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When a circular disk with an eccentric dot is set in slow rotary motion a compelling impression of a three-dimensional cone is observed. Similarly a line segment of constant length, a bar, rotating on the frontal plane appears slanted in depth. The two stereokinetic phenomena cannot be explained on the basis of Ullman's method of extracting depth from 2-D moving stimuli i.e. the rigidity assumption. A new analytic model is here presented based on the hypothesis that the visual system minimizes the relative velocity differences among all the points of the moving pattern. Two different methods of calculating the depth displacement are described: the velocity field method and the trajectories method. Both lead to the same results. A comparison of the theoretical results with the experimental ones supports the validity of the model.

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.

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