  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.
