Spatial summation among coextensive and parallel line segments across wide separations (50 degrees): egocentric localization and the great circle model.

The elevation at which an observer sets a target to appear at eye level (VPEL) is systematically related to the angle of pitch of the visual field and is only a little less for a visual field consisting of a single line in darkness than for a complexly structured field [Matin and Li (1994a) Vision Research, 34, 311-330]. Three experiments are described which measure the quantitative characteristics of spatial summation among individual pitched-from-vertical line segments that control the visual influence on VPEL. As the length of a one-line stimulus increased from 0 degrees to 64 degrees the slope of the VPEL-vs-pitch function (S) increased from 0 to +0.56 along a negatively accelerated exponential with a 15.1 degree space constant. The combined influence on S of two simultaneously-presented, parallel, pitched-from-vertical lines, horizontally separated by 50 degrees, is slightly greater than the combined influence of two coextensive line segments with the same total length. S saturates at a locus that lies beyond any separate neural locus for the processing of the individual line. The results are effectively treated by the Great Circle Model (GCM) which converts stimulus "nonlocality" to neural "locality" by mapping the intersections of the images of parallel line sets in a spherical approximation of the eye on to a set of neural nodes. A neurophysiological realization of GCM is compatible with mediation by the long horizontal connections afferent to layer 6 of primary visual cortex (V1). The combination of visual influences with extraretinal information is compatible with the characteristics of posterior parietal cortex downstream from V1. The increase in the effectiveness of a line with increase in length is in accord with a more general division between the utilization of long lines for egocentric orientation and short lines for figural processes; end-inhibition from elongated layer 6 cells (which process long lines) onto layer 4 cells (which process short lines) in V1 may provide a means for separating the two streams of information.