Estimation of global motion parameters by complex linear regression

Global motion is very likely to occur in image sequences analysis. For example, it arises ir the observer is moving during the sequence acquisition (ego-motion). Our aim is to get a simple method to estimate in a reliable way a set of parameters that can take into account the presence of a global motion component, using only local information, The novelty of our approach is in regarding spatial shift, change of scale, and rotation (corresponding to usual camera effects such as pan and zoom) as a two-dimensional (2-D) Doppler effect. The mathematical treatment is carried on in the complex plane, so that the results can be easily deduced as an extension of the one-dimensional (1-D) case; in this way, we obtain simple expressions, well suited for a practical realization of the estimate. The method has been experimentally validated by both real pictures with a synthetic motion and real image sequences.