The visual computation of 2-D area by human observers

Normal human observers compared either the width, height or area of two simultaneously-presented shapes (the standard and the test), with a cue to indicate which decision had to be made. On ‘area’ trials, test width was a random variable, ensuring that neither shape (aspect ratio), width nor height by themselves was a reliable signal. Weber fractions for width and height of both ellipses and rectangles were in the range 5–10%, but for area they were higher (10–20%) than predicted from the combination of noisy width and height decisions. With ellipses, observers were more likely to overestimate width or height when the other dimension differed from the standard in the same direction (e.g. both greater). We conclude that observers have no access to high-precision codes for 2-D area, and that they base their decisions on a variety of heuristics derived from 1-D codes. A second experiment measured acuity for changes in aspect ratio. For ellipses, accuracy for aspect ratio was higher than predicted by the combination of noisy width and height signals; for rectangles it was worse, suggesting that 2-D curvature is a potent cue to shape.