Unpaired Point Cloud Completion using Unbalanced Optimal Transport map

Real-world point cloud is incomplete and lacks corresponding complete point cloud pairs. To address the challenge of unpaired point cloud completion, we introduce UOT-UPC, a novel approach grounded in the (Unbalanced) Optimal Transport (OT) problem. Specifically, we demonstrate that solving OT-based framework provides an effective approach to unpaired point cloud completion; the optimal transport map $T^*$ can serve as an unpaired point cloud completion model. Furthermore, we extend this formulation to incorporate the Unbalanced Optimal Transport (UOT) Map, achieving competitive performance in unpaired point cloud completion. This extension also addresses the class imbalance, a phenomenon in which differences in the composition ratios of two distributions cause undesired distribution shifts in the OT problem. In this paper, we provide theoretical evidence supporting the UOT-based framework's competency to manage the class imbalance, and we validate its effectiveness through experiments.