On the Structural Failure of Chamfer Distance in 3D Shape Optimization
This addresses a critical issue for researchers and practitioners in 3D computer vision and graphics who rely on Chamfer distance for point cloud reconstruction, completion, and generation, offering a design criterion to prevent optimization collapse.
The paper identifies a structural failure in Chamfer distance optimization for 3D shape tasks, where direct optimization paradoxically worsens results due to gradient-induced collapse, and proposes a solution using non-local coupling that reduces the Chamfer gap by 2.5× on complex shapes.
Chamfer distance is the standard training loss for point cloud reconstruction, completion, and generation, yet directly optimizing it can produce worse Chamfer values than not optimizing it at all. We show that this paradoxical failure is gradient-structural. The per-point Chamfer gradient creates a many-to-one collapse that is the unique attractor of the forward term and cannot be resolved by any local regularizer, including repulsion, smoothness, and density-aware re-weighting. We derive a necessary condition for collapse suppression: coupling must propagate beyond local neighborhoods. In a controlled 2D setting, shared-basis deformation suppresses collapse by providing global coupling; in 3D shape morphing, a differentiable MPM prior instantiates the same principle, consistently reducing the Chamfer gap across 20 directed pairs with a 2.5$\times$ improvement on the topologically complex dragon. The presence or absence of non-local coupling determines whether Chamfer optimization succeeds or collapses. This provides a practical design criterion for any pipeline that optimizes point-level distance metrics.