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Three experiments were conducted to examine the accuracy of 3-D shape recovery from deformingcontour displays. The displays simulated silhouettes of ellipsoids rotating about a vertical axis. Subjects judged the horizontal cross-section of the ellipsoids. The shape of the ellipsoid, the position of the axis of rotation, and the type of projection were manipulated in Experiment 1. The results indicated relatively accurate shape recovery when the major axis of the ellipsoid was small. In Experiment 2, the shape of the ellipsoid and the velocity and curvature of the contour were manipulated. When the rate of deformation of curvature was decreased, more eccentric shapes were reported. In Experiment 3, the shape of the object and the amount of simulated rotation were manipulated. Subjects made both shape and extent of rotation judgments. The results showed that eccentricity of shape responses could be accurately predicted from rotation responses, suggesting that the recovery of 3-D shape from smooth, deforming contours is dependent on the perceived extent of rotation.Elaborating on the early work of Miles (1931) and Metzger (1934), Wallach and O'Connell (1953) demonstrated that 3-D shape could be recovered from orthographic projections of rotating objects. In one condition, a solid, truncated cylinder was rotated. The resulting image contour deformed over time in one dimension only, and subjects reported a perception of a nonrigid, 2-D object. However, when bent wire-frame figures or planarsurfaced solids were rotated, the contour simultaneously deformed in both the vertical and the horizontal dimensions. The subjects in these conditions reported a perception of a rotating, 3-D object. Wallach and O'Connell proposed the term kinetic depth effect for this phenomenon and suggested that contour length and direction changes were important for the perception of 3-D shape.More recently, researchers have examined the minimal conditions for the recovery of 3-D shape from motion. For example, Ullman (1979) showed that, for a rigid configuration, three orthographic views of four noncoplanar points were sufficient for the recovery of the 3-D structure. In recent studies, researchers have examined the validity of these models for human perception with the use of computer-generated displays in which points are depicted on a 3-D object. Such displays have been used to examine the importance of specific constraints (Braunstein & Andersen, 1984;Todd, 1984) and of minimal conditions

A metric representation of shape is preserved by a Fourier analysis of the cumulative angular bend of a shape's contour. Three experiments examined the relationship between variation in Fourier descriptors and judgments of perceptual shape similarity. Multidimensional scaling of similarity judgments resulted in highly ordered solutions for matrices of shapes generated by a Fourier synthesis of a few frequencies. Multiple regression analyses indicated that particular Fourier components best accounted for the recovered dimensions. In addition, variations in the amplitude and the phase of a given frequency, as well as the amplitudes of 2 different frequencies, produced independent effects on perceptual similarity. These results suggest that a Fourier representation is consistent with the perceptual similarity of shapes, at least for the relatively low-dimensional Fourier shapes considered.

E. N. Dzhafarov and R. Schweickert (1995, Journal of Mathematical Psychology, 39, 285-314) developed a mathematical theory for the decomposability of response time (RT) into two component times that are selectively influenced by different factors and are either stochastically independent or perfectly positively stochastically interdependent (in which case they are increasing functions of a common random variable). In this theory, RT is obtained from its component times by means of an associative and commutative operation. For any such operation, there is a decomposition test, a relationship between observable RT distributions that holds if and (under mild constraints) only if the RTs are decomposable by means of this operation. In this paper, we construct a sample-level version of these decomposition tests that serve to determine whether RTs that are represented by finite samples are decomposable by means of a given operation (under a given form of stochastic relationship between component times, independence or perfect positive interdependence). The decision is based on the asymptotic p-values associated with the maximal distance between empirical distribution functions computed by combining in a certain way the RT samples corresponding to different treatments.

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