DeepMend: Learning Occupancy Functions to Represent Shape for Repair

We present DeepMend, a novel approach to reconstruct restorations to fractured shapes using learned occupancy functions. Existing shape repair approaches predict low-resolution voxelized restorations, or require symmetries or access to a pre-existing complete oracle. We represent the occupancy of a fractured shape as the conjunction of the occupancy of an underlying complete shape and the fracture surface, which we model as functions of latent codes using neural networks. Given occupancy samples from an input fractured shape, we estimate latent codes using an inference loss augmented with novel penalty terms that avoid empty or voluminous restorations. We use inferred codes to reconstruct the restoration shape. We show results with simulated fractures on synthetic and real-world scanned objects, and with scanned real fractured mugs. Compared to the existing voxel approach and two baseline methods, our work shows state-of-the-art results in accuracy and avoiding restoration artifacts over non-fracture regions of the fractured shape.