These works are concerned with the issue of ill-posed image processing problems solved using the calculus of variation formulation. We investigate mainly the problems of optical flow determination and the 3D recovering from 2D image sequences. As these problems are ill-posed, a unique solution can be retrieved using spatial regularization techniques. We then propose to introduce alternative constraints in order to moderate the influence of the regularization. These constraints are deduced from heuristics on the experimental conditions. In a first chapter, we examine a study case in biological images. Spherical structures simulating cellular membranes are observed from a focal microscope. The spherical topology is taken into account in order to improve image processing tasks such as segmentation, optical flow estimation or tracking. The information is then used to recover 3D images from the 2D images. In a second chapter, we propose to deal with the temporal information within the image sequences. This information is first modeled as an evolution on the state (the quantity to determine) and the difficulty is to solve this equation with the equations linking the state and the images. To this end, we use the variational data assimilation framework. Without specific knowledge on the dynamics we consider a generic evolution equation and an error on this latter. Although the evolution equation is a rough approximation, we show the optical flow can be determined without spatial regularization. If the noisy or missing observations can be identified, we propose a simple way to evict these data in the computation of the solution and to provide a coherent solution, using the evolution equation. In a last chapter, we briefly describe another research works: resolution of non-linear variational image processing problems, ground occupation analyzing using high resolution satellite images and the tracking of targets.
