An ecological approach to binocular vision.

An ecological approach to binocular vision was already demonstrated in Wheatstone's initial stereograms and was explicitly called for by J. J. Gibson, but detailed analysis and experimentation supporting this approach has been more recent. This paper discusses several aspects of this more recent research on environmentally occurring spatial layouts that can influence binocular vision. These include gradients of depth and regions that can be seen by only one eye. The resolution of local stereoscopic ambiguity by more global factors is also discussed.

Gradients of relative disparity underlie the perceived slant of stereoscopic surfaces.

Perceived stereoscopic slant around a vertical axis is strongly underestimated for isolated surfaces, suggesting that neither uniocular image compression nor linear gradients of absolute disparity are very effective cues. However, slant increases to a level close to geometric prediction if gradients of relative disparity are introduced, for example by placing flanking frontal-parallel surfaces at the horizontal boundaries of the slanted surface. Here we examine the mechanisms underlying this slant enhancement by manipulating properties of the slanted surface or the flanking surfaces. Perceived slant was measured using a probe bias method. In Experiment 1, an outlined surface and a randomly textured surface showed similar slant underestimation when presented in isolation, but the enhancement in slant produced by flankers was significantly greater for the textured surface. In Experiment 2, we degraded the relative disparity gradient by (a) reducing overall texture density, (b) reducing flanker width, or (c) adding disparity noise to the flankers. Density had no effect while adding noise to the flankers, or reducing their width significantly decreased perceived slant of the central surface. These results support the view that the enhancement of slant produced by adding flanking surfaces is attributable to the presence of a relative disparity gradient and that the flanker effect can spread to regions of the surface not directly above or below the gradient.

Comparing subjective contours for Kanizsa squares and linear edge alignments ('New York Titanic' figures).

One current view is that subjective contours may involve high-level detection of a salient shape with back propagation to early visual areas where small receptive fields allow for scrutiny of relevant details. This idea applies to Kanizsa-type figures. However, Gillam and Chan (2002 Psychological Science, 13, 279-282) using figures based on Gillam's graphic 'New York Titanic' (Gillam, 1997 Thresholds: Limits of perception. New York: Arts Magazine) showed that strong subjective contours can be seen along the linearly aligned edges of a set of shapes if occlusion cues of 'extrinsic edge' and 'entropy contrast' are strong. Here we compared ratings of the strength of subjective contours along linear alignments with those seen in Kanizsa figures. The strongest subjective contour for a single set of linearly aligned shapes was similar in strength to the edges of a Kanizsa square (controlling for support ratio) despite the lack of a salient region. The addition of a second set of linearly aligned inducers consistent with a common surface increased subjective-contour strength, as did having four rather than two 'pacmen' in the Kanizsa figure, indicating a role for surface support. We argue that linear subjective contours allow for the investigation of certain occlusion cues and the interactions between them that are not easily explored with Kanizsa figures.

Monocular and binocular edges enhance the perception of stereoscopic slant.

Gradients of absolute binocular disparity across a slanted surface are often considered the basis for stereoscopic slant perception. However, perceived stereo slant around a vertical axis is usually slow and significantly under-estimated for isolated surfaces. Perceived slant is enhanced when surrounding surfaces provide a relative disparity gradient or depth step at the edges of the slanted surface, and also in the presence of monocular occlusion regions (sidebands). Here we investigate how different kinds of depth information at surface edges enhance stereo slant about a vertical axis. In Experiment 1, perceived slant decreased with increasing surface width, suggesting that the relative disparity between the left and right edges was used to judge slant. Adding monocular sidebands increased perceived slant for all surface widths. In Experiment 2, observers matched the slant of surfaces that were isolated or had a context of either monocular or binocular sidebands in the frontal plane. Both types of sidebands significantly increased perceived slant, but the effect was greater with binocular sidebands. These results were replicated in a second paradigm in which observers matched the depth of two probe dots positioned in front of slanted surfaces (Experiment 3). A large bias occurred for the surface without sidebands, yet this bias was reduced when monocular sidebands were present, and was nearly eliminated with binocular sidebands. Our results provide evidence for the importance of edges in stereo slant perception, and show that depth from monocular occlusion geometry and binocular disparity may interact to resolve complex 3D scenes.

Orientation contrast and entropy contrast in the genesis of subjective contours along thin lines.

