The Josefina Ramos de Cox museum in Lima, Peru, decided to digitize hundreds of archaeological pieces from pre-Colombian cultures to support further research and create virtual educational environments. However, the 3D scanning procedure led to imperfections in the objects’ surface, mainly due to the difficulty of manipulating the fragile objects during the acquisition. The problem was that many of the scanned artifacts do not contain the base because the contact surface during acquisition was not visible to the scanner. This paper proposes a method to repair the digital objects’ surface using a data-driven approach. We design and train a point cloud neural network that learns to synthesize the missing geometry in an end-to-end manner. Our model consists of a novel architecture and training protocol that addresses the problem of point cloud completion. We propose an end-to-end neural network architecture that focuses on calculating the missing geometry and merging the known input and the predicted point cloud. Our method is composed of two neural networks: the missing part prediction network and the merging-refinement network. The first module focuses on extracting information from the incomplete input to infer the missing geometry. The second module merges both point clouds and improves the distribution of the points. Our approach is effective in repairing pottery objects with large imperfections during the scanning. Besides, our experiments on ShapeNet and Completion3D datasets show that our method is effective in a general setting for shape completion.