GeoCD: A Differential Local Approximation for Geodesic Chamfer Distance
This addresses the problem of capturing intrinsic geometry in 3D shapes for researchers and practitioners in computer vision and 3D learning, representing an incremental improvement over existing methods.
The paper tackled the limitation of Chamfer Distance in 3D point cloud learning by proposing GeoCD, a topology-aware and differentiable approximation of geodesic distance, which improved reconstruction quality across various architectures and datasets, with fine-tuning for a single epoch yielding significant gains in multiple metrics.
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.