Perceived depth in non-transitive stereo displays

- Combinations of 1-D and 2-D stimuli yield inconsistent depth percepts.
- Horizontal disparity cannot account for the depth seen.
- Attention fails to select stimulus subsets for independent depth judgments.
- Yet the data reveal the particular computational strategies employed.
- Observers use a global stimulus-dependent disparity direction for depth calculations.

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.