Quantitative determination of the three-dimensional appearances of a rotating ellipse without a rigidity assumption

When a flat figure of uniform color and with an elliptic contour is slowly rotated around an axis orthogonal to the plane of the image, an observer set in the frontal position will perceive it first as a rotating ellipse. After a few seconds of inspection, the ellipse appears to deform with an amoeba-like movement until it appears as a rigid, circular disk tilting back and forth in 3-D space; finally it is seen as a rotating ellipsoid tilted in depth at a constant inclination angle with respect to the rotating platform. In an attempt to provide an explanation for the apparent ellipsoid, the authors present a mathematical model based on an hypothesis of velocity differences minimization, successfully used to describe other stereokinetic phenomena, such as "the rotating cone" and the "tilted bar". This technique does not make use of Ullman's "rigidity hypothesis" for extracting depth from 2-D moving stimuli. A comparison with experimental results supports the validity of the model.