Overestimation of the number of elements in a three-dimensional stimulus

Observers' numerosity judgments in binocular stereopsis were examined in four experiments, using random-dot stereograms (RDSs) that depicted a two-dimensional (2-D) stimulus side-by-side with a three-dimensional (3-D) stimulus. When the RDSs were correctly fused, a single surface and two (or three) transparent surfaces were observed for the 2-D and 3-D stimuli, respectively. Observers completed a numerosity discrimination task, where they judged which of the two stimuli had a greater number of dot elements. Results showed that (a) the 3-D stimulus was judged to contain more elements than the 2-D stimulus, even when both had the same number of elements, (b) the amount of overestimation increased as a function of the number of elements and the binocular disparity between the front and back surfaces of the 3-D stimulus, (c) the ratio of the physical number of elements in the front surface to that in the back surface of the 3-D stimulus had no effect on the magnitude of overestimation, and (d) when the number of elements for the two surfaces were judged separately, the ratio had more effect on the judged number of elements in the back surface than in the front surface. These results indicate that the extent of overestimation in the numerosity judgment of a set of elements in a stimulus depends on the number of depth layers in which the elements are embedded.