What are the uncurved lines in our visual field? A fresh look at Helmholtz's checkerboard

What are the uncurved lines in our visual field? To answer this question, Helmholtz developed a geometrical model of line-curvature perception, and demonstrated it with his famous checkerboard pattern with pin-cushion distortion. He claimed it looked perfectly regular when viewed monocularly at close range while fixating the centre. Recently, doubts have been expressed whether this demonstration actually works. We tested twenty monocular, stationary observers who could adjust the distortion of a checkerboard pattern over a large range, from barrel-shaped to pin-cushion-shaped. Their task was to adjust the curvature of the edges of the checks such that the checkerboard looked straight and regular. In one condition they had to fixate the centre of the pattern, in another condition they were instructed to let their gaze wander. We found that most observers indeed perceived a pattern with pin-cushion distortion as undeformed, thereby seeing hyperbolic curves in the figure as uncurved lines in the visual field. They set a more strongly curved pattern in the fixation condition than in the free-viewing condition, as also described by Helmholtz. Interestingly, the effect is about half as strong as Helmholtz claimed. Furthermore, we found considerable inter-individual differences.