In three experiments, difference thresholds (elLs) and points of subjective equality (PSEs) for three-dimensional (3-D) rotation simulations were examined. In the first experiment, observers compared pairs of simulated spheres that rotated in polar projection and that differed in their structure (points plotted in the volume vs. on the surface), axis of rotation (vertical, y, vs. horizontal, x), and magnitude of rotation (20°-70°). DLs were lowest (7%) when points were on the surface and when at least one sphere rotated around the y-axis and varied with changes in the independent variables. PSEs were closest to objective equality when points were on the surface of both spheres and when both spheres rotated about the x-axis.In the second experiment, subjects provided direct estimates of the rotations of the same spheres. Results suggested a reasonable agreement between PSEs for the indirect-scaling and direct-estimate procedures. The third experiment varied sphere diameter (and therefore mean linear velocity of stimulus elements) and showed that although rotation judgments are biased by mean linear velocity, they are not likely to be made solely on the basis of that information. These and past results suggest a model whereby recovery of structure is conducted by low-level motion-detecting mechanisms, whereas rotation (and other) judgments are based on a higher level representation.
465The capacity of the human visual system to discriminate stimuli varying by only small amounts on one or more dimensions is well known. With regard to linear motion, for example, velocity difference thresholds (dLs) for sinewave gratings can be as low as 1%-2 % or as high as 40%-50%, depending upon their spatial frequencies and drift rates (Pantle, 1978, Experiment 3). Nonetheless, despite a growing interest in the process whereby the visual system recovers three-dimensional (3-D) structure from two-dimensional (2-D) image motion (e.g., Braunstein, 1976;Braunstein & Tittle, 1988; Hildreth, 1984;Lappin, Doner, & Kottas, 1980;Petersik, 1979 Petersik, , 1980aPetersik, , 1987 Sperling, Landy, Dosher, & Perkins, 1989;Ullman, 1979), relatively little work has been done on the basic psychophysics of the 3-D motion percept produced with rotation simulations. For example, only Kaiser (1990Kaiser ( , 1991 has asked what the dL is for pairs of objects in 3-D rotation. The present experiments, although conceived independently, extend the issues addressed by Kaiser (1990Kaiser ( , 1991, as well as her data.Kaiser's (1990) stimuli were "pseudoshaded" simulations of solid cubes (and in one case, a bispherenoid) displayed in polar projection. In separate experiments, she examined the effects of pairs of stimuli rotating about I am grateful to G. Andersen, M. Braunstein, P. Werkhoven, and an anonymous reviewer for their detailed and insightful comments on an earlier version of this manuscript. Diane Gardetto, Niveen Iskandar, and Ted Uczen were patient and diligent subjects in this research and are thanked heartily. Reprint requests and other corre...