Analytic determination of the depth effect in stereokinetic phenomena without a rigidity assumption

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.