Estimation of visual motion and 3D motion parameters from singular points

The estimation of visual motion can be based on simple differential methods applied to image brightness, without using complex minimization techniques and exhaustive search for correspondence. A dense, smooth motion field is computed solving a system of linear equations. The properties of the motion field can be studied analyzing the singular points of the field - that is, points where the field is equal to zero or stationary - which, on the other hand, allow the computation of essential 3D motion parameters like object translation and rotation. In some particular, but even, quite common cases the estimation of 3D motion is fairly simple as it involves the solutions of a simple system of linear equations applied to set of image points. A least square approach, applied to the 2D motion field, has been used to estimate the rotational and translational velocity of real objects or of the moving camera. A series of experiments made on real scenes are presented with some quantitative results.