Influences of visual pitch and visual yaw on visually perceived eye level (VPEL) and straight ahead (VPSA) for erect and rolled-to-horizontal observers.

Localization within the space in front of an observer can be specified along two orthogonal physical dimensions: elevation ('up', 'down') and horizontal ('left','right'). For the erect observer, these correspond to egocentric dimensions along the long and short axes of the body, respectively. However, when subjects are rolled-to-horizontal (lying on their sides), the correspondence between the physical and egocentric dimensions is reversed. Employing egocentric coordinates, localization can be referred to a central perceptual point-visually perceived eye level (VPEL) along the long axis of the body, and visually perceived straight ahead (VPSA) along the short axis of the body. In the present experiment, measurements of VPEL and of VPSA were made on each of eight subjects who were either erect or rolled-to-horizontal while monocularly viewing a long 2-line stimulus (two parallel, 64 degrees -long lines separated by 50 degrees ) in otherwise complete darkness that was centered on the eye of the observer and was tilted out of the frontoparallel plane by a variable amount and direction (from -30 degrees to +30 degrees in 10 degrees steps). The stimulus tilt was either around an axis through the center of the two eyes (pitch; VPEL was measured) or around the long axis of the body that passed through the center of the viewing eye (yaw; VPSA was measured). Large variations in the localization settings were measured that were systematic with stimulus tilt. The slopes of the functions plouing the deviations from veridicality against the orientation of the 2-line stimulus ('induction functions') were larger for the rolled-to-horizontal observer than for the erect observer for both VPEL and VPSA, and for a given body orientation were larger for the VPEL discrimination than for the VPSA discrimination; the influences of body orientation in physical space and the direction of the discrimination relative to the body were lineraly additive. Both the y-intercepts of the induction functions and the central perceptual point measured in complete darkness were lower when the norm setting by the subject was along the vertical than when it was along the horizontal; this held for both the VPEL and VPSA discriminations. The systematic effects of body orientation on the slopes and of line orientation on the y-intercepts and dark values result from an effect of gravity on the settings and fit well to a general principle: any departure from erect posture increases the induction effects of the visual stimulus. The effect of gravity is consistent with the effect of gravity in previous work in high-g environments with the VPEL discrimination.

Neural model for processing the influence of visual orientation on visually perceived eye level (VPEL).

An individual line or a combination of lines viewed in darkness has a large influence on the elevation to which an observer sets a target so that it is perceived to lie at eye level (VPEL). These influences are systematically related to the orientation of pitched-from-vertical lines on pitched plane(s) and to the lengths of the lines, as well as to the orientations of lines of 'equivalent pitch' that lie on frontoparallel planes. A three-stage model processes the visual influence: The first stage parallel processes the orientations of the lines utilizing 2 classes of orientation-sensitive neural units in each hemisphere, with the two classes sensitive to opposing ranges of orientations; the signal delivered by each class is of opposite sign in the two hemispheres. The second stage generates the total visual influence from the parallel combination of inputs delivered by the 4 groups of the first stage, and a third stage combines the total visual influence from the second stage with signals from the body-referenced mechanism that contains information about the position and orientation of the eyes, head, and body. The circuit equation describing the combined influence of n separate inputs from stage 1 on the output of the stage 2 integrating neuron is derived for n stimulus lines which possess any combination of orientations and lengths; Each of the n lines is assumed to stimulate one of the groups of orientation-sensitive units in visual cortex (stage 1) whose signals converge on to a dendrite of the integrating neuron (stage 2), and to produce changes in postsynaptic membrane conductance (g(i)) and potential (V(i)) there. The net current from the n dendrites results in a voltage change (V(A)) at the initial segment of the axon of the integrating neuron. Nerve impulse frequency proportional to this voltage change signals the total visual influence on perceived elevation of the visual field. The circuit equation corresponding to the total visual influence for n equal length inducing lines is V(A)= sum V(i)/[n+(g(A)/g(S))], where the potential change due to line i, V(i), is proportional to line orientation, g(A) is the conductance at the axon's summing point, and g(S)=g(i) for each i for the equal length case; the net conductance change due to a line is proportional to the line's length. The circuit equation is interpreted as a basis for quantitative predictions from the model that can be compared to psychophysical measurements of the elevation of VPEL. The interpretation provides the predicted relation for the visual influence on VPEL, V, by n inducing lines each with length l: thus, V=a+[k(i) sum theta(i)/n+(k(2)/l)], where theta(i) is the orientation of line i, a is the effect of the body-referenced mechanism, and k(1) and k(2) are constants. The model's output is fitted to the results of five sets of experiments in which the elevation of VPEL measured with a small target in the median plane is systematically influenced by distantly located 1-line or 2-line inducing stimuli varying in orientation and length and viewed in otherwise total darkness with gaze restricted to the median plane; each line is located at either 25 degrees eccentricity to the left or right of the median plane. The model predicts the negatively accelerated growth of VPEL with line length for each orientation and the change of slope constant of the linear combination rule among lines from 1.00 (linear summation; short lines) to 0.61 (near-averaging; long lines). Fits to the data are obtained over a range of orientations from -30 degrees to +30 degrees of pitch for 1-line visual fields from lengths of 3 degrees to 64 degrees, for parallel 2-line visual fields over the same range of lengths and orientations, for short and long 2-line combinations in which each of the two members may have any orientation (parallel or nonparallel pairs), and for the well-illuminated and fully structured pitchroom. In addition, similar experiments with 2-line stimuli of equivalent pitch in the frontoparallel plane were also fitted to the model. The model accounts for more than 98% of the variance of the results in each case.

