Several authors report that the perceived shape of real or simulated objects is mis-scaled along the line of sight. When such a mis-scaled object is rotated rigidly, it should be perceived as changing shape (deforming non-rigidly) and each surface normals will follow a characteristic elliptical path. We investigate how perceived surface normals to a real object are transformed under rigid rotation and test the compression hypothesis.

Observers judged surface normals at 10 pre-marked points on an irregularly-shaped but smooth object (see a computer rendered drawing of  object ), before and after a 30 degree rotation of the object about its vertical axis. The object was coated with white matte paint, placed 70 cm in front of the observer, and illuminated by a near-punctate light source in one of two different positions. Viewing was monocular. Each observer completed 800 trials: 400 in each lighting condition: 200 before object rotation, 200 after. On each trial, the observer adjusted a gradient probe that was optically-superimposed on one of the ten marked points. Each block of 200 trials in a lighting-rotation condition comprised 20 repetitions of settings at 10 pre-marked points on the object. Four observers completed the task.

We analyzed each observers settings by fitting parametric models to the data. As expected, gradient settings were not consistent with transport of along circular paths (rigid rotation), but to a first approximation, with transport along elliptical paths (mis-scaling along the line of sight). We also found significant patterned deviations from the paths predicted by the compression hypothesis.
The pattern of deviations found cannot be explained by an overall compression of perceptual space in either lighting condition.