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The title of Dhanraj Vishwanath's (2014) Psychological Review article is, of course, adapted from the title of George Berkeley's (1709/1922) book, "Towards a New Theory of Vision," and, as a consequence, it promises to provide us with a radically new understanding of 3D vision. Does it succeed? Vishwanath certainly raised important questions about what we mean by stereopsis, and he does a good job in reviewing some of the more recent findings on how particular viewing conditions affect stereopsis; however, it disappoints with respect to the claim that it offers a "new theory of stereopsis." (PsycINFO Database Record (c) 2019 APA, all rights reserved).

The ability of human observers to judge the straightness and parallelism of extended lines has been a neglected topic of study since von Helmholtz's initial observations 150 years ago. He showed that there were significant misperceptions of the straightness of extended lines seen in the peripheral visual field. The present study focused on the perception of extended lines (spanning 90° visual angle) that were directly fixated in the visual environment of a planetarium where there was only minimal information about the distance to the lines. Observers were asked to vary the curvature of 1 or more lines until they appeared to be straight and/or parallel, ignoring any perceived curvature in depth. When the horizon between the ground and the sky was visible, the results showed that observers' judgements of the straightness of a single line were significantly biased away from the veridical, great circle locations, and towards equal elevation settings. Similar biases can be seen in the jet trails of aircraft flying across the sky and in Rogers and Anstis's new moon illusion (Perception, 42(Abstract supplement) 18, 2013, 2016). The biasing effect of the horizon was much smaller when observers were asked to judge the straightness and parallelism of 2 or more extended lines. We interpret the results as showing that, in the absence of adequate distance information, observers tend to perceive the projected lines as lying on an approximately equidistant, hemispherical surface and that their judgements of straightness and parallelism are based on the perceived separation of the lines superimposed on that surface.

Abstract. Patrick Hughes's 'reverspective' artworks provide a novel way of investigating the effectiveness of different sources of 3-D information for the human visual system. Our empirical findings show that the converging lines of simple linear perspective can be as effective as the rich array of 3-D cues present in natural scenes in determining what we see, even when these cues are in conflict with binocular disparities. Theoretical considerations reveal that, once the information provided by motion parallax transformations is correctly understood, there is no need to invoke higher-level processes or an interpretation based on familiarity or past experience in order to explain either the 'reversed' depth or the apparent, concomitant rotation of a reverspective artwork as the observer moves from side to side. What we see in reverspectives is the most likely real-world scenario (distal stimulus) that could have created the perspective and parallax transformations (proximal stimulus) that stimulate our visual systems.

Helmholtz's famous distorted chessboard pattern has been used to make the point that perception of the straightness of peripherally viewed lines is not always veridical. Helmholtz showed that the curved lines of his chessboard pattern appear to be straight when viewed from a critical distance and he argued that, at this distance, the contours stimulated particular 'direction circles' in the field of fixation. We measured the magnitude of the distortion of peripherally viewed contours, and found that the straightness of elongated contours is indeed misperceived in the direction reported by Helmholtz, but that the magnitude of the effect varies with viewing conditions. On the basis of theoretical considerations, we conclude that there cannot, in principle, be particular retinal loci ('loci' is used here in the sense of an arc or an extended set of points that provide a basis for judging collinearity) to underpin our judgments of the straightness and parallelity of peripheral contours, because such judgments also require information about the 3-D surface upon which the contours are located. Moreover, we show experimentally that the contours in the real world that are judged to be straight and parallel can stimulate quite different retinal loci, depending on the shape of the 3-D surface upon which they are drawn.

Helmholtz's famous pincushioned chessboard figure has been used to make the point that straight lines in the world are not always perceived as straight and, conversely, that curved lines in the world can sometimes be seen as straight. However, there is little agreement as to the cause of these perceptual errors. Some authors have attributed the errors to the shape of the retina, or the amount of cortex devoted to the processing of images falling on different parts of the retina, while others have taken the effects to indicate that visual space itself is curved. Helmholtz himself claimed that the 'uncurved lines on the visual globe' corresponded to 'direction circles' defined as those arcs described by the line of fixation when the eye moves according to Listing's law. Careful re-reading of Helmholtz together with some additional observations lead us to the conclusion that two other factors are also involved in the effect: (i) a lack of information about the distance of peripherally viewed objects and (ii) the preference of the visual system for seeing the pincushion squares as similar in size.