Independent mechanisms produce visually perceived eye level (VPEL) and perceived visual pitch (PVP).

Two aspects of the perception of extrapersonal space undergo systematic changes with variations in the pitch of the visual environment: (1) the physical elevation perceived to correspond to eye level (VPEL); and (2) the perception of the pitch of the visual environment (PVP). Thus, one might assume that both discriminations are controlled by a common mechanism utilizing visual information from the pitched surface. In fact this assumption has been made frequently, and - in different forms - underlies three substantial but very different historical streams in the literature. A quantitative theoretical development shows that two of these streams, although derived from very different viewpoints and appearing very different themselves (it is assumed that the basis for both PVP and VPEL is information about the pitch of the visual field in one, and information about the location of the subject's eye level within the visual field in the other), make identical predictions: each requires that the weighted sum of PVP and VPEL equal the magnitude of physical pitch and that the weighted sum of their first derivatives equal a constant. The third stream, which assumes that an internal representation of the visual field gives rise to both PVP and VPEL, requires that a weighted difference of PVP and VPEL be proportional to physical pitch and that the weighted difference of their derivatives equal a constant. In an experiment designed to examine the relation between VPEL and PVP, psychophysical measurements of VPEL and PVP were made on 20 subjects across a range of pitches from -30 degrees to +20 degrees. Contrary to the predictions from all three interpretations, we find no significant correlation between the two perceptual variables when the influence of pitch itself is removed, despite the fact that VPEL and PVP each increased systematically with increasing visual field pitch. The results not only rule out the specific predictions derived from all three historical streams, they also rule out any theoretical viewpoint that requires control of both perceptual responses by a single mechanism. The statistical independence between VPEL and PVP implies independence between the mechanisms that give rise to them. The correlation observed here and elsewhere between individual PVP and VPEL settings when the influence of the systematic variation of pitch is not eliminated is a consequence of the way in which variations in the two perceptions are generated experimentally, and not on an identity of the mechanisms mediating the generation of the two perceptual variables themselves.

Linear combinations of signals from two lines of the same or different orientations.

