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

Local feature extraction in Log-Polar images

We propose two different strategies to compute edges in the log-polar (cortical) domain. The space-variant processing is obtained by applying local operators (e.g. local derivative filters) directly on the logpolar images, or by embedding the same operators into the log-polar mapping, thus obtaining a cortical representation of the Cartesian features. The two approaches have been tested by taking into consideration three standard algorithms for edge detection (Canny, Marr-Hildreth and Harris), applied onto the BSDS500 dataset. Qualitative and quantitative comparisons show a first indication of the validity of the proposed approaches