Numerosity Comparison in Three Dimensions in the Case of Low Numerical Values

Effect of 3-D depth structure, element size, and area containing elements on total-element overestimation phenomenon

The number of elements distributed in a three-dimensional stimulus is overestimated compared to a two-dimensional stimulus when both stimuli have the same number of elements. We examined the effect of the properties of a three-dimensional stimulus (the number of overlapping stereo surfaces, size of the elements, and size of the area containing elements, on the overestimation phenomenon in four experiments. The two stimuli were presented side-by-side with the same diameters. Observers judged which of the three-dimensional standard and two-dimensional comparison had more elements. The results showed that (a) the overestimation phenomenon occurred for the three-dimensional standard stimuli, (b) the size of the areas affected the amount of overestimation, while the number of overlapping stereo surfaces and size of elements did not, and (c) the amount of overestimation increased when the stimuli included more than 100 elements. Implications of these findings were discussed in the framework of back-surface bias, occlusion, and disparity-processing interference models.