Horizontal and vertical noise tolerance of binocular correlation in random dot stereograms

Although our eyes are separated horizontally and binocular disparities are therefore mainly horizontal, binocular correlation tolerates substantial vertical disparities. To study the size of the vertical disparity range for binocular correlation, we measured the tolerance for both horizontal and vertical disparity noise, in detecting sinusoidal depth gratings in random dot patterns. We used dense, dynamic random dot stereograms and Gaussian distributed disparity noise. Trials consisted of two 0.8 s intervals, one containing the depth corrugation (stimulus), the other containing the same disparity values randomly distributed across the window (reference). For different grating parameters tolerance for vertical disparity noise was at least as large as for horizontal disparity noise. Moreover, the effects of horizontal and vertical noise added linearly, suggesting a horizontal-vertical isotropy. To find out whether these resultss indeed reflect the size of horizontal and vertical ranges for resolvable disparities, we performed a parametric model analysis for binocular correlation. The model was presented with random dot stereograms of sinusoidal depth gratings, similar to those in the psychophysical measurements, and solved the correspondence problem by determining all possible matches of a pixel in one eye within an ellipsoid correlation area around the corresponding point in the other eye. An arbitrary, but highly efficient algorithm determined whether the stimulus or reference presentation provided the best match to a sinusoidal depth corrugation. A comparison of horizontal and vertical noise tolerance for the human observer and for the model revealed upper and lower limits for the vertical disparity range. However, psychophysical results could be reproduced with different combinations of horizontal and vertical disparity range, and therefore do not reflect a low level horizontal-vertical isotropy for binocular correlation