When the corresponding horizontal meridia of the two eyes are aligned, the corresponding vertical meridia are tilted outwards in a temporal direction, a phenomenon first described by Helmholtz. However, it is not known if this effect is confined to the principal meridia or whether the same relationship exists between corresponding horizontal and corresponding vertical meridia at eccentric retinal locations. We sought to address this issue by exploiting the technique of Nakayama (1977 Proceedings of the Society of Photo-Optical Instrument Engineers 120 2-9) in which the positions of alternating dichoptic images that produce minimal apparent motion were used to measure the relative tilt of corresponding meridia at a range of eccentricities up to +/- 16 deg away from the fovea. Stimuli were composed of dichoptic images, one containing a blank field and the other a pair of dots, which alternated at a rate of 0.63 Hz and the relative tilt (binocular orientation difference) between the pairs of dots presented to the two eyes was varied between +/- 11 degrees. Nonius lines were used to maintain vergence angle, which was varied between 28 cm and infinity. Subjects judged which pair of alternating images produced the smallest amount of apparent motion (position change). It was found that at all eccentricities examined the corresponding horizontal meridia were generally aligned but the corresponding vertical meridia were consistently offset (extorted) by about +/- 2 degrees. The tilts of corresponding principal meridia were typically unaffected when vergence angle was varied, indicating that little or no cyclovergence accompanied changes in horizontal vergence. The results suggest that the binocular correspondence system appears to be mapped by a horizontal shear distortion that extends to retinal locations at least as far as 16 deg away from the foveae. The invariant extortion of corresponding principal vertical meridia with vergence state is consistent with previous suggestions that the empirical vertical horopter becomes progressively inclined with respect to the vertical as viewing distance increases.

Frisby et al (1993 Perception 22 Supplement, 115) proposed that the visual system might make cyclovergent eye movements in order to minimise the overall pattern of both vertical and horizontal disparities when an observer views an inclined stereoscopic surface. Their measurements of cyclovergence, which used vertically oriented nonius lines, were found to be consistent with that proposal. In our experiment 1, we measured torsional eye movements objectively, using scleral coils, and found no evidence of a cyclovergent response to either a real inclined surface or to a simulated inclined surface in which the two stereoscopic images were related by a horizontal shear transformation. These results are inconsistent with the disparity minimisation hypothesis. In order to account for the discrepant findings of the two studies, we propose that vertically oriented nonius lines may not be a valid method for assessing cyclovergence because the lines can be seen as lying 'within' the inclined surface. In experiment 2, we tested the predictions of the cyclovergence hypothesis of Frisby et al against our own 'within surface' explanation, using both horizontally and vertically oriented nonius lines and dichoptic images related by either a horizontal or a vertical shear. If cyclovergence were the cause of the misalignment, both horizontal and vertical nonius lines should appear misaligned to the same extent. This was not found to be the case. We conclude that vertical nonius lines may not be a valid technique for measuring cyclovergence when the lines are seen against a background of an inclined surface.

Disparity discrimination thresholds are known to increase with both retinal eccentricity and distance from the horopter. However, little is known about how the detectability of cyclopean gratings varies with retinal position. Thresholds for disparity corrugations were measured as a function of corrugation frequency for different visual eccentricities. Subjects viewed annular displays of random dot stereograms, and judged in which of two intervals a circumferential disparity modulation was present. For any given eccentricity, visual sensitivity to disparity corrugations was bandpass. As eccentricity increased from 3.5 to 21.0 degrees, peak-to-trough thresholds were found to increase, the optimal corrugation frequency for detection decreased, and the upper cutoff corrugation frequency also decreased. The M-Scaling functions of Rovamo and Virsu were used to replot the data in terms of cycles per unit cortical distance. Peak detection frequency was constant at 0.8 cycles per mm of cortex after this rescaling, demonstrating that acuity for disparity modulations is approximately M-scaled beyond the fovea.

