of the stimulus plane occupied collectively by all dots provides a basis for judging relative numerosity; the pattern with the larger occupancy value is chosen as more numerous. The occupancy model, besides providing a general explanation of known numerosity illusions in strictly quantitative terms, can explain some puzzling aspects of numerosity perception.

Size invariance in visual number discrimination.

This study deals with the observer's ability to discriminate the numerosity of two random dot-patterns irrespective of their relative size. One of these two patterns was a reference one that was always composed of 32 dots randomly distributed within a K x K invisible square window (K = 1.92 degrees). The second one was the test pattern with one of the five magnifications (K = 0.64 degrees, 1.28 degrees, 1.92 degrees, 2.56 degrees, 3.20 degrees) and the relative number of dots varied on 11 levels (N = -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, or 15 dots). The observer's task was to indicate which of the two patterns contained more dots. The results show that the stimulus size, as an irrelevant stimulus attribute, can be ignored in the judgements about relative numerosity. This means that the perceived numerosity is size invariant, at least for a 1.6-times magnification and a 3-times reduction of the test pattern. The size invariance observed constrains the range of potential models, since the perceived numerosity can be identified only by means of a feature of the stimulus that will remain invariant after any change in the absolute stimulus size.