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.     

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.     

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.     

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.     

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.     

Bimanual curvature discrimination of hand-sized surfaces placed at different positions

This study explores bimanual curvature discrimination of cylindrically curved, hand-sized surfaces. The setup was designed so that the postures of the observers' left and right arms and hands were thesame as if the observers were holding a large object in their hands. We measured psychometric curves for observers who used active, dynamic touch; these curvatures ranged from 1.18 to 4.05/m. Bimanual discrimination thresholds were found to be between 0.26 and 0.38/m on average; they were in the same range as unimanual thresholds reported in previous studies. Variation of (1) the horizontal distance between the stimuli or (2) the position of the setup had no effect on thresholds. In addition, we found that a number of observers showed discrimination biases in which they judged two physically different curvatures to be equal. Biases were of the same order of magnitude as the thresholds and could be either positive or negative. These biases can possibly be explained by small differences in left and right arm movements, an explanation that is supported by the position dependence of biases for individual observers.     

Variations in apparent spatial frequency with stimulus orientation: IL Matching data collected under normal and interferometric viewing conditions

Using an adjustment procedure, human observers matched the apparent spatial frequencies of sinusoidal gratings presented in different orientations (0, 45, 90, and 135 deg). Matches were made between all possible pairwise orientation combinations. Significant match deviations indicated that the apparent frequency of a grating depends on its orientation. The most consistent deviations were found between horizontal and vertical gratings, with horizontal gratings appearing to be of a lower spatial frequency than vertical gratings. These effects were relatively independent of stimulus contrast and persisted when the optics of the eye were bypassed with laser interferometry. A neurophysiological explanation of these effects is proposed.     

Visual long-term memory for spatial frequency?

It has been suggested that a visual long-term memory based on a sensory representation of the stimulus accounts for discrimination performance when the reference and the test stimuli are separated in time. Decision processes involved in setting response criteria, however, may also contribute to discrimination performance. In the present study, it is shown that under proper control, spatial frequency discrimination thresholds from a group of observers, each performing on a single trial, are significantly higher for a 2-h than for a 5-sec retention interval, whereas thresholds from individual observers performing in repeated trials with a 2-h retention interval are considerably lower. The results suggest that discrimination performance may depend on the retention of task-relevant information, such as a response criterion, rather than on visual memory of the stimulus. It is concluded that it is risky to postulate ahigh-fidelity long-term visual memory for spatial frequency on the basis of psychophysical group discrimination thresholds.     

The integration of orientation information in the motion correspondence problem

We examine how differently oriented components contribute to the discrimination of motion direction along a horizontal axis. Stimuli were two-frame random-dot kinematograms that were narrowband filtered in spatial frequency. On each trial, subjects had to state whether motion was to the left or the right. For each stimulus condition, Dmax (the largest displacement supporting 80% correct direction discrimination performance) was measured. In experiment 1, Dmax was measured for orientationally narrowband stimuli as a function of their mean orientation. Dmax was found to increase as the orientation of the stimuli became closer to the axis of motion. Experiment 2 used isotropic stimuli in which some orientation bands contained a coherent motion signal, and some contained only noise. When the noise band started at vertical orientations and increased until only horizontal orientations contained a coherent motion signal, Dmax increased slightly. This suggests that near-vertical orientations interfere with motion perception at large displacements when they contain a coherent motion signal. When the noise band started at horizontal and increased until only vertical orientations contained the motion signal, Dmax decreased steadily. This implies that Dmax depends at least partly on the most horizontal motion signal in the stimulus. These results were contrasted with two models. In the first, the visual system utilises the most informative orientations (nearest horizontal). In the second, all available orientations are used equally. Results supported an intermediate interpretation, in which all orientations are used but more informative ones are weighted more heavily.     

Orientation disparity, deformation, and stereoscopic slant perception.

Koenderink and van Doorn's theory, that the basis of stereoscopic slant perception is the deformation component of the disparity, field, was tested for slant around a horizontal axis, which produces images with a vertical ramp of horizontal disparity (horizontal shear) characterised by a global orientation disparity at the vertical meridian. The disparity field in this case can be parsed into two components, deformation and curl, which each contribute half of the orientation disparity. This case was compared with similar random-dot stimuli in which the deformation component was doubled and the curl component eliminated or vice versa. All three types of stimuli had identical orientation disparity at the vertical meridian. A condition in which there was no such orientation disparity, but deformation was present, was also included. It was found that perceived slant was not related to the deformation present, as Koenderink and van Doorn's theory would predict, but was predictable from the orientation disparity at the vertical meridian per se.     

