用几何距离改进点云重建，让模型更懂形状真实结构
GeoCD: A Differential Local Approximation for Geodesic Chamfer Distance
- 引入可微分的测地距离近似，捕捉点云内在几何结构
- 单轮微调即显著提升重建质量，多指标表现更优
- 适合做点云生成与重建的科研人员和工程师参考
Chamfer Distance（CD）因简洁高效被广泛用于3D点云学习，但其仅依赖欧氏距离，难以反映三维形状的内在几何特性。为此，我们提出GeoCD，一种拓扑感知且完全可微的测地距离近似方法，旨在作为3D点云学习中的新度量。实验表明，无论在何种网络架构与数据集上，GeoCD均能持续提升重建质量。通过将若干初始以标准CD训练的模型，仅用GeoCD进行单轮微调，即可在多个评估指标上取得显著提升，验证了其有效性与通用性。
原文摘要 · Abstract (English)
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.
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