Solving Ill-posed Problems using Data Assimilation - Application to Optical Flow Estimation

Data Assimilation is a mathematical framework used in environmental sciences to improve forecasts performed by meteorological, oceanographic or air quality simulation models. Data Assimilation techniques require the resolution of a system with three components: one describing the temporal evolution of a state vector, one coupling the observations and the state vector, and one defining the initial condition. In this article, we use this framework to study a class of ill-posed Image Processing problems, usually solved by spatial and temporal regularization techniques. A generic approach is defined to convert an ill-posed Image Processing problem in terms of a Data Assimilation system. This method is illustrated on the determination of optical flow from a sequence of images. The resulting software has two advantages: a quality criterion on input data is used for weighting their contribution in the computation of the solution and a dynamic model is proposed to ensure a significant temporal regularity on the solution.

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