Representation of 2D frame less visual space as a neural manifold and its information geometric interpretation

Representation of 2D frame less visual space as neural manifold and its modelling in the frame work of information geometry is presented. Origin of hyperbolic nature of the visual space is investigated using evidences from neuroscience. Based on the results we propose that the processing of spatial information, particularly estimation of distance, perceiving geometrical curves etc. in the human brain can be modeled in a parametric probability space endowed with Fisher-Rao metric. Compactness, convexity and differentiability of the space is analysed and found that they obey the axioms of G space, proposed by Busemann. Further it is shown that it can be considered as a homogeneous Riemannian space of constant negative curvature. It is therefore ensured that the space yields geodesics into it. Computer simulation of geodesics representing a number of visual phenomena and advocating the hyperbolic structure of visual space is carried out. Comparison of the simulated results with the published experimental data is presented.