Angle judgement: is the whole the sum of its parts?

This study concerns whether the discrimination of a geometric angle depends on the orientations of its bounding lines or on angle size. In Experiment 1, thresholds for angle discrimination were measured in three observers for angles ranging from 15 to 180 deg, oriented either vertically or obliquely. Angle discrimination thresholds were found to depend primarily on angle size for most of the range of angles (angle-dependent, or Weber's law regime). However, in a small region near 90 deg (orientation-dependent regime) angle discrimination depends on the orientations of the bounding lines. When our data in the angle-dependent regime were fitted with a power function, the exponents were close to or < 0.5, suggesting that a step-increment approach was used to calculate angle. In Experiment 2, orientation discrimination thresholds for lines corresponding to the bounding lines of the vertically and obliquely oriented 15, 90 and 165 deg angles were measured. Confirming previous studies, a strong meridional anisotropy in line orientation discrimination was found for all three observers. The orientation discrimination thresholds were then used to predict the discrimination thresholds for the corresponding angles based on a simple statistical model. The predicted angle discrimination thresholds were worse than those measured empirically except for the titled 90 deg angles. This result indicates that angle discrimination thresholds are not limited by the same noise as orientation discrimination for most angles except for the tilted 90 deg angle, where the limiting factor may be the precision in determining the orientations of the bounding lines. In Experiment 3, we show that angle discrimination is quite robust to small amounts of orientation jitter, suggesting that angle judgments are made at a level beyond the early filter representation.