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Xiaoyang Yang, Zili Liu; A computational explanation of the stereokinetic effect. Journal of Vision 2011;11(11):64. doi: https://doi.org/10.1167/11.11.64.
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Purpose: We aimed to explain (1) why a three-dimensional (3D) object is perceived when a 2D shape is rotated in the image plane; and (2) why, once the 3D object is perceived, it is nearly impossible to flip back to the 2D percept. We tested two competing hypotheses: (1) A motion interpretation is preferred if it gives rise to a slower and spatially smoother optic flow (Yuille and Grzywacy, 1988; Weiss, Simoncelli, and Adelson, 2002). (2) An object in 3D with better gestalt is preferred (e.g., a circle versus an ellipse). Method: We used a rotating ellipse as an example since it had been studied with in 2D (Weiss et al., 2002) and in 3D (Rokers, Yuille, and Liu, 2006), which were never compared, however. We first replicated Weiss (1998) and confirmed that a motion interpretation of a deforming ellipse has a lower optic flow than a rigidly rotating ellipse. We then computed the 2D motion flow under the interpretation of a wobbling disk, and found that the optic flow was even smaller than that of a deforming ellipse. Finally, we verified Yuille's proof (2006) that the slowest flow results from 2D, rather than 3D, motion, when there is no smoothness constraint. The resultant motion flow is not spatially smooth, and is never perceived. Hence, the necessity of smoothness constraint in motion perception is supported. Conclusions: Our results suggest that the perceptual transition from a deforming ellipse to a wobbling disk can be explained by the slow and smooth constraints alone. The third dimension in depth and rigidity are unneeded. Nor is the better gestalt of a circle than an ellipse, since this leaves unexplained the specific perceived motion. A better alternative interpretation is that a circle maximizes the options of correspondence, enabling slower and smoother motion to be perceived.
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