Riemannian geometries of variable curvature in visual space: visual alleys, horopters, and triangles in big open fields.

Luneburg's model for computation of the curvature K of visual two-dimensional space (horizontal visual surface) was tested with equidistant and parallel alleys in large open spaces. Forty-six subjects used stakes to produce 406 experimental alleys of variable sizes (from 5 x 1 to 240 m x 48m). The results show that, contrary to results obtained under laboratory conditions with small alleys and light spots, the individual curvature of visual space does not have negative constant value. K varies in the interval - 1 to + 1 in ninety computed settings: K greater than 0 (N = 38); K less than 0 (N = 52). Therefore the Lobachevskian gemetry currently attributed to visual space ought to be replaced by a Riemannian geometry of variable curvature. Moreover K is an individual function dependent on the size of the alley (distance from the subject), and visual perception would be better understood as scale-dependent. Independently of Luneburg's model we have tested the constancy of the curvature hypothesis in experiments with horopters and visual triangles. The results obtained invalidate Luneburg's hypothesis also.