Disparity scaling and the perception of frontoparallel surfaces

Binocular disparity can be defined in a variety of ways and its measurement depends upon the particular coordinate framework chosen. As a result of the inverse square law, binocular disparities need to be scaled by some estimate of absolute distance if they are to be interpreted correctly. The experiments described in this paper investigated the extent to which (i) the vergence angle and (ii) the horizontal gradient of vertical disparities or 'differential perspective' provide the necessary information for judging that a stereoscopic surface is flat and frontoparallel. For small displays (< 20 deg) vergence is more effective than differential perspective in scaling frontoparallel surfaces but for larger displays (> 30 deg), differential perspective plays the major role. When both cues together specify the viewing distance, the constancy of frontoparallel-surface scaling is close to perfect for all sizes of display up to 80 deg. Analysis of the geometry of stereoscopic images shows that when a surface patch lies in a frontal plane, the binocular horizontal size ratio of any surface feature is equal to the square of its binocular vertical size ratio, whatever its distance from the observer.