Geostatistical methods are commonly used to characterize oil field heterogeneities in order to establish a predictive reservoir model. To reduce the model uncertainties, dynamic information, such as production or 4D seismic data, are usually integrated in the modelling through history matching. However, despite the growing use of geostatistical methods to generate reservoir heterogeneities, random realizations cannot generally match these data. We need efficient parameterization techniques to constrain geostatistical realizations by measured dynamic data in history matching. In recent years, the gradual deformation method has been widely used to parameterize geostatistical realizations. This method can locally combine two or more realizations in a predefined domain delimited by gridblocks. In this paper, we propose a generalization of the local gradual deformation by parameterizing the domain geometry through the technique of the domain deformation. In this way, the geostatistical realization can be improved by selecting locally best realizations for the gradual deformation inside a local domain whose size is determined through domain deformation. This method allows a greater flexibility in the definition of the domains in which the gradual deformation is done. In addition, we propose a new way to initialize the problem which guaranties a good initial point for the optimization and to use the partial separability of the objective function to improve the efficiency of the history matching.