Chamfer距离优化会因梯度结构导致点云坍缩，需全局耦合才能解决
On the Structural Failure of Chamfer Distance in 3D Shape Optimization
- 发现Chamfer梯度存在多对一坍缩机制，局部正则化无法缓解
- 引入全局耦合后，20组3D形状对的Chamfer差距平均缩小2.5倍
- 适用于点云重建、补全等依赖点级距离的任务设计
Chamfer距离是点云重建、补全和生成的标准训练损失，但直接优化它反而可能导致比不优化更差的结果。我们揭示这一悖论源于梯度结构：每个点的Chamfer梯度引发多对一坍缩，成为前向项的唯一吸引子，任何局部正则化（包括排斥、平滑性和密度感知重加权）都无法解决。我们推导出抑制坍缩的必要条件：耦合必须超出局部邻域。在受控2D设置中，共享基变形通过全局耦合抑制坍缩；在3D形状变形中，可微分的MPM先验实现了相同原理，在20组有向对上一致降低Chamfer差距，复杂拓扑的dragon模型改善达2.5倍。非局部耦合的存在与否决定了Chamfer优化是否成功，为优化点级距离度量的任意流程提供了实用设计准则。
原文摘要 · Abstract (English)
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.
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