Perceptual distance and the constancy of size and stereoscopic depth

The relationship between distance and size perception is unclear because of conflicting results of tests investigating the size-distance invariance hypothesis (SDIH), according to which perceived size is proportional to perceived distance. We propose that response bias with regard to measures of perceived distance is at the root of the conflict. Rather than employ the usual method of magnitude estimation, the bias-free two-alternative forced choice (2AFC) method was used to determine the precision (1/sigma) of discriminating depth at different distances. The results led us to define perceptual distance as a bias free power function of physical distance, with an exponent of approximately 0.5. Similar measures involving size differences among stimuli of equal angular size yield the same power function of distance. In addition, size discrimination is noisier than depth discrimination, suggesting that distance information is processed prior to angular size. Size constancy implies that the perceived size is proportional to perceptual distance. Moreover, given a constant relative disparity, depth constancy implies that perceived depth is proportional to the square of perceptual distance. However, the function relating the uncertainties of depth and of size discrimination to distance is the same. Hence, depth and size constancy may be accounted for by the same underlying law.