Unpaired Point Cloud Completion via Unbalanced Optimal Transport

Unpaired point cloud completion is crucial for real-world applications, where ground-truth data for complete point clouds are often unavailable. By learning a completion map from unpaired incomplete and complete point cloud data, this task avoids the reliance on paired datasets. In this paper, we propose the \textit{Unbalanced Optimal Transport Map for Unpaired Point Cloud Completion (\textbf{UOT-UPC})} model, which formulates the unpaired completion task as the (Unbalanced) Optimal Transport (OT) problem. Our method employs a Neural OT model learning the UOT map using neural networks. Our model is the first attempt to leverage UOT for unpaired point cloud completion, achieving competitive or superior performance on both single-category and multi-category benchmarks. In particular, our approach is especially robust under the class imbalance problem, which is frequently encountered in real-world unpaired point cloud completion scenarios.

Most 3D scanning technologies capture only partial views of objects, making it difficult to reconstruct their complete shapes. Traditional methods for completing these “incomplete” 3D point clouds rely on paired data—matched examples of partial and full shapes—which are expensive and often unavailable in real-world settings.We propose a new method that completes 3D point clouds without requiring such paired training data. Our approach formulates the task as an “unbalanced optimal transport” problem— a mathematical framework for mapping one distribution (incomplete point clouds) to another (complete point clouds), even when their structures differ significantly, such as class imbalance.Our model, UOT-UPC, is the first to apply unbalanced optimal transport to unpaired point cloud completion. Our model not only outperforms previous methods on standard benchmarks but also shows strong robustness when the distributions of object types differ between incomplete and complete point clouds. This method enables more accurate 3D shape understanding, with broad applications in robotics, autonomous driving, and AR/VR systems.