No abstract

No abstract

This paper addresses the issue of motion estimation on image sequences. The standard motion equation used to compute the apparent motion of image irradiance patterns is an invariance brightness based hypothesis called the optical flow constraint. Other equations can be used, in particular the extended optical flow constraint, which is a variant of the optical flow constraint, inspired by the fluid mechanic mass conservation principle. In this paper, we propose a physical interpretation of this extended optical flow equation and a new model unifying the optical flow and the extended optical flow constraints. We present results obtained for synthetic and meteorological images.

Data Assimilation is a mathematical framework used in environmental sciences to improve forecasts performed by meteorological, oceanographic or air quality simulation models. It aims to solve an evolution equation, describing the temporal dynamics, and an observation equation, linking the state vector and observations. 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. An approach is proposed to convert an ill-posed Image Processing problem in terms of a Data Assimilation system, solved by a 4D-Var method. This is illustrated by the estimation of optical flow from a noisy image sequence, with the dynamic model ensuring the temporal regularity of the result. The innovation of the paper concerns first, the extensive description of the tasks to be achieved for going from an image processing problem to a data assimilation description; second, the theoretical analysis of the covariance matrices involved in the algorithm; and third a specific discretisation scheme ensuring the stability of computation for the application on optical flow estimation.

No abstract

Abstract. In this paper we propose a state estimation method for linear parabolic partial differential equations (PDE) that accounts for errors in the model, truncation, and observations. It is based on an extension of the Galerkin projection method. The extended method models projection coefficients, representing the state of the PDE in some basis, by means of a differential-algebraic equation (DAE). The original estimation problem for the PDE is then recast as a state estimation problem for the constructed DAE using a linear continuous minimax filter. We construct a numerical time integrator that preserves the monotonic decay of a nonstationary Lyapunov function along the solution. To conclude we demonstrate the efficacy of the proposed method by applying it to the tracking of a discharged pollutant slick in a 2D fluid.

No abstract

No abstract