Projected disparity, not horizontal disparity, predicts stereo depth of 1-D patterns

Abstract

Binocular disparities have a straightforward geometric relation to object depth, but the computation that humans use to turn disparity signals into depth percepts is neither straightforward nor well understood. One seemingly solid result, which came out of Wheatstone’s work in the 1830’s, is that the sign and magnitude of horizontal disparity predict the perceived depth of an object: ‘Positive’ horizontal disparities yield the perception of ‘far’ depth, ‘negative’ horizontal disparities yield the perception of ‘near’ depth, and variations in the magnitude of horizontal disparity monotonically increase or decrease the perceived extent of depth. Here we show that this classic link between horizontal disparity and the perception of ‘near’ versus ‘far’ breaks down when the stimuli are one-dimensional. For these stimuli, horizontal is not a privileged disparity direction. Instead of relying on horizontal disparities to determine their depth relative to that of two-dimensional stimuli, the visual system uses a disparity calculation that is non-veridical yet well suited to deal with the joint coding of disparity and orientation.

Perceived depth in non-transitive stereo displays

“…8). The difference was in the direction of seeing the grating as nearer than expected from its disparity, mirroring results of Experiment 1 and apparent to some extent in most observers' data in all experiments (it is also opposite in direction from the bias we observed in earlier experiments Farell, Chai, & Fernandez, 2009), where gratings and plaids had a center-surround configuration.) On the other hand, all the observers show a significant difference between PSEs for Parallel and Orthogonal Transitive displays and no difference between the Parallel and Orthogonal conditions of Non-Transitive displays.…”

“…The horizontal disparity, which is the same for all of the plaids appearing in the experiment, provides no basis for explaining differences in perceived depth between the three display types. However, if projected disparities formed the effective metric, then the psychometric functions for Parallel and Orthogonal Transitive displays should be laterally displaced but otherwise similar Farell, Chai, & Fernandez, 2009). The psychometric function for Non-Transitive displays, by contrast, might be expected to have a distinctive shape.…”

“…The perceived depth between a 1-D stimulus and a 2-D stimulus is a case in which horizontal disparities do not predict stereo depth perception Farell, Chai, & Fernandez, 2009). The depth between a grating and a plaid, for example, is predicted instead by a version of the intersection-of-constraints rule (Fennema & Thompson, 1979;Adelson & Movshon, 1982) applied to the two-dimensional disparity vectors.…”

“…1. The perceived depth separating the stimuli varies with the relative magnitude of disparity components along this axis (Farell, Chai, & Fernandez, 2009). Equivalently, the disparities can be compared in the direction of the plaid's disparity; the grating's disparity in this case is given by the intersection of its constraint line with the plaid's disparity axis.…”

“…We call the results of either version of this calculation the projected disparity value. Because relative but not absolute disparity directions enter into the computation, it is possible for two simultaneously presented stimuli, one 1-D and the other 2-D, to appear at the same depth even though the horizontal disparity of one is negative and that of the other is positive (Farell, Chai, & Fernandez, 2009). This allows us to create sets of stimuli that have contradictory depth relations.…”