Noise in horizontal-disparity and vergence signals predicts systematic distortions in the estimation of shape

Systematic distortions in shape from stereopsis have been attributed to incorrect distance scaling (Johnston, 1991 Vision Research 31 1351 - 1360). It has been shown previously that noise in early visual signals can predict both biases in three-dimensional structure from motion (Hogervorst and Eagle, 1998 Proceedings of the Royal Society of London, Series B 265 1587 - 1593), and various forms of geometrical illusion (Fermüller and Malm, 2004 Vision Research 44 727 - 749). Here, we investigated the role of noise in a maximum-likelihood-estimator (MLE) computer model of shape-from-horizontal disparity and vergence. Realistic estimates of noise in vergence and horizontal-disparity signals for human observers were entered into the MLE model. A psychophysical experiment was also performed, in which observers set the position of the central of three points of light, presented at eye height, so that its separation in depth from the other two points was equal to their horizontal separation. Depth was increasingly underestimated with increasing distance. These systematic distortions in the estimation of shape were predicted by the MLE model. The results demonstrate how distortions or biases in the perception of three-dimensional shape may represent a natural byproduct of 'optimal' processing given a noisy visual input.