How accurate is size and distance perception for very far terrestrial objects? Function and causality

This study investigated absolute estimation of size and distance for natural and artificial objects at viewing distances of 1.1-15.3 km (Experiments 1 and 2) and 0.4-5.0 m (Experiment 3). The main results were that, regardless of distance range, size and distance estimates (S' and D') were related to objective size and distance (S and D), respectively, by a power function with an exponent of unity, but great individual differences in exponent were obtained for the far objects. The ratio S'/D' was reasonably represented by S'/D' = K theta n and S'/D' = tan(a theta +b), rather than S'/D' = tan theta, where theta is the visual angle. Partial correlations were obtained to examine whether (1) apparent size is determined by taking apparent distance into account or (2) both apparent size and apparent distance are determined directly by external stimuli. The combined data for the far objects and the data for the close objects showed that there were high correlations between S and S' and between D and D' and a low correlation between D' and S'. The data of Experiment 2 showed that both D' and S' were highly correlated with S, D, and theta, and there was a high positive correlation between D' and S'. It was suggested that the direct-perception model is valid under some situations, but the taking-into-account model is not supported in any set of data.