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 field 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 disparity sensitivity in man. Our findings support the notion that our foveated, binocular visual system has been moulded by the statistics of our visual environment.\n\nAuthor summaryWe investigate how humans perceive depth from binocular disparity at different spatial scales and across different regions of the visual field. We show that small changes in disparity-defined depth are detected best in central vision, whereas peripheral vision best captures the coarser structure of the environment. We also demonstrate that depth information extracted from different regions of the visual field is combined into a unified depth percept. We then construct an image-computable model of disparity processing that takes into account how our brain organizes the visual input at our retinae. The model operates directly in cortical image space, and neatly accounts for human depth perception across the visual field.