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Binocular viewing geometry shapes the neural representation of the dynamic three-dimensional environment


Sensory signals give rise to patterns of neural activity, which the brain uses to infer properties of the environment. For the visual system, considerable work has focused on the representation of frontoparallel stimulus features and binocular disparities. However, inferring the properties of the physical environment from retinal stimulation is a distinct and more challenging computational problem—this is what the brain must actually accomplish to support perception and action. Here we develop a computational model that incorporates projective geometry, mapping the three-dimensional (3D) environment onto the two retinae. We demonstrate that this mapping fundamentally shapes the tuning of cortical neurons and corresponding aspects of perception. For 3D motion, the model explains the strikingly non-canonical tuning present in existing electrophysiological data and distinctive patterns of perceptual errors evident in human behavior. Decoding the world from cortical activity is strongly affected by the geometry that links the environment to the sensory epithelium.

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Fig. 1: MT neurons exhibit an atypical ‘terraced’ tuning structure for environmental velocities in 3D.
Fig. 2: An encoding model that incorporates the environment-to-retina geometry of 3D motion predicts atypical structures for binocular 3D motion tuning curves.
Fig. 3: A 3D model decoder successfully estimates the 3D direction of motion, but the resulting pattern of estimates is distinct from an idealized Gaussian (von Mises) model.
Fig. 4: Model estimates of the direction of 3D motion change with viewing distance, resulting in surprising model errors at far viewing distances.
Fig. 5: Systematic biases for towards or away motion emerge with increased viewing distances.
Fig. 6: Human performance on a 3D motion direction estimation task matches model observer performance.
Fig. 7: Subtle tuning differences across the two eyes enable the towards-versus-away aspect of decoding for the direction of 3D motion.

Data and code availability

The modeling code and simulations, and the human psychophysical data and analysis, are available here:


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This research was funded by the National Eye Institute at the National Institutes of Health (EY020592, to L.K.C., A.C.H., and A.K.), the National Science Foundation (DGE-1110007, to K.B.), the Harrington Fellowship program (to K.B.), and the National Institutes of Health (T32 EY21462-6, to T.B.C. and J.A.W.). Special thanks to J. Fulvio (University of Wisconsin) and B. Rokers (New York University, Abu Dhabi) for many insightful conversations and for sharing their psychophysical data early on in this project. We thank J. Kaas (Vanderbilt University) for dispensation in referring to ‘MT’ instead of ‘middle temporal area’.

Author information

Authors and Affiliations



T.C. and A.K. collected the electrophysiology data. K.B., L.K.C. and A.C.H. built the computational model. K.B., T.C., A.K, A.C.H. and L.K.C. interpreted the results from electrophysiology and modeling. K.B., A.C.H. and L.K.C. designed the human psychophysical experiments. K.B. and J.A.W. collected the human psychophysical data. K.B., J.A.W., A.C.H. and L.K.C. performed the analysis and interpreted the results. K.B., L.K.C. and A.C.H. wrote the paper. K.B., T.C., J.A.W., A.K., A.C.H. and L.K.C. edited the paper.

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Correspondence to Kathryn Bonnen.

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The authors declare no competing interests.

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Peer review information Nature Neuroscience thanks Gregory DeAngelis, Anthony Norcia, and Jenny Read for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figures 1–6 and Supplementary Video Captions 1 and 2.

Reporting Summary

Supplementary Video 1

Example motion cloud stimuli for free-fusing. These examples are high-contrast versions of the stimulus shown to subjects during our experiments. The spherical motion volume is shown up and to the right of fixation for more comfortable free-fusing but would be directly left or right of fixation in the actual experiment. This video shows eight motion epochs (0°, 45°, 90°, 135°, 180°, 225°, 270° and 315°).

Supplementary Video 2

Example motion cloud stimuli rendered in 2D with shading to simulate the binocular stimuli used in the experiment. This video is a 2D version of the stimulus rendered with shading on the dots to give a stronger sense of the depth percept. These example motion stimuli are high-contrast versions of the stimuli shown to subjects during our experiments. This video shows eight motion epochs (0°, 45°, 90°, 135°, 180°, 225°, 270° and 315°). An example of the motion indicator used during the experiment is shown below the stimulus and points in the direction of the motion. Additional indicator dots have been placed at the cardinal directions for reference (these were not present during the experiments). In the experiment, this indicator would appear below fixation after the motion epoch and subjects would use a knob to control which direction it pointed.

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Bonnen, K., Czuba, T.B., Whritner, J.A. et al. Binocular viewing geometry shapes the neural representation of the dynamic three-dimensional environment. Nat Neurosci 23, 113–121 (2020).

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