Mislocalizations of visual elevation and visual vertical induced by visual pitch: the great circle model

The elevation visually perceived as eye level (VPEL) changes linearly with the pitch of an illuminated visual field. The magnitude of influence is only slightly less when the visual field contains only two dim vertical lines in darkness than when it is complexly structured and normally illuminated. Pitching a visual field consisting of only a single line in darkness produces an influence that is only slightly smaller than the 2-line stimulus. The slopes of the VPEL-vs.-pitch functions for the complex room, 2-line stimulus, and 1-line stimulus are +0.63, +0.56, and +0.52 respectively. Although VPEL is systematically influenced by the pitch of the 2-line stimulus, the orientation of a small line within a frontal plane that is visually perceived as vertical is unaffected. However, when the two lines are pitched by equal amounts in opposite directions, the offset of VPV from true vertical changes linearly with pitch magnitude but VPEL is unaffected. These results are identical to those obtained when the two vertical lines are rolled within the frontal plane, a result that depends on some identities between roll and pitch: roll of two parallel lines in the same direction influences VPV but not VPEL; roll of the two lines in opposite directions influences VPEL but not VPV. The interaction between stimulus conditions and discriminations demonstrates that separate mechanisms are in control of VPEL and of VPV. The slope of the VPEL-vs.-pitch function increases exponentially with line length for the 1-line stimulus (space constant = 15.1 degrees). Summation of influences on VPEL for two lines horizontally separated by 50.3 degrees is as great as for two coextensive lines. The above results are predicted from the Great Circle Model which assumes (1) central projection on a spherical approximation to an erect stationary eye; (2) the sign and magnitude of influence of each line on VPEL and on VPV are determined by the direction and magnitude of the separation between the upper pole of the spherical eye and the intersection of the great circle containing the line's image with the central vertical retinal meridian and with the midfrontal retinal meridian, respectively; (3) the influence of individual nonparallel lines is determined by a weighted average of the influences of individual sets of parallel lines; (4) a generalized version of the Great Circle Model is indicated in which extraretinal signals from head and eye are taken into account.