Perspective, orientation disparity, and anisotropy in stereoscopic slant perception.

Stereoscopic depth estimates are not predictable from the geometry of point disparities. The configural properties of surfaces (surface contours) may play an important role in determining, for example, slant responses to a disparity gradient, and the marked anisotropy in favour of slant around a horizontal axis. It has been argued that variation in slant magnitude are attributable to the degree of perspective conflict present and that anisotropy is attributable to orientation disparity, which varies with the axis of slant. Three experiments were conducted in which configural properties were varied to try and tease apart the respective roles of orientation disparity and conflicting perspective in determining stereoscopic slant perception and slant axis anisotropy. The results could not be accounted for by the magnitude of the orientation disparities present. Conflicting perspective cues appeared to play a role but only for slant around a vertical axis. It was concluded that there are important configural effects in stereopsis attributable neither to orientation disparity nor to perspective.     

Temporal aspects of slant and inclination perception.

Linear transformations (shear or scale transformations) of either horizontal or vertical disparity give rise to the percept of slant or inclination. It has been proposed that the percept of slant induced by vertical size disparity, known as Ogle's induced-size effect, and the analogous induced-shear effect, compensate for scale and shear distortions arising from aniseikonia, eccentric viewing, and cyclodisparity. We hypothesised that these linear transformations of vertical disparity are processed more slowly than equivalent transformations of horizontal disparity (horizontal shear and size disparity). We studied the temporal properties of the stereoscopic slant and inclination percepts that arose when subjects viewed stereograms with various combinations of horizontal and vertical size or shear disparities. We found no evidence to support our hypothesis. There were no clear differences in the build-up of percepts of slant or inclination induced by step changes in horizontal size or shear disparity and those induced by step changes in vertical size or shear disparity. Perceived slant and inclination decreased in a similar manner with increasing temporal frequency for modulations of transformations of both horizontal and vertical disparity. Considerable individual differences were found and several subjects experienced slant reversal, particularly with oscillating stimuli. An interesting finding was that perceived slant induced by modulations of dilation disparity was in the direction of the vertical component. This suggests the vertical size disparity mechanism has a higher temporal bandwidth than the horizontal size disparity mechanism. However, conflicting perspective information may play a dominant role in determining the temporal properties of perceived slant and inclination.     

Aging and the perception of local surface orientation from optical patterns of shading and specular highlights

Younger and older observers' ability to perceive local surface orientation from optical patterns of shading and specular highlights was investigated in two experiments. On each trial, the observers viewed a randomly generated, smoothly curved 3-D object and manipulated an adjustable gauge figure until its orientation matched that of a specific local region on the object's surface (cf. Koenderink, van Doom, & Kappers, 1992). The performance of both age groups was facilitated by the presence of binocular disparity (Experiment 1) and object rotation in depth (Experiment 2). Observers in both age groups were able to judge the surface tilt component of orientation more precisely than the slant component. Significant, but modest, effects of age were found in Experiment 1, but not in Experiment 2. The ability to perceive local surface orientation appears to be relatively well preserved with increasing age, at least through the age of 80.     

Postfusional latency in stereoscopic slant perception and the primitives of stereopsis

Random dot stereograms of slanted surfaces were constructed, each representing one or two slanted surfaces in different relative arrangements and with different axes. Latency to fusion and from fusion to stereoscopic resolution was measured for each stimulus. It was found that latency to fusion was always very brief but that latency to stereoscopic resolution varied markedly, depending upon the orientation and arrangement of the stereoscopic surfaces. A gradient of discontinuities at a surface boundary produced an instant slant response for that surface, whereas a gradient of absolute disparities across the surface did not, except under conditions where vertical declination (a form of orientation disparity) was present. We conclude that stereopsis is not based on the primitives used in matching the images for fusion and that it is, at least initially, a response to disparity discontinuities which play no role in the fusion process. We also conclude that vertical declination is responded to globally as a slant around a horizontal axis but that other forms of orientation disparity are ineffective. The evidence from our experiments does not support the existence of a stereoscopic ability to respond globally to differences in magnification (or spatial frequency). It is suggested that stereoscopic perception of slant around a vertical axis is slow because it results from the integration of local processes.     

