Similar mechanisms underlie the detection of horizontal and vertical disparity corrugations

Near-optimal combination of disparity across a log-polar scaled visual field

The human visual system is foveated: we can see fine spatial details in central vision, whereas resolution is poor in our peripheral visual field, and this loss of resolution follows an approximately logarithmic decrease. Additionally, our brain organizes visual input in polar coordinates. Therefore, the image projection occurring between retina and primary visual cortex can be mathematically described by the log-polar transform. Here, we test and model how this space-variant visual processing affects how we process binocular disparity, a key component of human depth perception. We observe that the fovea preferentially processes disparities at fine spatial scales, whereas the visual periphery is tuned for coarse spatial scales, in line with the naturally occurring distributions of depths and disparities in the real-world. We further show that the visual system integrates disparity information across the visual field, in a near-optimal fashion. We develop a foveated, log-polar model that mimics the processing of depth information in primary visual cortex and that can process disparity directly in the cortical domain representation. This model takes real images as input and recreates the observed topography of human disparity sensitivity. Our findings support the notion that our foveated, binocular visual system has been moulded by the statistics of our visual environment.

Thresholds for sine-wave corrugations defined by binocular disparity in random dot stereograms: Factor analysis of individual differences reveals two stereoscopic mechanisms tuned for spatial frequency

Threshold functions for sinusoidal depth corrugations typically reach their minimum (highest sensitivity) at spatial frequencies of 0.2-0.4 cycles/degree (cpd), with lower thresholds for horizontal than vertical corrugations at low spatial frequencies. To elucidate spatial frequency and orientation tuning of stereoscopic mechanisms, we measured the disparity sensitivity functions, and used factor analytic techniques to estimate the existence of independent underlying stereo channels. The data set (N = 30 individuals) was for horizontal and vertical corrugations of spatial frequencies ranging from 0.1 to 1.6 cpd. A principal component analysis of disparity sensitivities (log-arcsec) revealed that two significant factors accounted for 70% of the variability. Following Varimax rotation to approximate "simple structure", one factor clearly loaded onto low spatial frequencies (≤0.4 cpd), and a second was tuned to higher spatial frequencies (≥0.8 cpd). Each factor had nearly identical tuning (loadings) for horizontal and vertical patterns. The finding of separate factors for low and high spatial frequencies is consistent with previous studies. The failure to find separate factors for horizontal and vertical corrugations is somewhat surprising because the neuronal mechanisms are believed to be different. Following an oblique rotation (Direct Oblimin), the two factors correlated significantly, suggesting some interdependence rather than full independence between the two factors.

Characterization of Spatial Frequency Channels Underlying Disparity Sensitivity by Factor Analysis of Population Data

It has been suggested that at least two mechanisms mediate disparity processing, one for coarse and one for fine disparities. Here we analyze individual differences in our previously measured normative dataset on the disparity sensitivity as a function of spatial frequency of 61 observers to assess the tuning of the spatial frequency channels underlying disparity sensitivity for oblique corrugations (Reynaud et al., 2015). Inter-correlations and factor analysis of the population data revealed two spatial frequency channels for disparity sensitivity: one tuned to high spatial frequencies and one tuned to low spatial frequencies. Our results confirm that disparity is encoded by spatial frequency channels of different sensitivities tuned to different ranges of corrugation frequencies.

The Stereoscopic Anisotropy Develops During Childhood

Purpose

Human vision has a puzzling stereoscopic anisotropy: horizontal depth corrugations are easier to detect than vertical depth corrugations. To date, little is known about the function or the underlying mechanism responsible for this anisotropy. Here, we aim to find out whether this anisotropy is independent of age. To answer this, we compare detection thresholds for horizontal and vertical depth corrugations as a function of age.

Methods

The depth corrugations were defined solely by the horizontal disparity of random dot patterns. The disparities depicted a horizontal or vertical sinusoidal depth corrugation of spatial frequency 0.1 cyc/deg. Detection thresholds were obtained using Bayesian adaptive staircases from a total of 159 subjects aged from 3 to 73 years. For each participant we computed the anisotropy index, defined as the log₁₀-ratio of the detection threshold for vertical corrugations divided by that for horizontal.

Results

Anisotropy index was highly variable between individuals but was positive in 87% of the participants. There was a significant correlation between anisotropy index and log-age (r = 0.21, P = 0.008) mainly driven by a significant difference between children and adults. In 67 children aged 3 to 13 years, the mean anisotropy index was 0.34 ± 0.38 (mean ± SD, meaning that vertical thresholds were on average 2.2 times the horizontal ones), compared with 0.59 ± 0.55 in 84 adults aged 18 to 73 years (vertical 3.9 times horizontal). This was mainly driven by a decline in the sensitivity to vertical corrugations. Children had poorer stereoacuity than adults, but had similar sensitivity to adults for horizontal corrugations and were actually more sensitive than adults to vertical corrugations.

Conclusions

The fact that adults show stronger stereo anisotropy than children raises the possibility that visual experience plays a critical role in developing and strengthening the stereo anisotropy.

A normative dataset on human global stereopsis using the quick Disparity Sensitivity Function (qDSF)

Global stereopsis results from the lateral displacement of distributed textured elements between the eyes. In this study, we investigate how the key parameters of the disparity sensitivity function such as its peak sensitivity and spatial bandwidth are distributed across a pool of normal observers and how large the individual differences are. For this purpose, we adapted the quick Contrast Sensitivity Function (qCSF, Lesmes et al., 2010) to the quick Disparity Sensitivity Function (qDSF). We show that this new method is accurate and allows a rapid measurement of disparity sensitivity for a range of different disparity spatial frequencies. Our results confirm that there is a greater variability in human disparity sensitivity tuning compared to other common visual features, for example, 1st or 2nd order contrast sensitivity.