This thesis aims at incorporating complex data derived from images into a data assimilation strategy available for mechanical systems. Our work relies on some recent developments that propose a sequential data assimilation method made of a Luenberger filter for the state space and an optimal filter reduced to the remaining parameter space. We aim at performing parameter identification for a biomechanical model of the heart and, within the scope of this application, we formalize the construction of shape discrepancy measurements for two types of data sets: first, the data expected of a processing step of tagged Magnetic Resonance Imaging (tagged-MRI) and, second, more standard data composed by the contours of the object. Initially based on simple distance measurements we enrich these discrepancy measures by incorporating the formalism of currents which enables to embed the contours of the object within the dual of an appropriate space of test functions. For each discrepancy operators we analyze its impact on the observability of the system and, in the case of tagged-MRI, we prove that they are equivalent to a direct measurement of the displacement. From a numerical standpoint, taking into account these complex data sets is a great challenge that motivates the creation of new numerical schemes that provide a more flexible management of the various observation operators. We assess these new means of extracting the rich information contained in the image by identifying in realistic cases the position and the intensity of an infarct in the heart tissue.
