Wenxun Li

Visually perceived eye level: changes induced by a pitched-from-vertical 2-line visual field

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.

The influence of saccade length on the saccadic suppression of displacement detection

The decrease in sensitivity to spatial displacement which accompanies a voluntary horizontal saccadic eye movement was measured as a function of the length of the saccade. Threshold for detecting the displacement increased linearly from about 0.3° to 1.2° as saccade length increased from 4° to 12°. The variability (standard deviation) of the discrimination increased linearly with saccade length as well, and hence also linearly with the displacement threshold. These results, along with our previous finding that the increase is not a consequence of the saccadically generated spatiotemporal smearing of the retinal image (Li & Matin, 1990), support the proposal that displacement detection is based on a constant internal signal/noise ratio whose denominator is a measure of the variability of the extraretinal signal regarding eye position, and that the reduction in sensitivity is a result of a transient increase of this variability in the temporal neighborhood of a saccade.

The influence of a stationary single line in darkness on the visual perception of eye level

The angle of pitch of a visual field consisting of only a single vertical, 64 degrees-long, eccentrically-located line in otherwise total darkness influences the elevation of a target set to appear at eye level (VPEL). The influence changes linearly with the magnitude of pitch over the range from -30 degrees to +20 degrees. The average slope of the VPEL-vs-pitch function is +0.53. The influence on VPEL of a pitched visual field consisting of two parallel vertical lines is slightly greater (slope = +0.56), and the influence of the pitch of a complexly-structured well-illuminated pitched room is slightly greater yet (slope = +0.63). The pitch of a frontoparallel plane containing one horizontal line has a small influence on VPEL (slope = +0.08); the influence with two horizontal lines is slightly greater (slope = +0.18). The slope of the VPEL-vs-pitch function differs among individual subjects but is linear for each of the eight subjects. A great deal of consistency is manifested by individual subjects across all of the visual fields: an individual with a steep slope with one visual field tends to have a steep slope with all visual fields. The individuals characteristic response in total darkness is strongly correlated with the response to an erect well-illuminated visual field. The significant aspect of the pitched-from-vertical line stimulus is the change in orientation of its retinal image. An additional experiment with a small pupil (pilocarpine) indicates that cues related to other retinal gradients or to accommodation play no role in the influence of the visual field on VPEL. The experiments provide support for treating the visual influence on VPEL by means of the Great Circle Model.

Mislocalizations of Visual Elevation and Visual Vertical Induced by Visual Pitch: the Great Circle Modela

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 lines 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.

Differences in influence between pitched-from-vertical lines and slanted-from-frontal horizontal lines on egocentric localization

The visual field exerts powerful effects on egocentric spatial localization along both horizontal and vertical dimensions. Thus, (1) prism-produced visual pitch and visual slant generate similar mislocalizations of visually perceived eye level (VPEL) and visually perceived straight ahead (VPSA) and (2) in darkness curare-produced extraocular muscle paresis under eccentric gaze generates similar mislocalizations in VPEL and VPSA that are essentially eliminated by introducing a normal visual field. In the present experiments, however, a search for influences of real visual slant on VPSA to correspond to the influences of visual pitch on VPEL failed to find one. Although the elevation corresponding to VPEL changes linearly with the pitch of a visual field consisting of two isolated 66.5°-long pitched-from-vertical lines, the corresponding manipulation of change in the slant of either a horizontal two-line or a horizontal four-line visual field on VPSA did not occur. The average slope of the VPEL-versus-pitch function across 5 subjects was +0.40 over a ±30° pitch range, but was indistinguishable from 0.00 for the VPSA-versus-slant function over a ±30° slant range. Possible contributions to the difference between susceptibility of VPEL and VPSA to visual influence from extraretinal eye position information, gravity, and several retinal gradients are discussed.

Two wrongs make a right: linear increase of accuracy of visually-guided manual pointing, reaching, and height-matching with increase in hand-to-body distance

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 lines 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.

Change in Visually Perceived Eye Level without Change in Perceived Pitch

Both the physical elevation that appears to correspond to eye level and the visually perceived pitch of a visual field are linear functions of the physical pitch of a normally illuminated, complexly structured visual field. One of the possible bases for the large effect of physical pitch on the elevation of visually perceived eye level (VPEL) is that the visual field generates a mental representation which specifies spatial coordinates and these determine the VPEL elevation (‘implicit-surface model’; ISM). The influence on the elevation of VPEL is nearly as large when the visual field contains either one or two long pitched-from-vertical or rolled-from-vertical lines in otherwise total darkness as when it consists of a well-illuminated and complexly structured pitched room (L Matin and W Li, 1994 Vision Research 34 311–330), and, in order to examine the ISM, we employed a rolled-from-vertical, two-line configuration within a frontoparallel plane viewed in otherwise total darkness. Measurements of visually perceived pitch were made by a manual matching procedure and VPEL measurements were made by the psychophysical setting of the elevation of a small visual target to appear at eye level while each of three subjects viewed the two-line configuration at each of three horizontal eccentricities with the configuration at each of seven roll orientations. In direct contradiction to the ISM, the perceived pitch of the two-line configuration did not deviate significantly from the erect orientation (‘vertical’) for any roll at any eccentricity, but the elevation of VPEL changed systematically with the roll of the configuration both at left and at right eccentricities, and did not change at all with the two-line configuration centered on the median plane. Consistent with our previous work and with our previous interpretation regarding the basis for VPEL (L Matin and W Li, 1994 Vision Research 34 2577 – 2598), the variation of VPEL for the two-line visual field equals the average of the VPEL variations produced by viewing each of the single lines separately.