Subjective contours are widely considered to be an aspect of the perception of occlusion, but considerations of occlusion do not always drive predictions of their strength. Occluding surfaces have no necessary relationship to the contours they occlude, yet it is commonly predicted that subjective contours will be strongest for inducer alignments that are orthogonal to inducer orientations. In several papers we have proposed that a lack of relationship between inducers and their alignment promotes seeing subjective contours. We explore this further here using horizontal or near-horizontal thin-line inducers arranged vertically with linearly aligned terminations along central gaps. Subjective contour strength was measured using the method of paired comparison in two experiments. The weakest subjective contours were found when the gap was orthogonal to the inducers and parallel to the outer edges of the line set. Subjective contours were strengthened by orientation contrast, defined either as a nonorthogonal relationship between the gap and the inducers or as nonparallelism between the gap and the outer alignments of the inducers. The effect was replicated at both high and low line densities. We also confirmed a strong effect of high inducer entropy (variations in inducer orientation and separation) with thin-line inducers. The results support the view that the lack of a relationship of alignments to what is aligned is a major determinant of subjective contour strength.

Color constrains depth in da Vinci stereopsis for camouflage but not occlusion.

Monocular regions that occur with binocular viewing of natural scenes can produce a strong perception of depth--"da Vinci stereopsis." They occur either when part of the background is occluded in one eye, or when a nearer object is camouflaged against a background surface in one eye's view. There has been some controversy over whether da Vinci depth is constrained by geometric or ecological factors. Here we show that the color of the monocular region constrains the depth perceived from camouflage, but not occlusion, as predicted by ecological considerations. Quantitative depth was found in both cases, but for camouflage only when the color of the monocular region matched the binocular background. Unlike previous reports, depth failed even when nonmatching colors satisfied conditions for perceptual transparency. We show that placing a colored line at the boundary between the binocular and monocular regions is sufficient to eliminate depth from camouflage. When both the background and the monocular region contained vertical contours that could be fused, some observers appeared to use fusion, and others da Vinci constraints, supporting the existence of a separate da Vinci mechanism. The results show that da Vinci stereopsis incorporates color constraints and is more complex than previously assumed.

Phantom surfaces in da Vinci stereopsis.

In binocular viewing of natural three-dimensional scenes, occlusion relationships between objects at different depths create regions of the background that are visible to only one eye. These monocular regions can support depth perception. There are two viewing conditions in which a monocular region can be on the nasal side of a binocular surface--(a) when a background surface is viewed through an aperture and (b) when a region is camouflaged against the background in one eye's view. We created stimuli with a monocular region using complex textures in which camouflage was not possible, and for which there was no physical aperture. For these stimuli, observers perceived a strong phantom contour in near depth at the edge of the monocular region, with the monocular texture perceived behind at the depth of the binocular surface. Depth-matching with a probe showed that the depth of the phantom occluding surface was as precise as for stimuli with regular binocular disparity. Monocular regions of texture on the opposite (temporal) side of the binocular surface were perceived behind, as predicted by occlusion geometry, and there was no phantom surface. We discuss the implications for models of da Vinci stereopsis and stereoscopic edge processing, and consider the involvement of a form of Panum's limiting case. We conclude that the visual system uses a combination of occlusion geometry and complex matching to precisely locate edges in depth that lack a luminance contour.

Subjective contours along truncated letters.

The truncation of upper-case words can result in a subjective contour along the truncated ends of the letters. We explored this effect in two experiments designed to tease apart the processes responsible: in particular, the possible role of letter recognition. Such a role would indicate an unprecedented involvement of "high-level vision" in the genesis of subjective contours. In experiment 1, we confirmed the basic effect of word truncation in eliciting a subjective contour, using only letters where truncation does not eliminate any critical features. In experiment 2, we showed that the effect is not confined to words/letters but is equally strong for controlled non-letter stimuli that, like words, have many forms that have an inflection or an intersection near the centre. Truncation at one end then introduces proportional imbalance between upper and lower sections of the figures. We conclude from the two experiments that part of the effect is due to vertical shortening per se and the rest to the proportional imbalance introduced by the truncation. The effect of proportional imbalance, a novel determinant of subjective contours, may result from experience with letters, although the effect is not "high level" in requiring the recognition of specific letters.

Electrophysiological correlates of binocular stereo depth without binocular disparities.

A small region of background presented to only one eye in an otherwise binocular display may, under certain conditions, be resolved in the visual system by interpreting the region as a small gap between two similar objects placed at different depths, with the gap hidden in one eye by parallax. This has been called monocular gap stereopsis. We investigated the electrophysiological correlate of this type of stereopsis by means of sum potential recordings in 12 observers, comparing VEP's for this stimulus ("Gillam Stereo", Author BG has strong reservations about this term) with those for similar stimuli containing disparity based depth and with no depth (flat). In addition we included several control stimuli. The results show a pronounced early negative potential at a latency of around 170 ms (N170) for all stimuli containing non- identical elements, be they a difference caused by binocular disparity or by completely unmatched monocular contours. A second negative potential with latency around 270 ms (N270), on the other hand, is present only with stimuli leading to fusion and the perception of depth. This second component is similar for disparity-based stereopsis and monocular gap, or "Gillam Stereo" although slightly more pronounced for the former. We conjecture that the first component is related to the detection of differences between the images of the two eyes that may then either be fused, leading to stereopsis and the corresponding second potential, or else to inhibition and rivalry without a later trace in the VEP. The finding that that "Gillam Stereo" leads to cortical responses at the same short latencies as disparity based stereopsis indicates that it may partly rely on quite early cortical mechanisms.

