GeoCD: A Differential Local Approximation for Geodesic Chamfer Distance

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.