Stereoscopic discrimination of interval and ordinal depth relations on smooth surfaces and in empty space

In a series of three experiments, observers judged the perceived relative depths of small probe dots, which could be presented in empty space or attached to a smoothly curved surface. Discriminations of ordinal depth were found to be more precise than discriminations of depth intervals. The amount of separation in the projected image between the locations in depth was also manipulated. Performance was higher when observers evaluated the depth relationships between nearby points in the projected images, and lower when the points were more widely separated. This effect was most pronounced when there was a continuous surface in between the points, suggesting that accurate knowledge of the three-dimensional structure of surfaces is primarily limited to relatively small local neighborhoods.