Visually Perceived Eye Level is Influenced Identically by Lines from Erect and Pitched Planes

The physical elevation that appears to correspond to eye level (VPEL), as measured with a small visual target, changes systematically with the orientation in depth (‘visual pitch’) of a visual field consisting of one or two pitched-from-vertical lines in darkness. The influence is large and, with a one-line stimulus, is only 15% smaller than the influence exerted by a complexly structured, well-illuminated, pitched visual field. A line from a frontoparallel plane can be presented to the same retinal locus as a pitched-from-vertical line; the three experiments in the present report were aimed at determining the influence on VPEL from such lines. In the first two experiments the subject viewed a visual field consisting of a one-line or two-line pitched-from-vertical stimulus from a pitched-only plane or an oblique one-line or two-line stimulus from an erect plane. Each of the pitched-from-vertical stimuli was presented at seven different orientations separated by 10° over a ±30° range. Each of the oblique-line stimuli was presented at an orientation that resulted in stimulation to the same retinal locus as one of the conditions with pitched-from-vertical lines, and thus a range of ‘equivalent pitches’ was examined that corresponded to the range of pitches for the pitched-from-vertical lines. The variation in orientation of the oblique-line stimulus and the pitched-from-vertical stimulus each produced systematic changes in VPEL; the two were indistinguishable. A third experiment specifically designed to examine the possibility that either stimulus sequencing or lack of naivity of the subjects might have been involved turned up no such effects. It is concluded that the aspect of a line stimulus that controls the influence on VPEL is the orientation of the image of the line on a projection sphere centered on the nodal point of the eye or, as in the present experiments with viewing in primary position, the retinal locus stimulated; the orientation-in-depth of the stimulating line provides no additional influence on VPEL for the stationary, erect, monocularly viewing observer. The results are interpreted within the framework of the great-circle model.

Mirror symmetry and parallelism: two opposite rules for the identity transform in space perception and their unified treatment by the Great Circle Model

Two opposite rules control the contributions of individual lines to the perceptual processing of two different spatial dimensions of egocentric localization and orientation. For lines restricted to the frontal plane, a tilted line on one side of the median plane induces a rotation of the orientation visually perceived as vertical (VPV) identical to that induced by the same tilt on the other side of the median plane, but the influences exerted on the elevation of visually perceived eye level (VPEL) are mirror symmetric. The rule for VPV fits our intuitions; the rule for VPEL does not. However, the reverse peculiarity holds when the inducing lines are rotated within sagittal planes (pitched): Two parallel, pitched-from-vertical lines on opposite sides of the median plane generate identical effects on VPEL but mirror symmetric effects on VPV. These counterintuitive symmetry reversals are reconciled by the Great Circle Model of spatial orientation (GCM), in which line orientations are represented by the great circle coordinates of their images on a sphere centered at the nodal point of the eye via central projection.

Light and dark adaptation of visually perceived eye level controlled by visual pitch.

The pitch of a visual field systematically influences the elevation at which a monocularly viewing subject sets a target so as to appear at visually perceived eye level (VPEL). The deviation of the setting from true eye level averages approximately 0.6 times the angle of pitch while viewing a fully illuminated complexly structured visual field and is only slightly less with one or two pitched-from-vertical lines in a dark field (Matin & Li, 1994a). The deviation of VPEL from baseline following 20 min of dark adaptation reaches its full value less than 1 min after the onset of illumination of the pitched visual field and decays exponentially in darkness following 5 min of exposure to visual pitch, either 30° topbackward or 20° topforward. The magnitude of the VPEL deviation measured with the dark-adapted right eye following left-eye exposure to pitch was 85% of the deviation that followed pitch exposure of the right eye itself. Time constants for VPEL decay to the dark baseline were the same for same-eye and cross-adaptation conditions and averaged about 4 min. The time constants for decay during dark adaptation were somewhat smaller, and the change during dark adaptation extended over a 16% smaller range following the viewing of the dim two-line pitched-from-vertical stimulus than following the viewing of the complex field. The temporal course of light and dark adaptation of VPEL is virtually identical to the course of light and dark adaptation of the scotopic luminance threshold following exposure to the same luminance. We suggest that, following rod stimulation along particular retinal orientations by portions of the pitched visual field, the storage of the adaptation process resides in the retinogeniculate system and is manifested in the focal system as a change in luminance threshold and in the ambient system as a change in VPEL. The linear model previously developed to account for VPEL, which was based on the interaction of influences from the pitched visual field and extraretinal influences from the body-referenced mechanism, was employed to incorporate the effects of adaptation. Connections between VPEL adaptation and other cases of perceptual adaptation of visual direction are described.