Flexible-Weighted Chamfer Distance: Enhanced Objective Function for Point Cloud Completion

The Chamfer Distance (CD) is a cornerstone objective function for point cloud completion, yet its inherent symmetric weighting mechanism limits the quality of the generated results. By penalizing local detail deviations and global coverage deficiencies equally, standard CD often causes structural defects such as point aggregation and incomplete spatial structures. We introduce the Flexible-weighted Chamfer Distance (FCD), which decouples CD into local precision and global completeness sub-objectives. FCD employs an asymmetric weighting strategy that prioritizes global structural integrity, steering the optimization away from sub-optimal solutions. As a plug-and-play module with negligible overhead, extensive experiments on state-of-the-art networks demonstrate that FCD significantly enhances global distribution metrics while preserving local precision. Specifically, on the ShapeNet55 benchmark using AdaPoinTr, FCD reduces the Density-aware Chamfer Distance (DCD) by approximately 12.4% (from 0.613 to 0.537), effectively mitigating point clustering. Similarly, on the PCN dataset, the proposed method reduces the Earth Mover's Distance (EMD) from 23.79 to 21.40, demonstrating superior global uniformity compared to the standard CD baseline. Furthermore, FCD demonstrates excellent generalization. When applied to diverse tasks and datasets, including real-world scans (KITTI), industrial components (ABC), and point cloud upsampling (PU-GAN), it yields significant quantitative gains and produces visually more uniform and structurally complete point clouds. These results underscore FCD's potential as a versatile objective function for the broader point cloud generation domain.