Local and non-local effects on surface-mediated stereoscopic depth.

The magnitude and precision of stereoscopic depth between two probes is often determined by the disparity each has to a common background. If stereoscopic slant of the background is underestimated, a bias is introduced in the PSE of the probes (G. Mitchison & G. Westheimer, 1984). Using random dot stimuli, we show here how more remote surfaces can influence probe PSE via their influence on perceived background surface slant. The bias was reduced when frontal flanking surfaces were placed above and below the background surface, increasing its perceived slant. In a similar experiment, the flankers were slanted and the central background surface was frontal. For flankers alone, probe bias did not diminish up to a 4.4° separation of flankers and probes. When the central surface was present, the effect of the flankers on probe bias was mediated by this surface and diminished with flanker separation, presumably because of the diminishing contrast slant of the background surface. Stereoscopic depth between probes is thus influenced by a common background surface, by neighboring surfaces acting (contiguously or non-contiguously) on the background surface, and by distant surfaces acting directly on the probes.

Depth interval estimates from motion parallax and binocular disparity beyond interaction space.

Static and dynamic observers provided binocular and monocular estimates of the depths between real objects lying well beyond interaction space. On each trial, pairs of LEDs were presented inside a dark railway tunnel. The nearest LED was always 40 m from the observer, with the depth separation between LED pairs ranging from 0 up to 248 m. Dynamic binocular viewing was found to produce the greatest (ie most veridical) estimates of depth magnitude, followed next by static binocular viewing, and then by dynamic monocular viewing. (No significant depth was seen with static monocular viewing.) We found evidence that both binocular and monocular dynamic estimates of depth were scaled for the observation distance when the ground plane and walls of the tunnel were visible up to the nearest LED. We conclude that both motion parallax and stereopsis provide useful long-distance depth information and that motion-parallax information can enhance the degree of stereoscopic depth seen.

Contour entropy: a new determinant of perceiving ground or a hole.

Figure-ground perception is typically described as seeing one surface occluding another. Figure properties, not ground properties, are considered the significant factors. In scenes, however, a near surface will often occlude multiple contours and surfaces, often at different depths, producing alignments that are improbable except under conditions of occlusion. We thus hypothesized that unrelated (high entropy) lines would tend to appear as ground in a figure-ground paradigm more often than similarly aligned ordered (low entropy) lines. We further hypothesized that for lines spanning a closed area, high line entropy should increase the hole-like appearance of that area. These predictions were confirmed in three experiments. The probability that patterned rectangles were seen as ground when alternated with blank rectangles increased with pattern entropy. A single rectangular shape appeared more hole-like when the entropy of the enclosed contours increased. Furthermore, these same contours, with the outline shape removed, gave rise to bounding illusory contours whose strength increased with contour entropy. We conclude that figure-ground and hole perception can be determined by properties of ground in the absence of any figural shape, or surround, factors.

Occlusion issues in early Renaissance art.

Early Renaissance painters innovatively attempted to depict realistic three-dimensional scenes. A major problem was to produce the impression of overlap for surfaces that occlude one another in the scene but are adjoined in the picture plane. Much has been written about perspective in art but little about occlusion. Here I examine some of the strategies for depicting occlusion used by early Renaissance painters in relation to ecological considerations and perceptual research. Perceived surface overlap is often achieved by implementing the principle that an occluding surface occludes anything behind it, so that occlusion perception is enhanced by a lack of relationship of occluding contour to occluded contours. Some well-known figure-ground principles are also commonly used to stratify adjoined figures. Global factors that assist this stratification include the placement of figures on a ground plane, a high viewpoint, and figure grouping. Artists of this period seem to have differed on whether to occlude faces and heads, often carefully avoiding doing so. Halos were either eliminated selectively or placed oddly to avoid such occlusions. Finally, I argue that the marked intransitivity in occlusion by architecture in the paintings of Duccio can be related to the issue of perceptual versus cognitive influences on the visual impact of paintings.

Stereopsis loses dominance over relative size as target separation increases.

