Perception of straightness and parallelism with minimal distance information.

The ability of human observers to judge the straightness and parallelism of extended lines has been a neglected topic of study since von Helmholtz's initial observations 150 years ago. He showed that there were significant misperceptions of the straightness of extended lines seen in the peripheral visual field. The present study focused on the perception of extended lines (spanning 90° visual angle) that were directly fixated in the visual environment of a planetarium where there was only minimal information about the distance to the lines. Observers were asked to vary the curvature of 1 or more lines until they appeared to be straight and/or parallel, ignoring any perceived curvature in depth. When the horizon between the ground and the sky was visible, the results showed that observers' judgements of the straightness of a single line were significantly biased away from the veridical, great circle locations, and towards equal elevation settings. Similar biases can be seen in the jet trails of aircraft flying across the sky and in Rogers and Anstis's new moon illusion (Perception, 42(Abstract supplement) 18, 2013, 2016). The biasing effect of the horizon was much smaller when observers were asked to judge the straightness and parallelism of 2 or more extended lines. We interpret the results as showing that, in the absence of adequate distance information, observers tend to perceive the projected lines as lying on an approximately equidistant, hemispherical surface and that their judgements of straightness and parallelism are based on the perceived separation of the lines superimposed on that surface.