The induced effect,vertical disparity,and stereoscopic theory

The induced effect is an apparent slant of a frontal plane surface around a vertical axis, resulting from vertical magnification of the image in one eye. It is potentially important in suggesting a role for vertical disparity in stereoscopic vision, as proposed by Helmholtz. The paper first discusses previous theories of the induced effect and their implications. A theory is then developed attributing the effect to the process by which the stereoscopic response to horizontal disparity is scaled for viewing distance and eccentricity. The theory is based on a mathematical analysis of vertical disparity gradients produced by surfaces at various distances and eccentricities relative to the observer. Vertical disparity is shown to be an approximately linear function of eccentricity, with a slope or gradient which decreases with observation distance. The effect of vertical magnification on such gradients is analyzed and shown to be consistent with a change in the eccentricity factor, but not the distance factor, required to scale horizontal disparity. The induced effect is shown to be an appropriate stereoscopic response to a zero horizontal disparity surface at the eccentricity indicated. However, since extraretinal convergence signals provide conflicting evidence about eccentricity, they may attenuate the induced effect from its mathematically predicted value. The discomfort associated with the induced effect is attributed to this conflict.     

The visual perception of surface orientation from optical motion

Observers viewed monocular animations of rotating dihedral angles and were required to indicate their perceived structures by adjusting the magnitude and orientation of a stereoscopic dihedral angle. The motion displays were created by directly manipulating various aspects of the image velocity field, including the mean translation, the horizontal and vertical velocity gradients, and the manner in which these gradients changed over time. The adjusted orientation of each planar facet was decomposed into components of slant and tilt. Although the tilt component was estimated with a high degree of accuracy, the judgments of slant exhibited large systematic errors. The magnitude of perceived slant was determined primarily by the magnitude of the velocity gradient scaled by its direction. The results also indicate that higher order temporal derivatives of the moving elements had little effect on observers' judgments.     

Perceived depth scales with disparity gradient.

Perceived difference in depth between two adjacent stimuli decreases with increasing disparity gradient even if the disparity stays constant, ie when the stimuli approach each other along paths within fronto-parallel planes. This depth scaling effect is more pronounced with line stimuli than with two isolated points or two small symbols and is insignificant for easily discriminable symbols. The decrease in perceived depth is more pronounced for horizontal orientation than for oblique or vertical orientation. The ratio of perceived depth difference to displayed disparity difference also decreases when the distance between the stimuli increases at a constant gradient in depth. This is to say that we are more correct in our depth estimates for steep gradients in depth when the euclidean distance between the stimuli is short.     

Visual field differences in recognizing letters

Differences due to visual field location were examined for single letters placed at one of 12 clockface positions 3° and 6° from fixation. Results compared closely with established findings using simple light stimuli, showing best recognition on the horizontal meridian, poorest on the vertical and intermediate on oblique meridians. Subjects’ confidence ratings followed the same pattern. There was evidence for a specific right superiority along the horizontal meridian, as found in previous studies, but no evidence for a general right hemifield superiority. The difficulty of arguing from these findings to available dominance or scanning explanations is pointed out. It is proposed that effects due to visual field variability may have a pervasive yet largely unrecognized influence in visual perception research.     

