Affine distortions of pictorial space: some predictions for Goldstein (1987) that La Gournerie (1859) might have made.

Goldstein (1987) studied the perception of pictures seen from the front and the side. Several distinctions arose from his results and analysis, but only one is central to the reanalysis presented here: The perceived orientation of objects within a picture with respect to the external world is a function of viewer position in front of the picture. For example, the eyes of a portrait subject appear to follow an observer who moves around a gallery. Viewed from many positions, such objects can be said to rotate, following a mobile viewer. Goldstein called this the differential rotation effect because those objects that point directly out of the picture (at 90 degrees) rotate most; those pointing at other angles rotate in decreasing amounts. Goldstein offered no theoretical model and little in the way of explanation for this effect. This Observation offers a model based on the affine geometry and the analyses of La Gournerie (1859). This analysis transforms pictorial space (the space behind a photograph or representational picture) by shears, compressions, and dilations according to the viewpoint of the observer in relation to the composition point of the picture. These effects account for Goldstein's differential rotation effect quite well.