Dense estimation of motion fields on meteosat second generation images using a dynamical consistency

In this paper, we present a framework for dynamic consistent estimation of dense motion fields over a sequence of Meteosat Second Generation (MSG) images. The originality of the approach is to exploit recipes related to optimal control theory developed in geophysical sciences. This framework, known as variational data assimilation, enables to perform the estimation of an unknown state function according to a given dynamical model and to noisy and incomplete measurements. In our work, the measurements are defined according to a smoothed brightness consistency model whereas the dynamical model on which we rely is derived from a velocity conservation law. The overall assimilation process is formalized through the minimization of a global spatio- temporal cost functional w.r.t to the complete sequence of motion fields. The minimization is handled considering an adjoint formulation. The resulting scheme consists in iterating a forward integration of the evolution model and a backward integration of the adjoint evolution model guided by a discrepancy measurement between the state variable and the available noisy observations. Such an approach allows us to cope with several delicate situations (such as the absence of data) which are not well managed with usual estimators. The efficiency of our approach is demonstrated on real data. It enables to estimate a sequence of dense motion fields even in situations where data are strongly corrupted.