Perceptual asymmetries are preserved in short-term memory tasks

Visual performance is heterogeneous at isoeccentric locations; it is better on the horizontal than on the vertical meridian and worse at the upper than at the lower region of the vertical meridian (Carrasco, Talgar, & Cameron, 2001; Talgar & Carrasco, 2002). It is unknown whether these performance inhomogeneities are also present in spatial frequency tasks and whether asymmetries present during encoding of visual information also emerge in visual short-term memory (VSTM) tasks. Here, we investigated the similarity of the perceptual and VSTM tasks in spatial frequency discrimination (Experiments 1 and 2) and perceived spatial frequency (Experiments 3 and 4). We found that (1) performance in both simultaneous (perceptual) and delayed (VSTM) spatial frequency discrimination tasks varies as a function of location; it is better along the horizontal than along the vertical meridian; and (2) perceived spatial frequency in both tasks is higher along the horizontal than along the vertical meridian. These results suggest that perceived spatial frequency may mediate performance differences in VSTM tasks across the visual field, implying that the quality with which we encode information affects VSTM.     

Pre-attentive detection of a target defined by stereoscopic slant.

Does the visual system represent stereoscopic depth purely as a map of local disparities, or does it explicitly represent local relationships of disparity, such as disparity gradients? Experiments are reported in which visual search for a target containing the same disparity range as other elements in the display, but differing in the relationship of the disparities (stereo slant), was used to determine whether the target showed 'pop-out' like a unitary feature, or the serial search characteristic of feature conjunctions. Each stereo pair of elements was selected randomly from a range of outline parallelograms leaning to the right or to the left, so that the target could not be identified using any monocular shape cue. Response times for detection of the target (present on 50% of the trials) were independent of the number of elements in the display. This result was confirmed by varying element size and spacing, and by using oblique crosses rather than parallelograms as stimuli. It is concluded that stereoscopically defined slant, or disparity gradient, can be processed and compared in parallel across the display, and acts in this respect as an explicit unitary visual property. This contrasts with findings in analogous experiments on movement, which show that targets defined by divergence or deformation of optic flow can only be identified by serial search.     

Hinge versus twist: the effects of 'reference surfaces' and discontinuities on stereoscopic slant perception

Stereoscopic slant perception around a vertical axis (horizontal slant) is often found to be strongly attenuated relative to geometric prediction. Stereo slant is much greater, however, when an adjacent surface, stereoscopically in the frontal plane, is added. This slant enhancement is often attributed to the presence of a 'reference surface' or to a spatial change in the disparity gradient (introducing second and higher derivatives of disparity). Gillam, Chambers, and Russo (1988 Journal of Experimental Psychology: Human Perception and Performance 14 163-175) questioned the role of these factors in that placement of the frontal-plane surface in a direction collinear with the slant axis (twist configuration) sharply reduced latency for perceiving slant whereas placing the same surface in a direction orthogonal to the slant axis (hinge configuration) had little effect. We here confirm these findings for slant magnitude, showing a striking advantage for twist over hinge configurations. We also examined contrast slant measured on the frontal-plane surface in the hinge and twist configurations. Under conditions where test and inducer surfaces have centres at the same depth for twist and hinge, we found that twist configurations produced strong negative slant contrast, while hinge configurations produced significant positive contrast or slant assimilation. We conclude that stereo slant and contrast effects for neighbouring surfaces can only be understood from the patterns and gradients of step disparities present. It is not adequate to consider the second surface merely as a reference slant for the first or as having its effect via a spatial change in the disparity gradient.     

Stereoscopic matching and the aperture problem

In order to perceive stereoscopic depth, the visual system must define binocular disparities. Consider an oblique line seen through an aperture formed by flanking occluders. Because the line is perceived behind the aperture, the line must have disparity relative to the aperture. What is the assigned disparity of the line in this aperture problem? To answer this question five observers adjusted the horizontal disparity of a probe until it was perceived at the same depth as the disparate line behind the aperture. The results show that, when both the horizontal and the vertical disparities of the occluders are well-defined, the probe must have the same horizontal disparity as the horizontal separation between the line half-images. However, when the horizontal and vertical disparities of the occluders are ill-defined, the intersections of the line and the occluder borders can determine the matching direction. In the latter case, the matching direction varies with the aperture orientation and there is considerable variability across observers.     

