Alleys on an extensive apparent frontoparallel plane: a second experiment

Small light points were presented, in the dark, around a point in the center which was fixed at a distance of about 3 m from the subject. In experiment 1, the subject adjusted the positions of points so that all were frontoparallel and in three horizontal series, each consisting of five points, with the middle series level with the eyes, to satisfy the following conditions: (i) the three series must appear straight and horizontally parallel; (ii) the points of each of the five triplets must appear equally separated vertically; (iii) the three points of each triplet must appear to move horizontally along straight and parallel paths; (iv) the three points of each triplet must appear to move horizontally with a constant vertical separation. The most distant points were about 0.51 rad to the left and right of center, and about 0.22 rad above and below. In experiment 2, with the configuration of points obtained in experiment 1, the subject assessed ratios of all perceptual distances between points and also from the subject to all points. From experiment 1 (three subjects used), Gaussian curvature K and a constant related to depth perception (sigma) were estimated under the assumption that the frontoparallel plane is a Riemannian plane of constant curvature K and that Luneburg's mapping functions between visual space and physical space hold. The analysis was made according to equations different from those used previously. The results of experiment 2 (two subjects used) were analyzed by a new computer program in which no preassumed mapping functions are necessary for the estimation of K. From both analyses it is clear that there is no need to assume any other value of K than 0 (Euclidean) to describe the geometry of the frontoparallel plane. This presents a striking contrast to the results from experiments on parallel and equidistance alleys running toward the subject on the horizontal plane.