Oomes Augustinus H J, Koenderink Jan J, van Doorn Andrea J, de Ridder Huib
Man-Machine Interaction Group, Delft University of Technology, 2600 GA Delft, The Netherlands.
Perception. 2009;38(9):1284-94. doi: 10.1068/p6288.
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.
我们视野中那些不弯曲的线是什么？为了回答这个问题，亥姆霍兹开发了一种线曲率感知的几何模型，并用他著名的带有枕形失真的棋盘图案进行了演示。他声称，当在近距离单眼注视中心时，它看起来完全规则。最近，有人对这个演示是否真的有效表示怀疑。我们测试了20名单眼静止的观察者，他们可以在很大范围内调整棋盘图案的失真，从桶形到枕形。他们的任务是调整方格边缘的曲率，使棋盘看起来笔直且规则。在一种情况下，他们必须注视图案的中心，在另一种情况下，他们被指示让目光游移。我们发现，大多数观察者确实将带有枕形失真的图案视为未变形的，从而将图中的双曲线视为视野中不弯曲的线。正如亥姆霍兹所描述的那样，他们在注视条件下设置的图案曲率比自由观看条件下更强。有趣的是，这种效果大约只有亥姆霍兹声称的一半强。此外，我们还发现了相当大的个体差异。
