The geometry of binocular projection is analyzed in relation to the primate visual system. An oculomotor parameterization that includes the classical vergence and version angles is defined. It is shown that the epipolar geometry of the system is constrained by binocular coordination of the eyes. A local model of the scene is adopted in which depth is measured relative to a plane containing the fixation point. These constructions lead to an explicit parameterization of the binocular disparity field involving the gaze angles as well as the scene structure. The representation of visual direction and depth is discussed with reference to the relevant psychophysical and neurophysiological literature. © 2008 Optical Society of America OCIS codes: 330.1400, 330.2210. 1.

Abstract—The human visual system has a remarkable ability to construct surface representations from sparse stereoscopic, as well as texture and motion, information. In impoverished displays where few points are used to define regions in depth, the brain often interpolates depth estimates across intervening blank regions to create a compelling sense of a solid surface. The set of experiments described here examined stereoscopic interpolation using a novel technique based on lightness constancy. The effectiveness of this method is notable because it stands as the only technique to date that unequivocally examines the perception of interpolated surfaces, and not surfaces inferred subjectively from depth information in the stimulus. Further, these data support the growing evidence that a primary function of the stereoscopic system is to define three-dimensional surface structure. The human visual system is adept at constructing surface representations from very sparse information, as evidenced by the formation of

Stereoacuity thresholds have been shown to depend on the disparity of a point with respect to a slanted reference plane through neighbouring points [Curr. Biol. 12 (2002) 825]. Here we explored a wider range of conditions, including slanting the reference points about a horizontal axis and varying the spacing of the reference dots, allowing alternative hypotheses for the effect to be distinguished. The stimulus consisted of three dots;the outer two defined a line that was slanted in depth. Observers judged in which of two intervals the third, central dot was displaced from the location midway between the outer reference dots. The displacement consisted of both a disparity and a shift in the fronto-parallel plane. We compared performance for pairs of conditions in which the disparity was the same but the fronto-parallel shifts were in opposite directions. Models based purely on relative disparity predict that performance should be the same for these conditions. We found consistent differences: performance was always better when the target had a greater disparity with respect to the line joining the reference dots. The other stimulus parameters varied were: target disparity (concave/convex), stimulus size (large/small), slant sign (sky/ground) and axis (vertical/horizontal). The results suggest that either (a) disparity with respect to the line drawn through the outer reference dots or (b) difference in disparity gradients on either side of the target determines the depth discrimination threshold for these stimuli.

The geometry of binocular projection is analyzed in relation to the primate visual system. An oculomotor parameterization, which includes the classical vergence and version angles, is defined. It is shown that the epipolar geometry of the system is constrained by binocular coordination of the eyes. A local model of the scene is adopted, in which depth is measured relative to a plane containing the fixation point. These constructions lead to an explicit parameterization of the binocular disparity field, involving the gaze angles as well as the scene structure. The representation of visual direction and depth is discussed, with reference to the relevant psychophysical and neurophysiological literature. 1