GeoCD: A Differential Local Approximation for Geodesic Chamfer Distance

2025-06-29

AI Summary

Chamfer Distance (CD) relies solely on Euclidean distances, failing to capture the intrinsic geometric structure of 3D shapes. To address this, we propose GeoCD—a topology-aware, fully differentiable approximation of geodesic Chamfer distance. Our method introduces the first differentiable local geodesic distance estimator: it constructs a local neighborhood graph and incorporates a gradient propagation mechanism to enable end-to-end optimization of geodesic distances. GeoCD is architecture-agnostic and can be seamlessly integrated into diverse point cloud learning models without architectural modification. Evaluated across multiple 3D reconstruction tasks and benchmarks, GeoCD achieves significant improvements in CD and F-Score with only a single round of fine-tuning—demonstrating its effectiveness in enhancing geometric structure modeling.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Chamfer Distance (CD) is a widely adopted metric in 3D point cloud learning due to its simplicity and efficiency. However, it suffers from a fundamental limitation: it relies solely on Euclidean distances, which often fail to capture the intrinsic geometry of 3D shapes. To address this limitation, we propose GeoCD, a topology-aware and fully differentiable approximation of geodesic distance designed to serve as a metric for 3D point cloud learning. Our experiments show that GeoCD consistently improves reconstruction quality over standard CD across various architectures and datasets. We demonstrate this by fine-tuning several models, initially trained with standard CD, using GeoCD. Remarkably, fine-tuning for a single epoch with GeoCD yields significant gains across multiple evaluation metrics.

Problem

• Overcome Euclidean limitation in Chamfer Distance
• Propose geodesic approximation for 3D shape geometry
• Improve reconstruction quality in point cloud learning

Innovation

• Differentiable geodesic distance approximation
• Topology-aware 3D point cloud metric
• Single-epoch fine-tuning improves reconstruction