An oblique effect in aesthetics: homage to Mondrian (1872-1944)

The effect of the orientation of Mondrian's paintings on their aesthetic appeal was examined. Eight paintings, four with horizontal/vertical frames in the original and four with oblique frames, were presented in eight different orientations and rated for aesthetic appeal on a 7-point scale. There was a stronger preference for pictures presented so that their component lines were horizontal and vertical than for pictures presented with their component lines in an oblique orientation. In addition, subjects showed a preference for the original orientation, perhaps because rotation changes the lateral balance of the paintings as well as the orientation of the component lines. There was no overall preference for one frame orientation over another, but there was an interaction between frame orientation and component orientation, resulting in a preference for paintings where the components were parallel to the surrounding frame. It is suggested that the aesthetic oblique effect reported here is related to the oblique effect in orientation perception and the privileged access which horizontal and vertical lines have to the visual system. This offers a possible mechanism for aesthetic judgments of abstract patterns: we find pleasing those stimuli which are closely tuned to the properties of the human visual system.     

Perceptual learning without feedback and the stability of stereoscopic slant estimation

Subjects were examined for practice effects in a stereoscopic slant-estimation task involving surfaces that comprised a large portion of the visual field. In most subjects slant estimation was significantly affected by practice, but only when an isolated surface (an absolute disparity gradient) was present in the visual field. When a second, unslanted, surface was visible (providing a second disparity gradient and thereby also a relative disparity gradient) none of the subjects exhibited practice effects. Apparently, stereoscopic slant estimation is more robust or stable over time in the presence of a second surface than in its absence. In order to relate the practice effects, which occurred without feedback, to perceptual learning, results are interpreted within a cue-interaction framework. In this paradigm the contribution of a cue depends on its reliability. It is suggested that normally absolute disparity gradients contribute relatively little to perceived slant and that subjects learn to increase this contribution by utilizing proprioceptive information. It is argued that--given the limited computational power of the brain--a relatively small contribution of absolute disparity gradients in perceived slant enhances the stability of stereoscopic slant perception.     

The stereoscopic anisotropy: individual differences and underlying mechanisms

Observers are more sensitive to variations in the depth of stereoscopic surfaces in a vertical than in a horizontal direction; however, there are large individual differences in this anisotropy. The authors measured discrimination thresholds for surfaces slanted about a vertical axis or inclined about a horizontal axis for 50 observers. Orientation and spatial frequency discrimination thresholds were also measured. For most observers, thresholds were lower for inclination than for slant and lower for orientation than for spatial frequency. There was a positive correlation between the 2 anisotropies, resulting from positive correlations between (a) orientation and inclination thresholds and (b) spatial frequency and slant thresholds. These results support the notion that surface inclination and slant perception is in part limited by the sensitivity of orientation and spatial frequency mechanisms.     

Orientational versus horizontal disparity in the stereoscopic appreciation of slant

Twenty stereograms with needles either plunging in depth or untilted were constructed. When the geometry of the needles was unbiased, the tilt of the needles was correctly and rapidly appreciated. When the needles were biased so as to remove either their orientational disparity, or the difference in horizontal disparities at the tips, they could be seen, depending on the subject and the nature of the bias, either with or without slant. Orientational disparity proved to be, with two different testing methods, clearly more effective than horizontal disparity in conveying the information of slant. Biased needles at -45 degrees were more often rejected as untilted than biased needles at +45 degrees. The orientational disparity information was ineffective with crosses that combined +45 degrees and -45 degrees needles. The reaction time and the nature of the percept were correlated, the tilted percept taking longer to mature than the untilted one in biased stereograms. Of the seventy tested subjects, one appeared to make no use at all of horizontal disparity in the stereoscopic appreciation of slant.     

