On the Structural Failure of Chamfer Distance in 3D Shape Optimization
2026-03-10 • Computer Vision and Pattern Recognition
Computer Vision and Pattern RecognitionGraphics
AI summaryⓘ
The authors studied why using Chamfer distance as a loss for training point cloud models can sometimes make results worse instead of better. They found that the problem comes from how gradients push points to collapse into the same spot, which local methods can’t fix. They show that to stop this collapse, the optimization must connect points beyond just their neighbors, using global interactions. Their experiments in 2D and 3D scenarios confirm that adding these global connections improves the results. This insight helps guide better designs for training with point-level distance metrics.
Chamfer distancepoint cloudgradient collapselocal regularizerglobal couplingMPM priorpoint cloud reconstructionshape morphingoptimizationdistance metrics
Authors
Chang-Yong Song, David Hyde
Abstract
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.