Change in visually perceived eye level without change in perceived pitch

Visually Perceived Eye Level and Horizontal Midline of the Body Trunk Influenced by Optic Flow

The eye level and the horizontal midline of the body trunk can serve, respectively as references for judging the vertical and horizontal egocentric directions. We investigated whether the optic-flow pattern, which is the dynamic motion information generated when one moves in the visual world, can be used by the visual system to determine and calibrate these two references. Using a virtual-reality setup to generate the optic-flow pattern, we showed that judged elevation of the eye level and the azimuth of the horizontal midline of the body trunk are biased toward the positional placement of the focus of expansion (FOE) of the optic-flow pattern. Furthermore, for the vertical reference, prolonged viewing of an optic-flow pattern with lowered FOE not only causes a lowered judged eye level after removal of the optic-flow pattern, but also an overestimation of distance in the dark. This is equivalent to a reduction in the judged angular declination of the object after adaptation, indicating that the optic-flow information also plays a role in calibrating the extraretinal signals used to establish the vertical reference.

Short-lived effects of a visual inducer during egocentric space perception and manual behavior

A pitched visual inducer has a strong effect on the visually perceived elevation of a target in extrapersonal space, and also on the elevation of the arm when a subject points with an unseen arm to the target's elevation. The manual effect is a systematic function of hand-to-body distance (Li and Matin Vision Research 45:533-550, 2005): When the arm is fully extended, manual responses to perceptually mislocalized luminous targets are veridical; when the arm is close to the body, gross matching errors occur. In the present experiments, we measured this hand-to-body distance effect during the presence of a pitched visual inducer and after inducer offset, using three values of hand-to-body distance (0, 40, and 70 cm) and two open-loop tasks (pointing to the perceived elevation of a target at true eye level and setting the height of the arm to match the elevation). We also measured manual behavior when subjects were instructed to point horizontally under induction and after inducer offset (no visual target at any time). In all cases, the hand-to-body distance effect disappeared shortly after inducer offset. We suggest that the rapid disappearance of the distance effect is a manifestation of processes in the dorsal visual stream that are involved in updating short-lived representations of the arm in egocentric visual perception and manual behavior.

Binocular spatial induction for the perception of depth does not cross the midline

Although horizontal binocular retinal disparity between images in the two eyes resulting from their different views of the world has long been the centerpiece for understanding the unique characteristics of stereovision, it does not suffice to explain many binocular phenomena. Binocular depth contrast (BDC), the induction of an appearance of visual pitch in a centrally located line by pitched-from-vertical flanking lines, has particularly been the subject of a good deal of attention in this regard. In the present article, we show that BDC does not cross the median plane but is restricted to the side of the visual field containing a unilateral inducer. These results cannot be explained by the use of retinal disparity alone or in combination with any additional factors or processes previously suggested to account for stereovision. We present a two-channel three-stage neuromathematical model that accounts quantitatively for present and previous BDC results and also accounts for a large number of the most prominent features of binocular pitch perception: Stage 1 of the differencing channel obtains the difference between the retinal orientations of the images in the two eyes separately for the inducer and the test line; stage 1 of the summing channel obtains the corresponding sums. Signals from inducer and test stimuli are combined linearly in each channel in stage 2, and in stage 3 the outputs from the two channels are combined along with a bias signal from the body-referenced mechanism to yield ', the model's prediction for the perception of pitch.

The field dependence/independence cognitive style does not control the spatial perception of elevation