Yang and Blake (1991 Vision Research 31 1177-1189) investigated depth detection in stereograms containing spatially narrow-band signal and noise energies. The resulting masking functions led them to conclude that stereo vision was subserved by only two channels peaking at 3 and 5 cycles deg-1. Glennerster and Parker (1997 Vision Research 37 2143-2152) re-analysed these data, taking into account the relative attenuation of low- and high-frequency noise masks as a consequence of the modulation transfer function (MTF) of the early visual system. They transformed the data using an estimated MTF and found that peak masking was always at the signal frequency across a 2.8 octave range. Here we determine the MTF of the early visual system for individual subjects by measuring contrast thresholds in a 2AFC orientation-discrimination task (horizontal vs vertical) using band-limited stimuli presented in a 7 deg x 7 deg window at 4 deg eccentricity. The filtered stimuli had a bandwidth of 1.5 octaves in frequency and 15 degrees in orientation at half-height. In the subsequent stereo experiment, the same (vertical) filters were used to generate both signal and noise bands. The noise was binocularly uncorrelated and scaled by each subject's MTF. Subjects performed a 2AFC depth-discrimination task (crossed vs uncrossed disparity) to determine threshold signal contrast as a function of signal and mask frequency. The resulting functions showed that peak masking was at the signal frequency over the three octave range tested (0.4-3.2 cycles deg-1). Comparison with simple luminance-masking data from experiments with similar stimuli shows that bandwidths for stereo masking are considerably larger. These data suggest that there are multiple bandpass channels feeding into stereopsis but that their characteristics differ from luminance channels in pattern vision.

Stereo thresholds for 84% correct detection of sinusoidal disparity corrugations depicted by narrow-band-filtered random dot stereograms were determined for surfaces as a function of (i) luminance center spatial frequency and (ii) disparity modulation frequency. In addition, supra-threshold depth matching functions for two amplitudes of peak-to-trough depth were determined using similar stimuli. Disparity thresholds followed a U-shaped function when plotted against luminance centre spatial frequency from 1 to 8 c/deg. The threshold functions for the three highest corrugation frequencies (ranging from 0.25 to 1 c/deg) formed a single family with a similar bandpass shape and a peak sensitivity at ca 4 c/deg. At the lowest frequency of depth modulation (0.125 c/deg) the shape of the luminance spatial frequency threshold function showed a reduced sensitivity to depth modulations when portrayed by patterns with high luminance centre frequencies (8 c/deg). The similarity of the threshold functions reveals luminance and corrugation frequency to be largely independent dimensions. The finding that the functions are not identical provides some evidence to support a weak luminance spatial frequency selectivity in stereoscopic channels tuned to corrugation frequency.

Depth from binocular disparity and motion parallax has traditionally been assumed to be the product of separate and independent processes. We report two experiments which used classical psychophysical paradigms to test this assumption. The first tested whether there was an elevation in the thresholds for detecting the 3D structure of corrugated surfaces defined by either binocular disparity or motion parallax following prolonged viewing (adaptation) of supra-threshold surfaces defined by either the same or different cue (threshold elevation). The second experiment tested whether the depth detection thresholds for a compound stimulus, containing both binocular disparity and motion parallax, were lower than the thresholds determined for each of the components separately (sub-threshold summation). Experiment 1 showed a substantial amount of within- and between-cue threshold elevation and experiment 2 revealed the presence of sub-threshold summation. Together, these results support the view that the combination of binocular disparity and motion parallax information is not limited to a linear, weighted addition of their individual depth estimates but that the cues can interact non-linearly in the computation of depth.

Under identical viewing conditions, observers made two types of judgement about the shape of stereoscopically defined surfaces: one required an estimate of viewing distance for correct performance (e.g. setting the depth of a hemi-cylinder to equal its half-height or a dihedral angle to 90 deg), the other did not (matching the depth of, for example, sinusoidal corrugations or hemi-cylinders presented at two distances). Depth constancy for the two types of task was about 75% and 100%, respectively. We argue that observers may use a simple "direct" strategy to perform the depth matching task rather than constructing and comparing a metric representation of each surface.

The present study compared the relative effectiveness of differential perspective and vergence angle manipulations in scaling depth from horizontal disparities. When differential perspective and vergence angle were manipulated together (to simulate a range of different viewing distances from 28 cm to infinity), approximately 35% of the scaling required for complete depth constancy was obtained. When manipulated separately the relative influence of each cue depended crucially on the size of the visual display. Differential perspective was only effective when the display size was sufficiently large (i.e., greater than 20 deg) whereas the influence of vergence angle, although evident at each display size, was greatest in the smaller displays. For each display size the independent effects of the two cues were approximately additive. Perceived size (and two-dimensional spacing of elements) was also affected by manipulations of differential perspective and vergence. These results confirm that both differential perspective and vergence are effective in scaling the perceived two-dimensional size of elements and the perceived depth from horizontal disparities. They also show that the effect of the two cues in combination is approximately equal to the sum of their individual effects.