Detection of amplitude modulation and frequency modulation in tactual gratings: a critical bandwidth for active touch

Since most natural surfaces are complex and vary in amplitude and spatial frequency, it might be interesting to consider gratings not in the spatial domain, but in the spatial-frequency domain. Detection thresholds for amplitude modulation (AM) and frequency modulation (FM) in sinusoidal gratings were measured for seven participants. Participants moved their fingers actively across the gratings. Although the two types of modulation are quite different in the spatial domain, they have many features in common in the frequency domain. In previous research (Nefs et al 2001 Perception 30 1263-1274) we measured the discrimination thresholds for amplitude and frequency for sinusoidal gratings. We hypothesised then that these thresholds could be used to predict the discriminability of other types of gratings. In the present study, we did indeed find that the FM and AM detection thresholds can be understood quite well by these discrimination thresholds. The results indicate that the tactual system contains parallel psychophysical channels that filter and integrate the power of stimuli within critical bands. With these results, we are also able to calculate the critical bandwidth for active dynamic touch. We estimated the critical bandwidth surrounding the spatial frequency of 2 cycles cm(-1) to be about 125% of that spatial frequency. This value for the critical band for spatial frequency is incompatible with previous findings for temporal frequencies in vibrotactile research. This indicates that dynamic spatial-frequency discrimination is not likely to be done by temporal frequency.     

Sensitivity to shearing and compressive motion in random dots

The sensitivity of the visual system to motion of differentially moving random dots was measured. Two kinds of one-dimensional motion were compared: standing-wave patterns where dot movement amplitude varied as a sinusoidal function of position along the axis of dot movement (longitudinal or compressional waves) and patterns of motion where dot movement amplitude varied as a sinusoidal function orthogonal to the axis of motion (transverse or shearing waves). Spatial frequency, temporal frequency, and orientation of the motion were varied. The major finding was a much larger threshold rise for shear than for compression when motion spatial frequency increased beyond 1 cycle deg-1. Control experiments ruled out the extraneous cues of local luminance or local dot density. No conspicuous low spatial-frequency rise in thresholds for any type of differential motion was seen at the lowest spatial frequencies tested, and no difference was seen between horizontal and vertical motion. The results suggest that at the motion threshold spatial integration is greatest in a direction orthogonal to the direction of motion, a view consistent with elongated receptive fields most sensitive to motion orthogonal to their major axis.     

The backward inclination of a surface defined by empirical corresponding points

Three experiments were conducted to investigate whether a locus of binocular correspondence extends eccentrically from the vertical horopter. In experiment 1, we investigated whether the backward inclination of the vertical horopter was manifested in the angle at which readers prefer to orient the page. All observers preferred a page inclined backwards to any other orientation. This backward inclination was less than predicted from previous psychophysical reports, however. In experiment 2, we investigated the extent of binocular correspondence, defined by minimal apparent interocular horizontal motion, in the central 24 deg of the binocular field. Our data define a planar surface inclined top-away from the observer as a locus from which psychophysical corresponding points are stimulated. In experiment 3, we measured vertical adjustments required to eliminate apparent vertical motion. Together, the pattern of results from experiments 2 and 3 is most consistent with a planar surface, inclined top-away from the observer. This is consistent with Helmholtz's account of the backward inclination of the vertical horopter and expands the locus of zero horizontal disparity from a single line in the median plane to eccentric loci extending at least +/- 12 deg in the central binocular field.     

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.     

Visual orientation estimation

A systematic error is reported in orientation estimation, in that on average, estimates are closer to the vertical axis than are the stimuli by up to 6°. This systematic error results from a specific mechanism that may be related to depth perception, and that is avoided in certain circumstances or when other mechanisms take over. For example, the estimates of one observer who was a welltrained professional draughtsman did not show this systematic error. Furthermore, for all observers tested, estimation of clock time is not subject to the regular orientation estimation error. Rather, observers tend to estimate timesas slightly further from the quarter hour than they really are. Orientation judgment channel capacity was also studied under various conditions. The number of discriminable orientations is far above the magic number “7“ limit, reaching over 20 in optimal circumstances. The distribution of discriminable orientations is nonlinear, in that these are more closely packed about the horizontal and vertical axis than at the oblique.     