Variations in apparent spatial frequency with stimulus orientation: L Incidence of the effect in the general population

The human visual system is anisotropic not only for stimulus detection and discrimination but also for stimulus appearance. The apparent length of a stationary stimulus and the apparent velocity of a moving stimulus vary with orientation. These variations are predictable from a model assuming a compression of the horizontal spatial meridian relative to the vertical meridian. In this paper, the apparent spatial frequency of a suprathreshold grating is shown to depend on the grating orientation. Specifically, horizontal gratings appear coarser than vertical gratings of equivalent spatial frequency. Additional data collected from the same group of observers show that horizontal lines appear shorter than vertical lines of the same extent. The presence of the spatial frequency and length illusions, although both predictable from the compression model, were not found to be correlated within observers. Implications of these results for other data in the literature are discussed.     

Hemispatial asymmetries in judgment of stimulus size

Recent research has demonstrated a leftward bias in judgments of size. In the present experiments, hemispatial size bias was measured through simultaneous presentation of a circle and an ellipse varying in horizontal or vertical extent. A consistent leftward bias of horizontal size judgments (but not vertical) was obtained; at the point of subjective equality, the width of the objects that were presented in left hemispace was smaller than the width of the objects that were presented in right hemispace. These data suggest that the horizontal extent of stimuli appear larger in left hemispace than in right hemispace. Results also indicated that symmetrical stimulus presentation, with respect to the vertical meridian, is required for the bias to emerge. Furthermore, increasing or decreasing stimulus eccentricity weakened the effect. Attenuation of this bias upon the manipulation of parameters indicates that this phenomenon is context specific and is affected by similar parameters that are known to influence the magnitude of error in pseudoneglect.     

An application of the optic sphere theory in discrimination of slant with minimal information

In Johansson and Börjesson (1989), a new theory of visual space perception—the optic sphere theory—was presented in which the hemispheric shape of the retina is utilized for determination of slant of plane surfaces in wide-angle perception. The process of the optic sphere mechanism can be described as the projection of a translating distal line on the optic sphere, and an extrapolation of this projection to a great circle. The determination of the 3-D slant of the distal line is made by identification of points of no change on the great circle during its rotation. The main objective of the present study was to investigate this process as applied to central stimulation of the retina with reduced and minimal information of slant or horizontal orientation. Each stimulus pattern consisted of either two continuous lines or two pairs of dots in motion presented on a computer screen. The pairwise lines and the pairs of dots defined simulated 3-D slants (or horizontal orientations) of different magnitude within each pair, and the subjects' task was to discriminate between these simulated slants. It was shown that the simulations evoke percepts of 3-D slants, and of horizontal orientations, and that it is possible to discriminate between them even from minimal information (pairs of dots). Further, the empirical findings of Börjesson (1994) indicated that longer extrapolations of the projected arc to a point of no change yield less accurate discriminations of slant. We failed to replicate this in Experiment 4, in which case stimulus variables that covaried with extrapolation length were eliminated or minimized. It is suggested that this raises some doubt about discrimination accuracy as dependent on extrapolation length per se. The overall conclusion, however, is that the optic sphere theory represents a possible explanation of, or analogy to, the process utilized by the visual system for determination of the simulated 3-D slants and horizontal orientations in the present study.     

Perceived path of oblique motion: horizontal-vertical and stimulus-orientation effects

Subjects adjusted the path of moving stimuli to produce apparent slopes of 45 degrees with respect to horizontal. The stimulus was either a single moving dot or a vertical or horizontal bar. In separate experiments either the stimuli were tracked or fixation was maintained on a stationary fixation target positioned 8 deg to the right of the center of stimulus motion. In both experiments the selected path slopes were in general more horizontal than 45 degrees. This pattern indicates that subjects overestimate the vertical component of motion along an oblique path, and is interpreted as a manifestation of the spatial anisometropy generally termed the 'horizontal-vertical illusion'. Additionally, paths selected for horizontal bars were more vertical than those for vertical bars. This finding is interpreted in the context of a previous report of the influence of stimulus orientation on perceived velocity.