Naive observers of random-dot stereograms depicting complex surfaces often find that they require several tens of seconds before the impression of depth emerges. With practice, however, perception times often decrease markedly: perceptual learning occurs. Current explanations of these effects were assessed in two experiments. In the first experiment the perception times of naive observers for random-dot stereograms which depicted the same complex shape but contained different ranges of disparity were measured. In the second experiment the minimum times required by experienced observers to perceive a given complex shape in stereograms that contained different ranges of disparity were determined. Perception times for the naive observers were all very fast (<3 s) and showed no evidence of perceptual learning. There was no effect of disparity range on perception times in either experiment. It was found that very large-disparity (80 min arc) complex stereograms could be perceived quickly, even by naive observers. It is concluded that the long initial latencies previously reported are not due to surface complexity nor to the range of disparities present. Other factors. such as dot size, dot density, and the correlation of the stereo images, appear to be important determinants of efficient stereoscopic performance when viewing complex random-dot stereograms.

We measured stereoscopic slant detection thresholds for surfaces slanting about a horizontal or a vertical axis. For random-dot covered surfaces, 1.25 deg of slant was required to detect slant about a horizontal axis, whereas 2.1 deg of slant was required to detect slant about a vertical axis. This anisotropy could be due to the fact that orientation disparities, which contain information about surface slant, are generally smaller for surfaces slanting about a vertical axis. To test this possibility, slant thresholds were measured for surfaces whose orientation disparity content was manipulated independently of the other slant information present. When the magnitude of orientation disparity was the same for surfaces slanting about a horizontal and a vertical axis, both surface orientations required about 1.5 deg of slant to be detected; thus the anisotropy became negligible. In contrast, when the orientation disparity content of a surface slanting about a vertical axis was zero, 3-4 deg of slant was required for detection; thus the anisotropy became larger. Under the conditions of these experiments, it appears that the visual system utilizes orientation disparities.

To calculate the depth difference between a pair of points on a three-dimensional surface from binocular disparities, it is necessary to know the absolute distance to the surface. Traditionally, it has been assumed that this information is derived from non-visual sources such as the vergence angle of the eyes. It has been shown that the horizontal gradient of vertical disparity between the images in the two eyes also contains information about the fixation distance. Recent results, however indicated that manipulations of the vertical disparity gradient have no effect on either the perceived shape or the perceived depth of surfaces defined by horizontal disparities. Following the reasoning of Longuet-Higgins and Tyler, we suggest that vertical disparities are best understood as a consequence of perspective viewing from two different vantage points and the results we report here show that the human visual system is able to exploit vertical disparities and use them to scale the perceived depth and size of stereoscopic surfaces, if the field of view is sufficiently large.

Motion parallax has been shown to be an effective and unambiguous source of information about the structure of three-dimensional (3-D) surfaces, both when an observer makes lateral movements with respect to a stationary surface and when the surface translates with respect to a stationary observer (Rogers & Graham, 1979). When the same pattern of relative motions among parts of the simulated surface is presented to a stationary observer on an unmoving monitor, the perceived corrugations are unstable with respect to the direction of the peaks and troughs. The lack of ambiguity in the original demonstrations could be due to the presence of (1) non-visual information (proprioceptive and vestibular signals) produced when the observer moves or tracks a moving surface, and/or (2) additional optic flow information available in the whole array. To distinguish between these two possibilities, we measured perceived ambiguity in simulated 3-D surfaces in situations where either nonvisual information or one of four kinds of visual information was present. Both visual and nonvisual information were effective in disambiguating the direction of depth within the simulated surface. Real perspective shape transformations affecting the elements of the display were most effective in disambiguating the display.

Random dot techniques were used to investigate the human visual system's sensitivity to sinusoidal depth modulations specified by motion parallax information. Thresholds for perceiving depth were found to be smallest when the spatial frequency of the depth corrugations was between 0.2 and 0.5 c/deg visual angle. These data were compared with the equivalent thresholds for perceiving depth corrugations specified by binocular disparity using similar apparatus and psychophysical procedures. The similarity between the sensitivity functions is suggestive of a closer relationship between the two systems than has previously been thought.

