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The research presented in this paper consists in developing an automatic system for people re-identification across multiple cameras with non-overlapping fields of view. We first propose a robust algorithm for silhouette extraction which is based on an adaptive spatio-colorimetric background and foreground model coupled with a dynamic decision framework. Such a method is able to deal with the difficult conditions of outdoor environments where lighting is not stable and distracting motions are very numerous. A robust classification procedure, which exploits the discriminative nature of sparse representation, is then presented to perform people re-identification task. The global system is tested on two real data sets recorded in very difficult environments. The experimental results show that the proposed system leads to very satisfactory results compared to other approaches of the literature.