Earlier work described the presence of a significant connection between an individual's ability to disregard distracting aspects of a visual field in the classical rod-and-frame test (RFT), in which a subject is required to set a rod so that it will appear vertical in the presence of a square frame that is roll tilted from vertical, and in paper-and-pencil tests, in which the subject is required to find a hidden figure embedded in a more complex figure (the Embedded Figures Test [EFT]; see, e.g., Witkin, Dyk, Faterson, Goodenough, & Karp, 1962; Witkin et al., 1954; Witkin, Oltman, Raskin, & Karp, 1971). This has led to a belief in the existence of a bipolar dimension of cognitive style that is utilized in such disembedding tasks--namely, the extent to which an individual is dependent on or independent from the influence of a distracting visual field. The influence of an inducing visual field on the perception of elevation measured by the setting of a visual target to appear at eye level (the visually perceived eye level [VPEL] discrimination) has also been found to be correlated with the RFT. We have thus explored the possible involvement of the dependence/independence cognitive style on the VPEL discrimination. Measurements were made on each of 18 subjects (9 of them female, 9 male) setting a small target to the VPEL in the presence of a pitched visual field across a range of six pitches from -30 degrees (topbackward) to +20 degrees (topforward) and on each of three tests generally recognized as tests of cognitive spatial abilities: the EFT, the Gestalt Completion Test, and the Snowy Pictures Test (SPT). Although there were significant pairwise correlations relating performance on the three cognitive tests (+.73, +.48, and +.71), the correlation of each of these three with the slope of the VPEL-versus-pitch function was not significant, as it was with the slope of the perception of visual pitch of the field (PVP)-versus-pitch function. VPEL, PVP, and a cognitive factor separated into three essentially independent factors in a multiple-factor analysis, with the three cognitive tests clustering at the cognitive factor, and with no significant loading on either of the other two factors. From the above considerations and a multiple-factor analytic treatment including additional results from this and other laboratories, we conclude that the cognitive-processing style held to be involved in the performance on the EFT and the perception of vertical as measured by the RFT is not general for egocentric space perception; it does not involve the perception of elevation.

Visually perceived vertical (VPV): induced changes in orientation by 1-line and 2-line roll-tilted and pitched visual fields

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.

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 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.

Visually perceived eye level with reversible pitch stimuli: implications for the great circle and implicit surface models

Visually perceived eye level (VPEL) and perceived pitch were measured while subjects viewed two sets of stimuli that were either upright or pitched top-toward or top-away from them. The first set of stimuli, a pair of vertical lines viewed at various angles of pitch, caused systematic changes in perceived pitch and upward and downward VPEL shifts for the top-toward and top-away pitches, respectively. Neither the perceived pitch nor the VPEL measures with these stimuli differed between monocular and binocular viewing. The second set of stimuli was constructed so that, when viewed at the appropriate pitch angle, the projected orientations of the lines in the retinal image of each stimulus were similar to those generated by a pair of vertical lines pitched by a lesser amount in the opposite direction. When viewed monocularly, these stimuli appeared pitched in the direction opposite their physical pitch, yet produced VPEL shifts consistent with the direction of their physical pitch. These results clearly demonstrate a dissociation between perceived pitch and VPEL. The same stimuli, when viewed binocularly, appeared pitched in the direction of their physical pitch and caused VPEL shifts indistinguishable from those obtained monocularly. The retinal image orientations of these stimuli, however, corresponded to those of vertical line stimuli pitched in the opposite direction. This finding is therefore consistent with the hypothesis that VPEL and perceived pitch are processed independently, but inconsistent with the specific version of this hypothesis which states that differences in VPEL are determined solely on the basis of the orientation of lines in the retinal image.

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.

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.