Binocular disparity produces less stereoscopic depth if the targets are separated by several degrees. It is thus possible that separation decreases the influence of stereopsis as a relative depth cue. Here, four experiments tested the strength of disparity in determining the direction of relative depth in the face of strongly conflicting relative size for a range of target separations. Under conditions of natural fixation-permitting sequential stereopsis-disparity dominated completely at small separations (0.42 degrees) but gradually gave way to relative size domination at large separations. However, when brief presentations prevented changes in fixation, disparity completely dominated at a separation of 0.5 degrees while relative size mostly dominated by 0.75 degrees - 1 degrees of separation. By varying target separation at different retinal eccentricities, we showed that separation per se was the critical factor in the dominance switch. Stereoacuity as a function of target separation for the same observers did not predict the switch from disparity to relative size. Stereoscopic dominance was found for the same small separations that are immune to stereoscopic reversals (Gillam, 1993 Perception 22 1025-1036). Our results suggest that relative disparity has a compulsory influence on perceived depth at small separations, suggesting a different mechanism from the one operating at larger separations.

Stereoscopic perception of real depths at large distances.

There has been no direct examination of stereoscopic depth perception at very large observation distances and depths. We measured perceptions of depth magnitude at distances where it is frequently reported without evidence that stereopsis is non-functional. We adapted methods pioneered at distances up to 9 m by R. S. Allison, B. J. Gillam, and E. Vecellio (2009) for use in a 381-m-long railway tunnel. Pairs of Light Emitting Diode (LED) targets were presented either in complete darkness or with the environment lit as far as the nearest LED (the observation distance). We found that binocular, but not monocular, estimates of the depth between pairs of LEDs increased with their physical depths up to the maximum depth separation tested (248 m). Binocular estimates of depth were much larger with a lit foreground than in darkness and increased as the observation distance increased from 20 to 40 m, indicating that binocular disparity can be scaled for much larger distances than previously realized. Since these observation distances were well beyond the range of vertical disparity and oculomotor cues, this scaling must rely on perspective cues. We also ran control experiments at smaller distances, which showed that estimates of depth and distance correlate poorly and that our metric estimation method gives similar results to a comparison method under the same conditions.

The role of remote closure in the perception of occlusion at junctions and illusory contours.

Abstract. Perceived occlusion at T-junctions or illusory contours at implicit T-junctions are often modelled by using edge information without surface context. We explored the effect of closure on perceived occlusion at T-junctions. Two vertical lines separated by a gap each had six abutting horizontal lines on opposite sides forming T-junctions. These lines were either closed or not closed into pairs at the stem ends of the Ts. In experiment 1, closed T-junction stems gave a much stronger sense of occlusion at the vertical lines than unclosed ones, even though closure information was remote from the putative occlusion and local T-junction information remained constant. When the outer two T-junctions were converted to L-junctions, perceived occlusion considerably diminished. The effect of closure on illusory-contour strength for stimuli like those of experiment 1 but with the vertical lines omitted was explored in experiment 2. The two sets of horizontal lines, separated by a gap, were either closed or not closed into pairs at their outer ends. Illusory-contour strength along the vertical alignments was much greater for closed pairs. Line terminations on both sides of the gap enhanced illusory-contour strength, but whether they were collinear or not had little effect.

The B73 maize genome: complexity, diversity, and dynamics.

We report an improved draft nucleotide sequence of the 2.3-gigabase genome of maize, an important crop plant and model for biological research. Over 32,000 genes were predicted, of which 99.8% were placed on reference chromosomes. Nearly 85% of the genome is composed of hundreds of families of transposable elements, dispersed nonuniformly across the genome. These were responsible for the capture and amplification of numerous gene fragments and affect the composition, sizes, and positions of centromeres. We also report on the correlation of methylation-poor regions with Mu transposon insertions and recombination, and copy number variants with insertions and/or deletions, as well as how uneven gene losses between duplicated regions were involved in returning an ancient allotetraploid to a genetically diploid state. These analyses inform and set the stage for further investigations to improve our understanding of the domestication and agricultural improvements of maize.

Failure of facial configural cues to alter metric stereoscopic depth.

J. Burge, M. A. Peterson, and S. E. Palmer (2005) reported that an ordinal cue to depth can influence the perception of metric depth in stereoscopic displays. They argued that when a familiar figure--a face--is placed stereoscopically closer than a background there is greater perceived depth relative to the ground than when the face shape is placed stereoscopically further and becomes the ground. This result suggests the possibility that a non-metric depth cue--the familiarity of a figure--can influence the perception of metric depth in stereoscopic displays. However, the method leaves open the possibility that these results were due to a response bias, rather than from a genuine change in perceived depth. To assess this possibility, we used the same basic stimulus but directly measured the perceived depth difference between the face and non-face surfaces when arranged as figure and ground or ground and figure respectively using a separate double depth probe to measure perceived depth. We found no difference between the perceived depth of familiar and unfamiliar figures as a function of whether they were stereoscopically figure or ground. We conclude that the J. Burge et al. (2005) result depends on their particular task and is likely to reflect a response bias. It is premature to conclude that facial configural cues distort perception of metric depth although we argue that there are circumstances in which ordinal cues do influence metric depth.