Interaction of disparity size and depth structure on perceived numerosity in a three-dimensional space.

Saori Aida,Koichi Shimono,Yusuke Matsuda,Claudio Mulatti

doi:10.1371/journal.pone.0230847

Saori Aida, Koichi Shimono + Show 2 more

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https://doi.org/10.1371/journal.pone.0230847

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Abstract

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-overlapping-surface 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 stereo-stimulus, and the disparity range within which the interference occurs may depend on the stimulus depth structure.

Highlights

Humans are capable of determining the number of objects that are scattered in front of them rather accurately
The analysis showed that the main effect of the stimulus, F (2, 12) = 2.87, p = 0.10, and that of binocular disparity, F (1, 6) = 0.61, p = 0.46, and their interaction, F (2, 12) = 1.08, p = 0.37, were not statistically significant
We analyzed the 95% confidence interval (95% CI) for the mean bias of each condition as an index of the overestimation phenomenon; when the limit was larger than zero, we regarded that the overestimation of the number of elements on the two-POTS stimulus had occurred

Summary

Introduction

Humans are capable of determining the number of objects that are scattered in front of them rather accurately. The back-surface-bias hypothesis postulates that when elements seen behind in a two-POTS stimulus are perceived as a background surface, the apparent density (or number) of the constituent elements on the background surface increases [19], resulting in a 3-D overestimation phenomenon [17]. The elements in a 2-D stimulus and the background had zero disparity with respect to the monitor plane, and those of a two-POTS and a stepwise stimulus had 6.8 or 12.7 arcmin total disparity. With respect to the monitor plane, the outermost elements had +6.4 and -6.4 arcmin disparities, the middle elements had Interaction of disparity size and depth structure on perceived numerosity in a three-dimensional space zero disparity, and the innermost elements had +3.4 and -3.4 arcmin disparity for the stimulus with 12.7 arcmin total disparity. The positions of the 3-D stimulus elements were manipulated to ensure binocular fusion (see [18, 20, 21])

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Results and discussion