Perceived surface orientation and angular velocity were investigated for orthographic projections of 3-D rotating random-dot planes. It was found that (a) tilt was accurately perceived and (b) slant and angular velocity were systematically misperceived. It was hypothesized that these misperceptions are the product of a heuristic analysis based on the deformation, one of the differential invariants of the first-order optic flow. According to this heuristic, surface attitude and angular velocity are recovered by determining the magnitudes of these parameters that most likely produce the deformation of the velocity field, under the assumption that all slant and angular velocity magnitudes have the same a priori probability. The results of the present investigation support this hypothesis. Residual orientation anisotropies not accounted for by the proposed heuristic were also found.

Many visual tasks are carried out by using multiple sources of sensory information to estimate environmental properties. In this paper, we present a model for how the visual system combines disparity and velocity information. We propose that, in a first stage of processing, the best possible estimate of the affine structure is obtained by computing a composite score from the disparity and velocity signals. In a second stage, a maximum likelihood Euclidean interpretation is assigned to the recovered affine structure. In two experiments, we show that human performance is consistent with the predictions of our model. The present results are also discussed in the framework of another theoretical approach of the depth cue combination process termed Modified Weak Fusion.

Recent investigators have proposed that amodal completion is a sequential process requiring a preliminary mosaic stage. Results of 6 studies of the time course of completion processes show support for this mosaic-first view with pictorial displays, but not with displays involving occlusion specified by binocular parallax or when pictorial displays were observed monocularly. These results still do not rule out the mosaic-first view. A parallel model, however, can account more economically for the available data.

Accuracy in discriminating rigid from nonrigid motion was investigated for orthographic projections of three-dimensional rotating objects. In 3 experiments the hypothesis that magnitudes of angular velocity are misperceived in the kinetic depth effect was tested, and in 4 other experiments the hypothesis that misperceiving angular velocities leads to misperceiving rigidity was tested. The principal findings were (a) the magnitude of perceived angular velocity is derived heurisdcally as a function of a property of the first-order optic flow called deformation and (b) perceptual performance in discriminating rigid from nonrigid motion is accurate in cases when the variability of the deformations of the individual triplets of points of the stimulus displays favors this interpretation and not accurate in other cases.The human perceptual system is capable of extracting three-dimensional (3-D) information from moving images from which every static pictorial cue to depth has been removed, a phenomenon called the kinetic depth effect (Wallach & O'Cormell, 1953). Numerous attempts to reach a theoretical understanding of this phenomenon have been made Bennett, Hoffman, Nicola, & Prakash, 1989;Koenderink, 1986;Koenderink & Van Doom, 1975,1977Longuet-Higgins & Prazdny, 1980;Prazdny, 1980; Ullman, 1979Ullman, , 1983 Ullman, , 1984. Mathematical analyses have revealed that the recovery of 3-D properties from projected motions is characterized by an inherent ambiguity: The mapping from two-dimensional (2-D) images to 3-D properties is one to many (i.e., different 3-D motions project to the same 2-D image). Without a priori constraints on the nature of the structure or the motion of the projected objects, the problem of finding a unique 3-D interpretation for a moving image (the so-called Structurefrom-Motion, or SfM, problem) cannot be solved. One way This research was supported by National Institute of Mental Health Grant MH52640-03 and National Aeronautics and Space Administration Grant NCC2-925.We thank Mike Braunstein for helpful discussions and comments on an earlier version of this article.Correspondence concerning this article should be addressed to to overcome this inherent ambiguity is to introduce constraints in the interpretation process in order to restrict the space of possible interpretations to only one solution. The constraints that have been used, are, for example, the rigidity assumption (Ullman, 1979), smoothness of flow field (Hildreth, 1984), rotation at a constant angular velocity , 1986, and so on. The rigidity assumption has been used in many computer vision algorithms; moreover, in some psychological theories (Gibson, 1979;Johansson, 1978;Musatti, 1924) it has been hypothesized that the perceptual recovery of 3-D shape from motion could be based on a rigidity constraint (see Cutting, 1987;Zanforlin, 1988).In current research the psychological plausibility of the rigidity assumption has been examined by studying human performance in the minimal conditions theoretically necessary for discriminating rigi...

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