Reconstruction of ancient artifacts from fragments found at archaeological sites, is a tedious task that requires many hours of work from the archaeologist and restoration personnel. In this paper, we introduce an automatic technique for fragment reconstruction based on projective GPU depth maps that takes, as input data, a set of geometric representations of broken flat fragments, and finds the best rigid transformation that maximizes the contact area between them. In order to efficiently perform the calculations, instead of using input B-REP models, we focus on the characterization of the fragments. Thus, with some pre-processing entirely executed in the GPU, the representation of the 3D models proposed in this paper reduces significantly the complexity of the automatic reconstruction problem. Since the amount of data to process is huge, exhaustive search techniques cannot be used in order to provide fast results. On the other hand, solving the correspondence problem implies providing the best solution among all possible ones. To solve the stated duality between efficiency and correctness, the search process hierarchically analyzes the orthographic projections of the fragments and, recursively, refines the representation ensuring the validity of provided results. Global convergency and correctness is granted using an optimistic estimation of the potential match during the search process. This way, the proposed algorithm can be classified as a global registration technique, that efficiently converges to the optimal solution without stopping in local minima solutions.