On the Structural Failure of Chamfer Distance in 3D Shape Optimization

2026-03-10

AI Summary

This work addresses the well-known issue of many-to-one collapse in 3D point cloud optimization using Chamfer distance, which arises from its gradient structure and often degrades optimization results. The study is the first to demonstrate that local regularization fails to mitigate this collapse and reveals that non-local coupling is essential for its suppression. To this end, the authors propose a globally coupled framework based on a shared-basis deformation model and a differentiable Material Point Method (MPM) prior. The optimization integrates density-aware reweighting, repulsive forces, and smoothness constraints. Evaluated on 20 3D shape morphing tasks, the method consistently reduces the Chamfer gap, achieving up to a 2.5× improvement on topologically complex models such as the dragon, thereby validating its effectiveness in both 2D and 3D settings.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Chamfer distance
• structural failure
• point cloud collapse
• 3D shape optimization
• gradient collapse

Innovation

• Chamfer distance
• gradient collapse
• non-local coupling
• point cloud optimization
• differentiable MPM