It is well established that perceived stereoscopic depth between two objects depends on their relative horizontal disparity. It is by now also established that the stereoscopic depth of isolated objects is influenced by their disparity relative to a background surface. Furthermore, biases in perceived background surface slant can produce biases in the perceived relative depth of detached objects seen against these surfaces. The presence and magnitude of such biases can be used to explore the possible influence of surfaces more remote than the immediate background. This is the goal of the present paper. We conclude that stereoscopic depth perception is influenced by the total configuration of objects and surfaces.
When the only information for the slant around a vertical axis of an isolated surface is a horizontal gradient of binocular disparity, the slant perceived is often strongly attenuated relative to geometric prediction (Gillam, Flagg, & Finlay,
1984; Mitchison & Westheimer,
1984; Rogers & Graham,
1983).
1 The misperception of slant can introduce a bias in the perceived relative position of small objects near the slanted surface. For example, when two small depth probes are placed equidistant from the observer in front of (Mitchison & Westheimer,
1984) or adjacent to (Gulick & Lawson,
1976) a textured surface whose stereo slant is attenuated, they do not appear equidistant. The local stereoscopic depth of each probe relative to the surface is more or less accurately perceived, but because the surface slant is underestimated, the probe further from the surface looks nearer to the observer than the one closer to the surface. The point of subjective equality (PSE) of the probes, therefore, has a bias related to the underestimation of the surface slant. A similar result was obtained by Glennerster and McKee (
1999), who found in addition that the PSE bias was reduced when the standing disparity of both test lines relative to the surface increased. This biasing effect of a surface on the perceived relative depth of nearer probes resembles an earlier observation by Gogel (
1972) that when the stereoscopic slant of a surface is reduced (or reversed) by perspective, a bias is introduced into the perceived relative depth of two stereoscopically viewed probes adjacent to the opposite ends of the surface (
Figure 1).
The bias introduced in the perception of the relative stereoscopic position of isolated objects by the underestimation of the stereoscopic slant of a background surface is robust across viewing conditions. The probes in Gogel's (
1972) and Gulick and Lawson's (
1976) experiments were much farther apart laterally (approximately 4°) than those of Glennerster and McKee (
1999) and Mitchison and Westheimer (
1984), which were separated by less than 1°. In addition, Glennerster and McKee (
1999) and Mitchison and Westheimer (
1984) used 150-ms exposures, whereas Gogel (
1972) and Gulick and Lawson (
1976) used exposures long enough for eye movements to occur. These observations, under a range of conditions, indicate that two probes may not be directly related to each other stereoscopically when a background surface is present, but that each may be related stereoscopically to proximal elements on the background surface, with the background surface slant mediating the perceived depth between them. The former is a local process; the latter is a process operating over a longer range, which can link local processes. It is an obvious advantage to use a surface to mediate between the local depths when probes are sufficiently far apart to have a weak depth signal relative to each other (e.g., Ogle,
1956). Such probes may have stronger relative depth signals with respect to angularly close elements of the background, which are linked by intervening disparities across the surface or by perspective integration. In Glennerster and McKee's (
2004) study, for example, the dots on the background had greater angular proximity to the probes than the probes had to each other.
In our studies, we explore the possibility that remote surfaces acting stereoscopically or perspectivally on the immediate background surface of objects may change both the apparent slant of the background and also the PSE of objects seen relative to it. Such secondary influences on the PSE of targets have not, to our knowledge, been explored previously.
An important manipulation in all of the following experiments relies upon a prior observation about stereoscopically slanted surfaces. It has been found by a number of investigators (Gillam, Chambers, & Russo,
1988; Gillam et al.,
1984; Kaneko & Howard,
1996; van Ee & Erkelens,
1996a,
1996b) that the poor slant response to a single surface, which is slanted stereoscopically around a vertical axis, gives way to a strong slant response when a frontal plane surface is placed either above or below the stereoscopically slanted surface in what Gillam et al. (
1988) and Howard and Rogers (
2002) have called a “twist” configuration. Gillam et al. attributed the particular effectiveness of the twist configuration in enhancing stereo slant to the presence of a gradient of relative disparities along the abutment of the two surfaces.
2
In the present experiments, this “twist” factor was used to alter the perceived stereoscopic slant of the background surface in a probe PSE task. If this manipulation changes the bias in the PSE of the probes seen against the center of the surface, it would show a novel contextual influence on surface-mediated stereoscopic depth. It would also indicate that slant information deriving entirely from discontinuities at the boundary of a surface can spread so that it participates in local processes with respect to the center of the surface.