Perceived depth in non-transitive stereo displays

Abstract

The separation between the eyes shapes the distribution of binocular disparities and gives a special role to horizontal disparities. However, for one-dimensional stimuli, disparity direction, like motion direction, is linked to stimulus orientation. This makes the perceived depth of one-dimensional stimuli orientation dependent and generally non-veridical. It also allows perceived depth to violate transitivity. Three stimuli, A, B, and C, can be arranged such that A > B (stimulus A is seen as farther than stimulus B when they are presented together) and B > C, yet A ⩽ C. This study examines how the visual system handles the depth of A, B, and C when they are presented together, forming a pairwise inconsistent stereo display. Observers' depth judgments of displays containing a grating and two plaids resolved transitivity violations among the component stimulus pairs. However, these judgments were inconsistent with judgments of the same stimuli within depth-consistent displays containing no transitivity violations. To understand the contribution of individual disparity signals, observers were instructed in subsequent experiments to judge the depth of a subset of display stimuli. This attentional instruction was ineffective; relevant and irrelevant stimuli contributed equally to depth judgments. Thus, the perceived depth separating a pair of stimuli depended on the disparities of the other stimuli presented concurrently. This context dependence of stereo depth can be approximated by an obligatory pooling and comparison of the disparities of one- and two-dimensional stimuli along an axis defined locally by the stimuli.

The whole is faster than its parts: evidence for temporally independent attention to distinct spatial locations

“…Microconsciousness theory aims to explain intriguing psychophysically measured mismatches among attended features. Examples include mismatches between the timing of color and motion changes (Moutoussis & Zeki, 1997 ) as well as transitivity violations in stereoscopic depth (Farell & Ng, 2014 ). 3 Because distinct stimulus attributes such as color, motion, binocular disparity, orientation (and arguably spatial position; Patzwahl & Treue, 2009 ) register in distinct cortical ensembles, mismatches in feature binding can arise.…”

“… 3 A transitivity violation in stereoscopic depth occurs when participants perceive X nearer than Y, Y nearer then Z, but perceive X as either farther than or in the same depth plane as Z (Farell & Ng, 2014 ). …”

Attentional selection in judgments of stereo depth

“…When these stimuli have the same disparity directions and magnitudes, they should have the same apparent depth, as measured by the point of subjective equality (PSE). When their disparity directions are perpendicular, however, the 1-D stimulus has an expected disparity magnitude of zero at the PSE, independent of the disparity magnitude of the 2-D stimulus (Farell et al, 2009;Farell & Ng, 2014). These (Farell & Ng, 2014) in ways we explore in detail below.…”

“…We previously used the effect of irrelevant stimuli to investigate the mechanisms contributing to the perceived depth between 1-D and 2-D stimuli (Farell & Ng, 2014).…”

“…Depth from the disparity of 1-D stimuli is generally non-veridical, a consequence of the orientation dependence of the effective disparity direction. Pairing a 1-D and a 2-D stimulus can result in depth-order reversals and non-transitive depth relations (Farell et al, 2009;Farell & Ng, 2014).…”