A physiologically-based explanation of disparity attraction and repulsion

Westheimer and Levi [(1987) Vision Research, 27, 1361-1368] found that when a few isolated features are viewed foveally, the perceived depth of a feature depends not only on its own disparity but also on those of its neighbors. The nature of this interaction is a function of the lateral separation between the features: When the distance is small the features appear to attract each other in depth but the interaction becomes repulsive at larger distances. Here we introduce a two-dimensional extension of our recent stereo model based on the physiological studies of Ohzawa, DeAngelis and Freeman [(1990) Science, 249, 1037-1041] and demonstrate through analyses and simulations that these observations can be naturally explained without introducing ad hoc assumptions about the connectivity between disparity-tuned units. In particular, our model can explain the distance-dependent attraction/repulsion phenomena in both the vertical-line configuration used by Westheimer [(1986) Journal for Neurophysiology, 370, 619-629], and the horizontal-line-and-point configuration used by Westheimer and Levi. Thus, the psychophysically observed disparity interaction may be viewed as a direct consequence of the known physiological organization of the binocular receptive fields. We also find that the transition distance at which the disparity interaction between features changes from attraction to repulsion is largely determined by the preferred spatial frequency and orientation distributions of the cells used in the disparity computation. This result may explain the observed variations of the transition distance among different subjects in the psychophysical experiments. Finally, our model can also reproduce the observed effect on the perceived disparity when the disparity magnitude of the neighboring features is changed.