Prolonged inspection of a three-dimensional corrugated surface resulted in a successive contrast effect, or aftereffect, of depth, whereby a subsequently-viewed physically-flat test surface appeared to be corrugated in depth with the opposite phase to the adapting surface. The aftereffect occurred both when the depth was specified by motion parallax, in the absence of all other sources of depth information, and when it was specified solely by stereoscopic information. The depth aftereffect was measured by 'nulling' the apparent depth in the test surface with physical relative motion or binocular disparity until the test surface appeared flat. Up to 70% of the depth in the adapting surface was necessary to null the aftereffect. Simultaneous contrast effects in the perception of three-dimensional surfaces were used to investigate the spatial interactions that exist in the processing of motion-parallax and stereoscopic information. A physically vertical surface appeared to slope in depth in the opposite direction to the slope of a surrounding surface. In this case up to 50% of the slope of the inducing surface was necessary to null the contrast effect. Similar results were again obtained for motion-parallax and stereoscopic depth.

The experiments reported in this paper were designed to investigate how depth information from binocular disparity and motion parallax cues is integrated in the human visual system. Observers viewed simulated 3-D corrugated surfaces that translated to and fro across their line of sight. The depth of the corrugations was specified by either motion parallax, or binocular disparities, or some combination of the two. The amount of perceived depth in the corrugations was measured using a matching technique. A monocularly viewed surface specified by parallax alone was seen as a rigid, corrugated surface translating along a fronto-parallel path. The perceived depth of the corrugations increased monotonically with the amount of parallax motion, just as if observers were viewing an equivalent real surface that produced the same parallax transformation. With binocular viewing and zero disparities between the images seen by the two eyes, the perceived depth was only about half of that predicted by the monocular cue. In addition, this binocularly viewed surface appeared to rotate about a vertical axis as it translated to and fro. With other combinations of motion parallax and binocular disparity, parallax only affected the perceived depth when the disparity gradients of the corrugations were shallow. The discrepancy between the parallax and disparity signals was typically resolved by an apparent rotation of the surface as it translated to and fro. The results are consistent with the idea that the visual system attempts to minimize the discrepancies between (1) the depth signalled by disparity and that required by a particular interpretation of the parallax transformation and (2) the amount of rotation required by that interpretation and the amount of rotation signalled by other cues in the display.

Random-dot techniques were used to examine the interactions between the depth cues of dynamic occlusion and motion parallax in the perception of three-dimensional (3-D) structures, in two different situations: (a) when an observer moved laterally with respect to a rigid 3-D structure, and (b) when surfaces at different distances moved with respect to a stationary observer. In condition (a), the extent of accretion/deletion (dynamic occlusion) and the amount of relative motion (motion parallax) were both linked to the motion of the observer. When the two cues specified opposite, and therefore contradictory, depth orders, the perceived order in depth of the simulated surfaces was dependent on the magnitude of the depth separation. For small depth separations, motion parallax determined the perceived order, whereas for large separations it was determined by dynamic occlusion. In condition (b), where the motion parallax cues for depth order were inherently ambiguous, depth order was determined principally by the unambiguous occlusion information.

The perspective transformations of the retinal image, produced by either the movement of an observer or the movement of objects in the visual world, were found to produce a reliable, consistent, and unambiguous impression of relative depth in the absence of all other cues to depth and distance. The stimulus displays consisted of computer-generated random-dot patterns that could be transformed by each movement of the observer or the display oscilloscope to simulate the relative movement information produced by a three-dimensional surface. Using a stereoscopic matching task, the second experiment showed that the perceived depth from parallax transformations is in close agreement with the degree of relative image displacement, as well as producing a compelling impression of three-dimensionality not unlike that found with random-dot stereograms.

The appearance of certain three-dimensional surfaces was found to depend on the orientation of the depth contours forming the surface. This was true both when the depth was specified by motion parallax and when it was specified by binocular disparities. Slowly changing depth surfaces that generated a pattern of relative motions or disparities characterized by a one-dimensional expansion-compression were perceived differently from those that produced a shear transformation.