A series of four experiments was designed to investigate the minimal amounts of information required to perceive the structure of a smoothly curved surface from its pattern of projected motion. In Experiments 1 and 2, observers estimated the amplitudes of sinusoidally corrugated surfaces relative to their periods. Observers' judgments varied linearly with the depicted surface amplitudes, but the amount of perceived relative depth was systematically overestimated by approximately 30%. The observers' amplitude judgments were also influenced to a lesser extent by the amount of rotary displacement of a surface at each frame transition, and by increasing the length of the apparent motion sequences from two to eight frames. The latter effect of sequence length was quite small, however, accounting for less than 3% of the variance in the observers' judgments. Experiments 3 and 4 examined observers' discrimination thresholds for sinusoidally corrugated surfaces of variable amplitude and for ellipsoid surfaces of variable eccentricity. The results revealed that observers could reliably detect differences of surface structure as small as 5%. The length of the apparent motion sequences had no detectable effect on these tasks, although there were significant effects of angular displacement and surface orientation. These results are considered with respect to the analysis of affine structure from motion proposed by Todd and Bressan (1990).