Computation of relative numerosity of circular dot textures.

To find out whether there are separate visual mechanisms for size, density, and numerosity computation in textures, we investigated the ability of human observers both to discriminate differences in numerosity between approximately circular textures and to decide whether the differences were due to a change in circle size or dot density. The standard texture always contained 64 irregularly spaced fuzzy dots of random contrast polarity. Dots were added or subtracted from the test pattern either by changing the dot density with the pattern size constant or the pattern size with density constant. Observers had to decide whether size or density had changed and whether the change was an increase or a decrease (mixed task condition). In a separate condition, they reported differences in numerosity (numerosity condition). Numerosity changes were more accurately reported when they were correlated with changes in size than with changes in density, arguing against a single mechanism for numerosity. Observers showed a bias toward reporting larger patterns as denser and vice versa. The data were consistent with a mechanism in which observers compute numerosity from size and density signals and decide whether size or density had changed by the signal detection theory MAX rule after transforming signals into z-values. Because thresholds were not significantly lower in the numerosity condition than in the mixed task condition, we conclude that the direct numerosity mechanism, if it exists, must be noisier than the mechanisms that respond to changes in size and density.