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Open AccessArticle

A Riemannian Geometry Theory of Three-Dimensional Binocular Visual Perception

1
School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney NSW 2052, Australia
2
Independent Researcher, late School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney NSW 2052, Australia
3
Cyber-Physical Systems Laboratory, Department of ICT and Natural Sciences, NTNU—Norwegian University of Science and Technology, NO-6025 Ålesund, Norway
*
Author to whom correspondence should be addressed.
Vision 2018, 2(4), 43; https://doi.org/10.3390/vision2040043
Received: 3 September 2018 / Revised: 2 November 2018 / Accepted: 27 November 2018 / Published: 5 December 2018
(This article belongs to the Special Issue The Perspective of Visual Space)
We present a Riemannian geometry theory to examine the systematically warped geometry of perceived visual space attributable to the size–distance relationship of retinal images associated with the optics of the human eye. Starting with the notion of a vector field of retinal image features over cortical hypercolumns endowed with a metric compatible with that size–distance relationship, we use Riemannian geometry to construct a place-encoded theory of spatial representation within the human visual system. The theory draws on the concepts of geodesic spray fields, covariant derivatives, geodesics, Christoffel symbols, curvature tensors, vector bundles and fibre bundles to produce a neurally-feasible geometric theory of visuospatial memory. The characteristics of perceived 3D visual space are examined by means of a series of simulations around the egocentre. Perceptions of size and shape are elucidated by the geometry as are the removal of occlusions and the generation of 3D images of objects. Predictions of the theory are compared with experimental observations in the literature. We hold that the variety of reported geometries is accounted for by cognitive perturbations of the invariant physically-determined geometry derived here. When combined with previous description of the Riemannian geometry of human movement this work promises to account for the non-linear dynamical invertible visual-proprioceptive maps and selection of task-compatible movement synergies required for the planning and execution of visuomotor tasks. View Full-Text
Keywords: visual space; Riemannian geometry; binocular vision; stereopsis; size perception; shape perception; place encoding; occlusions; computational model visual space; Riemannian geometry; binocular vision; stereopsis; size perception; shape perception; place encoding; occlusions; computational model
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Neilson, P.D.; Neilson, M.D.; Bye, R.T. A Riemannian Geometry Theory of Three-Dimensional Binocular Visual Perception. Vision 2018, 2, 43.

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