No abstract

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.

Three experiments, using two sets of Nonius lines placed in a random-dot stereogram, indicated that Nonius alignment does not always reflect binocular eye position and, thus, a caveat is necessary when Nonius alignment is used to monitor binocular eye position. We found that: (a) two Nonius lines with visual line values that differed by up to 7.6 min of arc can appear aligned; (b) the two lines of each of the two Nonius sets continued to appear aligned despite a change in vergence angle of 5.9 min of arc; and (c) the Nonius alignment reflected eye position better, when the binocular dots near the Nonius lines were eliminated.

We investigated spatial perception of virtual images that were produced by convex and plane mirrors. In Experiment 1, 36 subjects reproduced both the perceived size and the perceived distance of virtual images for five targets that had been placed at a real distance of 10 or 20 m. In Experiment 2, 30 subjects verbally judged both the perceived size and the perceived distance of virtual images for five targets that were placed at each of five real distances of 2.5 -45 m. In both experiments, the subjects received objective-size and objective-distance instructions. The results were that (1) size constancy was attained for a distance of up to 45 m, (2) distance was readily discriminated within this distance range, although virtual images produced by the mirror of strong curvature were judged to be farther away than those produced by the mirrors of less curvature, and (3) the ratio of perceived size to perceived distance was described as a power function of visual angle, and the ratio for the convex mirror was larger than that for the plane mirror. We compared the taking-into-account model and the direct perception model on the basis of a correlation analysis for proximal, virtual, and real levels of the stimuli. The taking-into-account model, which assumes that visual angle is transformed into perceived size by taking perceived distance into account, was supported by an analysis for the proximal level of stimuli. The direct perception model, which assumes that there is no inferential process between perceived size and perceived distance, was partially supported by an analysis for the distal level of the stimuli.

The number of elements in two stereo-surfaces parallelly overlapped in depth is overestimated compared to that in a single flat surface, even when both have the same number of elements. Using stereoscopic pairs of elements, we evaluated two hypotheses on the overestimation: one that a higher-order process, forming a background surface, increases the number of perceived elements, and the other that the number of elements potentially occluded by the elements on a front surface is taken accounted for. The data from four experiments showed that (a) when binocular disparity between (or among) stereoscopic elements was small, the overestimation occurred for the stimuli we used-a two-surface-overlapping stimulus, where the likelihood for the process to operate was manipulated by changing the averaged luminance of each surface, a volumetric stimulus, where the likelihood for the background surface to be formed would decrease, and a two-non-overlappingsurface stimulus, where the surfaces in depth were not overlapped-, and (b) when binocular disparity was large, the overestimation occurred for the two-surfaces-overlapping stimulus, when the averaged luminance of the two surfaces were the same, and for the volumetric stimulus, but diminished for the surface-overlapping stimulus, when the averaged luminance differed between the surfaces and for the surfaces-non-overlapping stimulus. These results cannot be explained either hypothesis only. We explain the results by postulating that the sensory system processing disparities of elements interferes with that estimating the number of elements, resulting in an overestimation of the elements in a stereostimulus, and the disparity range within which the interference occurs may depend on the stimulus depth structure.