Mathematical analyses of motion perception have established minimum combinations of points and distinct views that are sufficient to recover three-dimensional (3D) structure from two-dimensional (2D) images, using such regularities as rigid motion, fixed axis of rotation, and constant angular velocity. To determine whether human subjects could recover 3D information at these theoretical levels, vie presented subjects with pairs of displays and asked them to determine whether they represented the same or different 3D structures. Number of points was varied between two and five; number of views was varied between two and six; and the motion was fixed axis with constant angular velocity, fixed axis with variable velocity, or variable axis with variable velocity. Accuracy increased with views, decreased with points, and was greater with fixed-axis motion. Subjects performed above chance levels even when motion was eliminated, indicating that they exploited regularities in addition to those in the theoretical analyses.Theoretical investigations of visual motion have provided a number of specific analyses of the minimum number of points and views required to recover three-dimensional (3D) structure from two-dimensional (2D) images. Recovery of 3D structure, in this context, is denned as determining the x, y, and z coordinates of each point, up to a scale factor. These analyses differ in the constraints that are imposed. UUman (1979) showed that under a rigidity constraint, three views of four noncoplanar points are sufficient to recover structure in an orthographic projection, up to a reflection about the frontal plane. The required numbers of points and views are reduced by adding further constraints, such as planarity (Hoffman & Flinchbaugh, 1982), fixed axis of rotation (Hoffman & Bennett, 1986;Webb & Aggarwal, 1981), and constant angular velocity (Hoffman & Bennett, 1985). These proofs are summarized in Table 1.A number of empirical studies have addressed issues related to theoretical analyses of the recovery of structure from motion. Several studies (e.g., Braunstein & Andersen, 1986;Schwartz & Sperling, 1983;Todd, 1985) have questioned the generality of the rigidity constraint. Other studies have considered the recovery of structure with small numbers of views or with small numbers of points. Lappin, Doner, and Kotlas (1980) found that subjects could make accurate judgments based on 3D structure This research was supported by a contract to D. Hoffman from the Office of Naval Research, Cognitive and Neural Sciences Division, Perceptual Sciences Group. We thank Joseph Lappin and James Todd for helpful comments on an earlier version of this article and Johnna Eastbum and James Tittle for assistance in various aspects of this research.