The computation of relative numerosity, size and density

- Observers could accurately discriminate dot number in irregularly shaped arrays.
- Accuracy was less than that previously reported for regular shaped arrays.
- Observers could discriminate changes of dot density from changes in array size.
- Results are consistent with a computation of number from size and density.

To investigate the mechanisms for the perception of relative numerosity, we used two-interval forced-choice (temporal 2AFC) to measure thresholds for area, density and numerosity differences between dot textures, and a 2 × 2 FC task to measure the ability of observers to distinguish changes in area from changes in density. To prevent the use of a one-dimensional size signal we used textures in which dots were scattered within irregular polygonal areas. Numerosity thresholds were similar in the area and density-varying conditions, consistent with a single numerosity mechanism. Thresholds for area and density discriminations were raised when number was held constant, consistent with numerosity thresholds being lower than those for size and density. Also, area thresholds for polygonal outlines were increased when no dots were present in the outline. However, a single numerosity mechanism cannot account for all the data, because we find that observers in randomly-interleaved size-varying and density-varying conditions are also able to discriminate between changes in size and density with a precision predicted from independently-noisy size and density channels that have similar noise to that in the putative numerosity channel. A complication, previously noted with circular shapes, is that denser textures tend to be confused with larger textures, and vice versa. This could explain why thresholds rise when density and size changes are in opposition, in the constant-number case. These findings taken together do not rule out an independent numerosity mechanism, but they are equally compatible with a flexible computation of numerosity from size and density cues.