Section: New Results
Data Assimilation for Image Processing
In the image processing area, most of problematics correspond to ill-posed problems (edge detection, segmentation, optical flow estimation, deblurring, ...). A common method used to solve ill-posedness is to regularize solutions by adding smoothing constraints. For example, Tikhonov like approach proposes to minimise a functional measuring the discrepancy between model and solution and constraining the spatial variations of the solution. It is now well known  that the Euler-Lagrange evolution equation associated to this functional corresponds to a diffusion process.
Similar equations are found in the modelling in many physical situations (meteorology, oceanography, air quality, ...), and data assimilation techniques  have proven their efficiency for solving them, even when partial and/or indirect observations of state variables are available.
We propose to exploit this property in order to formulate ill-posed image processing problems in a variational data assimilation framework. The research addresses the definition of evolution models for the image information to be retrieved. In a first step this approach is studied for 3D reconstruction from a sequence of 2D observations: we try to reconstruct the evolution of a 3D object from a sequence of 2D image acquisitions. The observations consist of the 2D images, obtained by projection of the 3D space. The evolution model can be as simple as an optical-flow like constraint (transport of grey level over 3D sequence).