Four experiments related human perception of depth–order relations in structure-from-motion displays to current Euclidean and affine theories of depth recovery from motion. Discrimination between parallel and nonparallel lines and relative-depth judgments was observed for orthographic projections of rigidly oscillating random-dot surfaces. We found that (1) depth–order relations were perceived veridically for surfaces with the same slant magnitudes, but were systematically biased for surfaces with different slant magnitudes. (2) Parallel (virtual) lines defined by probe dots on surfaces with different slant magnitudes were judged to be nonparallel. (3) Relative-depth judgments were internally inconsistent for probe dots on surfaces with different slant magnitudes. It is argued that both veridical performance and systematic misperceptions may be accounted for by a heuristic analysis of the first-order optic flow. Appropriate 2-D motions produce phenomenal impressions of movement in depth (see, e.g., Miles, 1931; Musatti, 1924; Wallach & O’Connell, 1953). Certain types of these phenomena have been named structure from motion (SFM). The questions of how these impressions arise and what type of geometric structure is derived from these motions have led to both experimental and theoretical work on depth recovery from motion. The psychophysical research has evaluated the capabilities of the human visual system in light of the constraints and the scope of the algorithms devised to derive 3-D geometric properties from 2-D motions (for a review, see Braunstein,

Image movement provides one of the most potent twodimensional cues for depth. From motion cues alone, the brain is capable of deriving a three-dimensional representation of distant objects. For many decades, theoretical and empirical investigations into this ability have interpreted these percepts as faithful copies of the projected 3-D structures. Here we review empirical findings showing that perceived 3-D shape from motion is not veridical and cannot be accounted for by the current models. We present a probabilistic model based on a local analysis of optic flow. Although such a model does not guarantee a correct reconstruction of 3-D shape, it is shown to be consistent with human performance. To perceive the 3-D shape of objects from two-dimensional