Reservoir model needs to be constrained by various data, including dynamic production data. Reservoir heterogeneities are usually described using geostatistical approaches. Constraining geological/geostatistical model realizations by dynamic data is generally performed through history matching, which is a complex inversion process and requires a parameterization of the geostatistical realizations for model updating. However, the parameterization techniques are still not very efficient and need to be improved.In recent years, the local gradual deformation method has been widely used to parameterize geostatistical realizations. The domain deformation technique has also been developed to improve the history matching efficiency. Both methods can smoothly modify model realizations while conserving spatial geostatistical properties. The first one consists in locally combining two or more realizations while the second one allows the optimization process to change the model realization via the variation of the shape of geometrical domains. In this paper, we generalize the local gradual deformation method by adding the possibility to change the geometry of local zones through the domain deformation. This generalization provides a greater flexibility in the definition of the local domains for the local gradual deformation method. In addition, we propose a new way to initialize the realization which guarantees a good initial point for the optimization and potentially improves the efficiency of history matching.