When texture takes precedence over motion in depth perception

Both texture and motion can be strong cues to depth, and estimating slant from texture cues can be considered analogous to calculating slant from motion parallax (Malik and Rosenholtz 1994, report UCB/CSD 93/775, University of California, Berkeley, CA). A series of experiments was conducted to determine the relative weight of texture and motion cues in the perception of planar-surface slant when both texture and motion convey similar information. Stimuli were monocularly viewed images of planar surfaces slanted in depth, defined by texture and motion information that could be varied independently. Slant discrimination biases and thresholds were measured by a method of single-stimuli binary-choice procedure. When the motion and texture cues depicted surfaces of identical slants, it was found that the depth-from-motion information neither reduced slant discrimination thresholds, nor altered slant discrimination bias, compared to texture cues presented alone. When there was a difference in the slant depicted by motion and by texture, perceived slant was determined almost entirely by the texture cue. The regularity of the texture pattern did not affect this weighting. Results are discussed in terms of models of cue combination and previous results with different types of texture and motion information.     

Context superiority in a detection task with line-element stimuli: a low-level effect

Detection and identification performances for vertical and horizontal target elements embedded within an array of oriented noise elements were measured as a function of the orientation difference between the target and noise elements. Detection performances obtained with one vertical and three horizontal target elements clustered together and displayed such that they formed a schematic face-like pattern were significantly better than those obtained with the same clustered target elements displayed in an arbitrary, symmetrical or asymmetrical, configuration. This was so even though the identification of the face and nonface stimuli was well below the detection threshold of their parts. Detection thresholds for the clustered nonface patterns were slightly but significantly lower than those for the same target elements dispersed among the noise elements. Probability summation calculations based on the detection results obtained with one single target element predict detection thresholds which are intermediate between those of the clustered and dispersed targets, suggesting that inhibitory and facilitatory spatial interactions respectively are at work for the two types of stimuli. The existence of a context(face)-superiority effect at the detection level indicates top-down/bottom-up interactions between remote visual processing stages.     

Visual orientation estimation

A systematic error is reported in orientation estimation, in that on average, estimates are closer to the vertical axis than are the stimuli by up to 6 degrees. This systematic error results from a specific mechanism that may be related to depth perception, and that is avoided in certain circumstances or when other mechanisms take over. For example, the estimates of one observer who was a well-trained professional draughtsman did not show this systematic error. Furthermore, for all observers tested, estimation of clock time is not subject to the regular orientation estimation error. Rather, observers tend to estimate times as slightly further from the quarter hour than they really are. Orientation judgement channel capacity was also studied under various conditions. The number of discriminable orientations is far above the magic number "7" limit, reaching over 20 in optimal circumstances. The distribution of discriminable orientations is nonlinear, in that these are more closely packed about the horizontal and vertical axis than at the oblique.     

Monkeys perceive the orientation of objects relative to the vertical axis

Orientation processing is essential for segmenting contour from the background, which allows perception of the shape and stability of objects. However, little is known about how monkeys determine the degree and direction of orientation. In this study, to determine the reference axis for orientation perception in monkeys, post-discrimination generalization tests were conducted following discrimination training between the 67.5° and 112.5° orientations and between the 22.5° and 157.5° orientations. After discrimination training between the 67.5° and 112.5° orientations, the slope of the generalization gradient around the S⁺ orientation was broad, while the slope was steep after discrimination training between the 22.5° and 157.5° orientations. Comparing the shapes of the gradients indicated that the subjective distance between the 67.5° and 112.5° orientations was small, while the subjective distance between the 22.5° and 157.5° orientation was large. In other words, the monkeys recognized that the former and the latter distances were 45° and 135° across the vertical axis, rather than 135° and 45° across the horizontal axis, respectively. These findings indicate that the monkeys determined the degree and direction of the tilt using the vertical reference.     

Visual discrimination of spectral distributions

Human observers seem to be able to use different features that classify materials with a large degree of accuracy. In this paper, we look at human perception of statistical properties of the spectral distribution in a scene. We investigated whether human observers can discriminate just as accurately between coloured textures that have a spectral distribution due either to shading only or to both shading and specular reflectance as between uniform colours. Thresholds for the discrimination of coloured textures are about 15 times as high as thresholds for the discrimination of uniform colours, provided there is a sharp transition between the two colours. However, the coloured texture thresholds are only 1.5 times higher when we introduce a gradual transition between the two colours. There are also distinct qualitative differences in discrimination thresholds for different base colours. These differences cannot be predicted from discrimination thresholds for uniform colours. Human observers are surprisingly good at discriminating between a material edge and a shadow edge in complex scenes. Statistical differences in the orientation of the colour distributions in colour space might be used to accomplish this. In a second experiment we investigated how well observers can discriminate between two linear distributions in colour space that have the same base colour but different orientations. When we vary the line-length in R, G, B space, thresholds cannot be predicted completely by the conservation of the average distance between the two distributions. This means that observers use not only the maximum colour difference in the stimulus to do the task, but other cues are also involved.