The physical elevation corresponding to visually perceived eye level (VPEL) changes linearly with the pitch of a visual field. Deviations from true eye level average more than 0.5 times the angle of pitch over a 65 degrees pitch range. A visual field consisting of 2 dim, isolated vertical lines in darkness is more than 4/5 as effective as that of a complexly structured visual field; 2 horizontal lines have a small and inconsistent effect. Differences in influence on VPEL between pitched-from-vertical and horizontal lines were predicted from an analysis that extracted differences in retinal perspective resulting from changes in pitch. The Great Circle Model (GCM), based on a spherical approximation to the erect, stationary eye, predicts the present results and results of 8 other sets of experiments. The model treats the influence of a single line on VPEL as systematically related to the elevation of the intersection between the great circle containing the image of the line and the central vertical retinal meridian; generalized GCM combines visual inputs with inputs from the body-referenced mechanism and maps onto the central nervous system.
We report a series of nine experiments which show that a single roll-tilted line in darkness induces changes of the orientation perceived as vertical (VPV) that are similar in magnitude and direction to those measured by Witkin and Asch (1948a) [Studies in space orientation. I. Perception of the upright with displaced visual fields. Journal of Experimental Psychology, 38, 762-782] with the classical square 4-sided frame, and we describe the configuration-independent mass-action rules by which the influences of the individual lines influences are combined. Clockwise (cw) and counterclockwise (ccw) orientations of a line produce cw and ccw displacements of the VPV setting, respectively, with effect magnitude increasing approximately linearly with line orientation (e.g., a 66.25 degrees - long line at 25 degrees horizontal eccentricity that varies in roll-tilt through +/-13.2 degrees around vertical generates a systematic variation in VPV over +/-7 degrees). The slope of the VPV-vs-roll-tilt function increases with line length along a negatively accelerated exponential function (length constant = 17.1 degrees). The influences of two bilaterally symmetric lines combine linearly and algebraically and the combined influence is linearly related to the sum of the VPVs for the 1-line components with a slope equal to 0.91 for short lines and 0.66 for long lines; thus, VPV for short lines manifests nearly complete additive summation, but for long lines, the 2-line VPV is nearer to the average of the VPV values for the two components measured separately. The effectiveness of the conjunction of two line segments within a visual scene does not depend on their separate orientations, only on their sum. Individual lines from pitched-only planes or from combinations of such planes generate identical influences to those generated from lines in frontoparallel planes with the same image orientations at the eye of the observer (their "retinal orientations"). Retinal orientation is the key to the induction of VPV change independently of the line's plane of origin.
Measurements were made of the accuracy of open-loop manual pointing and height-matching to a visual target whose elevation was perceptually mislocalized. Accuracy increased linearly with distance of the hand from the body, approaching complete accuracy at full extension; with the hand close to the body (within the midfrontal plane), the manual errors equaled the magnitude of the perceptual mislocalization. The visual inducing stimulus responsible for the perceptual errors was a single pitched-from-vertical line that was long (50 degrees), eccentrically-located (25 degrees horizontal), and viewed in otherwise total darkness. The line induced perceptual errors in the elevation of a small, circular visual target set to appear at eye level (VPEL), a setting that changed linearly with the change in the line's visual pitch as has been previously reported (pitch: -30 degrees topbackward to 30 degrees topforward); the elevation errors measured by VPEL settings varied systematically with pitch through an 18 degrees range. In a fourth experiment the visual inducing stimulus responsible for the perceptual errors was shown to induce separately-measured errors in the manual setting of the arm to feel horizontal that were also distance-dependent. The distance-dependence of the visually-induced changes in felt arm position accounts quantitatively for the distance-dependence of the manual errors in pointing/reaching and height matching to the visual target: The near equality of the changes in felt horizontal and changes in pointing/reaching with the finger at the end of the fully extended arm is responsible for the manual accuracy of the fully-extended point; with the finger in the midfrontal plane their large difference is responsible for the inaccuracies of the midfrontal-plane point. The results are inconsistent with the widely-held but controversial theory that visual spatial information employed for perception and action are dissociated and different with no illusory visual influence on action. A different two-system theory, the Proximal/Distal model, employing the same signals from vision and from the body-referenced mechanism with different weights for different hand-to-body distances, accounts for both the perceptual and the manual results in the present experiments.
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