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

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.

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.

Multiple sources of information and time-to-contact judgments

Four experiments examined how the visual system deals with multiple information sources for perceiving dynamic events. Two tau-type optical variables, one defined by the expanding object's image and the other defined by the expanding angular extent composed of the line of sight and the object's shadow, were manipulated in time-to-contact judgments. When the information specified by both variables was consistent, little perceptual accuracy was gained by having two information sources. When the two sources conflicted, perceptual accuracy deteriorated in proportion to the degree of conflict. Based on these results, we concluded that the visual system integrates multiple sources of event-specific information, and that a reliable source of information can be the shadows cast by moving objects.

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.

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.