Whereas the influence on the elevation of visually perceived eye level (VPEL) by two bilaterally symmetric, long (64 degrees-long), pitched-from-vertical lines in total darkness is only a little more than the average of the VPELs of the two lines measured separately [Matin & Li (1999). Vision Research, 39, 307-329], in the present experiments with 49 2-line combinations of seven orientations (-30 degrees to +30 degrees pitch), the VPEL for two short (12 degrees-long) lines equals the additive sum of the separate influences of the two lines. With one line at a fixed orientation, the slope of the VPEL-versus-pitch function with the second line variable equals the slope of the function when viewing one line alone, but is shifted from the 1-line-alone function by the magnitude of the VPEL of the fixed line. Both the near-averaging and the additivity are summarized by V(theta l, theta r) = k1 + k2 [V(theta l) + V(theta r)], where V(theta l) and V(theta r) are the 1-line VPELs for the pitches of the left and right lines, and V(theta l, theta r) is the 2-line VPEL; the slope constant k2 equals 0.5 for averaging, and 1.00 for simple additivity of the separate visual influences. Measured values are k2 = 0.99 and k2 = 0.61 for short and long lines, respectively. The shift of slope constant is determined by line length and not orientation: parallel and nonparallel lines follow the same rules of combination for short lines as they do for long lines. As for long lines, the short-line results are clear in showing that the visual influence on VPEL is controlled by an opponent-process mechanism. Although 'saturation-near-an-asymptote' along with opponency are required components of the interpretation for the basis of the combination of lines of different orientations and different lengths, they are not by themselves sufficient: All results conform to a neurophysiologically-based model [Matin and Li (1997b). Society for Neuroscience, 23, 175; Matin & Li, under review] that parallel processes feedforward signals from orientation-selective neural units in V1; the model accounts for the shift from additivity to near-averaging with increase in line length as a consequence of the increased contribution of shunting.

Averaging and summation of influences on visually perceived eye level between two long lines differing in pitch or roll-tilt.

The presence of one or two long, dim, eccentrically-placed, parallel, pitched-from-vertical lines in darkness generates a systematic influence on the physical elevation that appears to correspond to eye level (VPEL). The influence of the line(s) in darkness is nearly as large as that produced by a complexly-structured, well-illuminated visual field (Matin L, Li W. Vis Res, 1994;34:311-330); oblique lines in a frontoparallel plane that strike the same projected orientations generate the same influences as those generated by pitched-from-vertical lines (Li W, Matin L. Perception, 1996;25:831-852). The two experiments described here examined the influence on the physical elevation of VPEL due to simultaneous viewing of two long lines of different pitch (Experiment 1) or two long lines of different obliquity in a frontoparallel plane (Experiment 2). Experiment 1 employed two long (66 degrees), simultaneously-presented, pitched-from-vertical lines in darkness on bilaterally symmetric locations at 25 degrees horizontal eccentricity, with each line at one of seven pitches in the range from -30 degrees to +30 degrees; VPELs were measured for all 49 possible pitch combinations. Experiment 2 was identically constructed, but employed oblique 2-line stimuli from a frontoparallel plane that struck the same projected orientations as did the pitched-from-vertical lines in Experiment 1. VPELs measured on four subjects in the two experiments were indistinguishable for corresponding conditions of pitch and obliquity. For a given pitch (obliquity) of one of the lines the elevation of VPEL increased linearly with the pitch (obliquity) of the second line. The VPEL for any 2-line combination is very close to the average of the VPELs for the two individual lines; a small amount of additive summation between the influences of the two lines was also found. Parallel and nonparallel 2-line stimuli appear to follow the same rules of combination. The results are clear in showing that the visual influence on VPEL is controlled by an opponent-process mechanism.

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.

Combined influences of gravitoinertial force level and visual field pitch on visually perceived eye level.

Psychophysical measurements of the level at which observers set a small visual target so as to appear at eye level (VPEL) were made on 13 subjects in 1.0 g and 1.5 g environments in the Graybiel Laboratory rotating room while they viewed a pitched visual field or while in total darkness. The gravitoinertial force was parallel to the z-axis of the head and body during the measurements. The visual field consisted of two 58 degrees high, luminous, pitched-from-vertical, bilaterally symmetric, parallel lines, viewed in otherwise total darkness. The lines were horizontally separated by 53 degrees and presented at each of 7 angles of pitch ranging from 30 degrees with the top of the visual field turned away from the subject (top backward) to 30 degrees with the top turned toward the subject (top forward). At 1.5 g, VPEL changed linearly with the pitch of the 2-line stimulus and was depressed with top backward pitch and elevated with top forward pitch as had been reported previously at 1.0 g (1,2); however, the slopes of the VPEL-vs-pitch functions at 1.0 g and 1.5 g were indistinguishable. As reported previously also (3,4), the VPEL in darkness was considerably lower at 1.5 g than at 1.0 g; however, although the y-intercept of the VPEL-vs-pitch function in the presence of the 2-line visual field (visual field erect) was also lower at 1.5 g than at 1.0 g as it was in darkness, the G-related difference was significantly attenuated by the presence of the visual field. The quantitative characteristics of the results are consistent with a model in which VPEL is treated as a consequence of an algebraic weighted average or a vector sum of visual and nonvisual influences although the two combining rules lead to fits that are equally good.

