A preference for minimal deformation constrains the perceived depth of a stereokinetic stimulus

The current study examined whether the 'slow and smooth' hypothesis (Hildreth, 1984; Yuille & Grzywacz, 1989; Weiss, Simoncelli, & Adelson, 2002) could be extended to explaining a three-dimensional (3D) stereokinetic percept by specifying the smoothness term as a preference for minimal deformation. Stereokinetic stimuli are two-dimensional (2D) configurations that lead to 3D percepts when rotated in the image plane. In particular, a rotating ellipse with an eccentric dot gives rise to the percept of a cone with a defined height. In the current study, the spatial relationship between the ellipse and dot varied across trials in terms of the dot's relative location and the aspect ratio of the ellipse. During each trial, participants (n = 8) adjusted the length of a 2D bar centered along the minor axis of the ellipse to indicate their perceived height of the cone. Upon rotation, the 2D bar was perceived to be perpendicular to the circular base of the cone. Our results were qualitatively and quantitatively consistent with the traditional hypothesis of minimum object change (Jansson & Johansson, 1973), which is also similar to the maximal rigidity assumption (Ullman, 1979). As the dot shifted from the major axis towards the minor axis of the ellipse, observers consistently reported an increasingly taller cone. The results illustrate the tendency of observers to perceive the apex of the cone at a height that minimized its 3D distance to the surface normal at the center of the circular base of the cone to reduce the relative motion between the dot and the base of the cone. The current study provides empirical evidence suggesting that, when presented with an ambiguous stereokinetic stimulus, the visual system prefers the interpretation that corresponds to a 3D percept that is slowest and maximally rigid.