The functions of the proprioceptors of the eye muscles

This article sets out to present a fairly comprehensive review of our knowledge about the functions of the receptors that have been found in the extraocular muscles--the six muscles that move each eye of vertebrates in its orbit--of all the animals in which they have been sought, including Man. Since their discovery at the beginning of the 20th century these receptors have, at various times, been credited with important roles in the control of eye movement and the construction of extrapersonal space and have also been denied any function whatsoever. Experiments intended to study the actions of eye muscle receptors and, even more so, opinions (and indeed polemic) derived from these observations have been influenced by the changing fashions and beliefs about the more general question of how limb position and movement is detected by the brain and which signals contribute to those aspects of this that are perceived (kinaesthesis). But the conclusions drawn from studies on the eye have also influenced beliefs about the mechanisms of kinaesthesis and, arguably, this influence has been even larger than that in the converse direction. Experimental evidence accumulated over rather more than a century is set out and discussed. It supports the view that, at the beginning of the 21st century, there are excellent grounds for believing that the receptors in the extraocular muscles are indeed proprioceptors, that is to say that the signals that they send into the brain are used to provide information about the position and movement of the eye in the orbit. It seems that this information is important in the control of eye movements of at least some types, and in the determination by the brain of the direction of gaze and the relationship of the organism to its environment. In addition, signals from these receptors in the eye muscles are seen to be necessary for the development of normal mechanisms of visual analysis in the mammalian visual cortex and for both the development and maintenance of normal visuomotor behaviour. Man is among those vertebrates to whose brains eye muscle proprioceptive signals provide information apparently used in normal sensorimotor functions; these include various aspects of perception, and of the control of eye movement. It is possible that abnormalities of the eye muscle proprioceptors and their signals may play a part in the genesis of some types of human squint (strabismus); conversely studies of patients with squint in the course of their surgical or pharmacological treatment have yielded much interesting evidence about the central actions of the proprioceptive signals from the extraocular muscles. The results of experiments on the eye have played a large part in the historical controversy, now in at least its third century, about the origin of signals that inform the brain about movement of parts of the body. Some of these results, and more of the interpretations of them, now need to be critically re-examined. The re-examination in the light of recent experiments that is presented here does not support many of the conclusions confidently drawn in the past and leads to both new insights and fresh questions about the roles of information from motor signals flowing out of the brain and that from signals from the peripheral receptors flowing into it. There remain many lacunae in our knowledge and filling some of these will, it is contended, be essential to advance our understanding further. It is argued that such understanding of eye muscle proprioception is a necessary part of the understanding of the physiology and pathophysiology of eye movement control and that it is also essential to an account of how organisms, including Man, build and maintain knowledge of their relationship to the external visual world. The eye would seem to provide a uniquely favourable system in which to study the way in which information derived within the brain about motor actions may interact with signals flowing in from peripheral receptors. The review is constructed in relatively independent sections that deal with particular topics. It ends with a fairly brief piece in which the author sets out some personal views about what has been achieved recently and what most immediately needs to be done. It also suggests some lines of study that appear to the author to be important for the future.

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.

Why do pitched horizontal lines have such a small effect on visually perceived eye level?

In two experiments, visually perceived eye level (VPEL) was measured while subjects viewed two-dimensional displays that were either upright or pitched 20 degrees top-toward or 20 degrees top-away from them. In Experiment 1, it was demonstrated that binocular exposure to a pair of pitched vertical lines or to a pitched random dot pattern caused a substantial upward VPEL shift for the top-toward pitched array and a similarly large downward shift for the top-away array. On the other hand, the same pitches of a pair of horizontal lines (viewed binocularly or monocularly) produced much smaller VPEL shifts. Because the perceived pitch of the pitched horizontal line display was nearly the same as the perceived pitch of the pitched vertical line and dot array, the relatively small influence of pitched horizontal lines on VPEL cannot be attributed simply to an underestimation of their pitch. In Experiment 2, the effects of pitched vertical lines, dots, and horizontal lines on VPEL were again measured, together with their effects on resting gaze direction (in the vertical dimension). As in Experiment 1, vertical lines and dots caused much larger VPEL shifts than did horizontal lines. The effects of the displays on resting gaze direction were highly similar to their effects on VPEL. These results are consistent with the hypothesis that VPEL shifts caused by pitched visual arrays are due to the direct influence of these arrays on the oculomotor system and are not mediated by perceived pitch.

Mental rotation for spatial environment recognition

We investigated the importance of retinal and body inclination in the recognition of spatial environment. The paradigm involved the recognition, in body upright and tilted conditions, of tilted images -intervals of 15 degrees from 0 degrees to 90 degrees leftward and rightward respective to head coordinates - of known spatial layouts encountered while walking in Paris. The analysis of reaction times was consistent with the subjects mentally rotating the spatial layout so that the environment was subjectively vertical before making their decisions. In contrast, when the body was roll-tilted (33 degrees ), overall reaction time was not affected; however, reaction time and spatial layout tilt with respect to the head were correlated when the body was tilted but not when upright. Both results indicate that gravity was slightly important in performing the task.

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.