Saccadic suppression of displacement: separate influences of saccade size and of target retinal eccentricity.

The threshold for detection of displacements of visual objects is higher during voluntary saccades than it is during steady gaze ("saccadic suppression of displacement"; SSD). Relative contributions to SSD of extraretinal and retinal factors were investigated by measuring displacement thresholds in four experiments in which three observers judged whether a test flash, presented after a saccade or a period of fixation, was located to the left or right of a reference point viewed earlier. The experiments, involving saccades ranging from 4 to 12 deg in length, separated the effects of saccade size from the effects of retinal eccentricity of the reference point, and also separated the effects of retinal eccentricity of the test flash from both. The influences of the three are nearly linearly independent. Approximately 20% of the total influence on SSD derives from retinal influences of test flash and reference point; 80% is due to extraretinal influence associated with saccade size. A signal/noise model that accounted well for our previous on SSD (Li & Matin, 1990a,b) was extended to account for the present results. The model also provides a unified treatment of SSD and of the saccadic suppression of visibility (SSV).

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 degrees over a +/-30 degrees 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.

Multimodal basis for egocentric spatial localization and orientation.

The perceptual and sensorimotor mechanisms that guide our abilities at localizing and orienting in space integrate sensory information from vision and from a "body-referenced mechanism" that itself makes use of extraretinal signals regarding eye position relative to the head and head orientation relative to the body and to gravity. The experiments and theoretical treatment center on two perceptual dimensions: the visual perception of elevation and of orientation within the frontoparallel plane. Several experiments measuring localization in the horizontal plane are also treated. The experiments involve measurements of the physical elevation of visually perceived eye level (VPEL, a norm for perceived elevation), measurements of the physical orientation within the frontoparallel plane corresponding to visually perceived vertical (VPV), and measurements of the direction within a horizontal plane perceived as straight ahead (VPSA). VPEL and VPV are each significantly and systematically influenced by both the pitch and the roll of visual fields, and it is these influences that provide the basis for experimentally isolating the contributions of vision from those of the body-referenced mechanism. The VPEL discrimination is nearly invariant with variation in head and eye orientation. The possibility that influences from vision and from the body-referenced mechanism combine linearly is well supported. The visual influences on VPEL and VPV are controlled by the action of individual lines, and the same pitched-from-vertical lines (from pitched planes) or oblique lines within erect planes influence both discriminations. The Great Circle Model (GCM) accounts for the influences of individual lines, and contains rules for the influence of combinations of lines on both VPEL and VPV. GCM is interpreted by a 3-dimensional vector treatment in "egocentric orientation space."

Dissociation between two modes of spatial processing by a visual form agnosic.

We report a dissociation between two aspects of visuospatial processing in a patient with a profound impairment in the visual perception of objects ('visual form agnosia'). The orientation-in-depth of a visual field ('visual pitch') was found to systematically influence the elevation at which she perceived her own eye level, just as it does in normal individuals; but at the same time, she was unable to discriminate perceptually the orientation-in-depth of the same visual field, a trivial task for individuals with normal vision. These results suggest that, in the normal brain, the processes that integrate orientation information from the visual field with extraretinal information about eye position are separable from those supporting the perception of the orientation of the visual field itself. The pattern of brain damage in D.F., in conjunction with the reported dissociation, suggests that the former set of processes maps onto the stream of information flowing from primary visual cortex to the posterior parietal cortex, the so-called dorsal stream, whereas the latter involves the projections from primary visual cortex to the inferotemporal cortex, the so-called ventral stream.

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 degrees-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 degrees pitch range, but was indistinguishable from 0.00 for the VPSA-versus-slant function over a +/- 30 degrees 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.

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 average 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 degrees topbackward or 20 degrees 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.

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.

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 individual's 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.

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.

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.

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 degrees to 1.2 degrees as saccade length increased from 4 degrees to 12 degrees. 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.