Stereo Depth Perception Uses First-Order Phase and Second-Order Position Disparities

We examined the nature and variety of cues underlying the use of binocular disparity in depth perception. Stimuli were Gabor patches (Gaussian-windowed sine-wave gratings, 2 cycles deg⁻¹) and horizontal disparities were produced by varying the phase of the carrier grating or the position of the Gaussian envelope (SD=24 min arc), or both. Disparity varied from −180° to +180° of carrier phase (or the positional equivalent) at carrier orientations 0°, 30°, 60° or 90° from vertical. Direction and magnitude of perceived depth were reported in a 2IFC procedure where the comparison interval contained a zero disparity vertical patch. Use of different orientations allowed phase disparity to be distinguished from horizontal position disparity.

Two main conditions were tested. (1) In the ‘patch’ condition carrier and envelope disparity varied together, and perceived depth was found to vary monotonically with positional disparity. When carrier disparity was ambivalent (at ±180° phase disparity) or zero (with horizontal orientation) perceived depth followed envelope disparity, showing that 2nd-order (envelope) disparity alone can produce depth. (2) When carrier disparity was varied with the envelope held fixed, perceived depth and discrimination thresholds depended on phase disparity rather than horizontal position disparity, lending support to the phase-based theory of De Angelis, Ohzawa, and Freeman (1995 Perception 24 3 – 31). At the larger crossed disparities (−90° to −180°) depth reversed sign, suggesting a role for occlusion cues as well as phase and envelope disparity in stereo depth coding.