In this report, we present a novel framework to deform mutually a population of n-examples based on an optimality criterion. The optimality criterion comprises three terms, one that aims to impose local smoothness, a second that aims to minimize the individual distances between all possible pairs of images, while the last one is a global statistical measurement based on "compactness" criteria. The problem is reformulated using a discrete MRF, where the above constraints are encoded in singleton (global) and pair-wise potentials (smoothness (intra-layer costs) and pair-alignments (inter-layer costs)). Furthermore,we propose a novel grid-based deformation scheme, that guarantees the diffeomorphism of the deformation while computationally favorably compared to standard deformation methods. Towards addressing important deformations we propose a compositional approach where the deformations are recovered through the sub-optimal solutions of successive discrete MRFs. The resulting paradigm is optimized using efficient linear programming. The proposed framework for the mutual deformation of the images is applied to the group-wise registration problem as well as to an atlas-based population segmentation problem. Both artificially generated data with known deformations and real data of medical studies were used for the validation of the method. Promising results demonstrate the potential of our method.