Conditions in which saccadic gaze shifts within planar surfaces facilitate stereo-slant discrimination for slant about the horizontal and vertical axis were investigated. When horizontal disparity noise was added, large gaze shifts in the direction of the slant lowered stereo-slant discrimination thresholds compared to thresholds measured with steady central fixation, whereas eye movements orthogonal to the slant orientation did not lower slant-discrimination thresholds. When no horizontal noise was added, performance was the same with and without gaze shifts. These results suggest that slant is recovered from depth differences between target edges when horizontal disparity signals are variable and that foveal fixation improves the measures of disparity. Eye movements did not lower slant thresholds by providing multiple foveal samples of slant at different target locations that were averaged to reduce disparity noise levels, because eye movements only lowered the thresholds when there was a depth difference between the fixation points. To study which signals for azimuth are used when slant is recovered from the difference in depth between target edges, vertical disparity noise was added and stimulus height was reduced. Both methods elevated slant-discrimination thresholds when horizontal disparity noise was present, suggesting that vertical disparity is used as a cue for azimuth.

*i*the interocular distance, ϑ the eccentricity from straight-ahead, and

*D*the distance (depth). When accurately fixating a certain target location in space, the binocular parallax of that location is equal to the vergence angle. If there is a vergence error or fixation disparity, then the binocular parallax is equal to the vergence angle plus the residual horizontal disparity (assuming that there is no cyclo-torsion). Azimuth signals are needed to correct depth estimates from binocular parallax signals (Fendick & Westheimer, 1983) and to compute the separation between the two depth estimates. In the “Appendix,” we derive an expression of how slant can be computed from binocular parallax estimates at two locations (γ

_{2}and γ

_{2}) and the azimuth eccentricities of the same locations (ϑ

_{1}and ϑ

_{2}).

^{2}when viewed through the Ferro-shutters. Each slant stimulus presentation was a different random-dot display to avoid changes in perceived image compression as a cue. The stimuli were presented at the center of the screen (straight-ahead). Horizontally slanted stimuli were obtained by applying a horizontal magnification of one eye’s image. At the 30-cm viewing distance, a 1% magnification of the left eye’s image (

*M*= 1.01) corresponds to a slant angle of approximately 2.6 deg. Vertically slanted stimuli were obtained by applying a horizontal shear to one eye’s image. At the 30-cm viewing distance, a 1° shear of the left eye’s image corresponds to a vertical slant angle of approximately 4.6 deg.

*d′*= 1). We estimated the SEs of the discrimination thresholds by performing Monte-Carlo simulations on the data sets. Three observers (authors) were tested (EB, ZZ, and CS).

*y*yields a constant VSR (vertical size ratio) noise, because VSR is proportional to the vertical gradient of vertical disparity: .

*d′*of 1.

_{1}and γ

_{2}) and the eccentricities of the same locations (ϑ

_{1}and ϑ

_{2}).

*z*) divided by the change in horizontal direction (

*x*):

*z*and

*x*depend on distance,

*D*and the eccentricity, ϑ of a location.

*D*can be substituted with by means of the binocular parallax equation (Foley, 1978). Then we obtain the following expressions for

*z*and

*x*: Substituting the expressions for

*x*

_{1},

*x*

_{2},

*z*

_{1}and

*z*

_{2}in Δ

*z*/Δ

*x*gives the following expression for slant: .