The aperture problem in stereopsis

Stereoacuity was determined for gratings and gabor patches as their orientation was varied. Acuity was constant for 1 c/deg and 2 c/deg gratings over the range 0-80 deg when it was expressed as positional shift at right angles to the grating orientation. The same was true of an 8 c/deg elongated gabor patch. However, the threshold disparity at right angles to the major axis of an oriented gaussian patch rose as it was tilted away from the vertical. Also, thresholds for a circularly symmetrical gaussian patch rose steeply with the angle of the disparity away from the horizontal. Disparities of the centroids of 4 c/deg gabor patches could be detected equally well at angles of 0 and 70 deg, independently of the angle of the carrier grating. The data indicate a variety of rules for stereoscopic matching. Large-field gratings are matched by detecting orthogonal phase shifts, or alternatively phase shifts along the horizontal axis. Smaller patches of grating are matched by their centroids, independently of their angle. Small gaussian patches are difficult to match in any direction other than along the horizontal axis. The difference between gaussian patches and 4 c/deg gabor patches with the same envelope argues against the involvement of a second-order rectifying non-linearity preceding matching.