Unleash the Potential of 3D Point Cloud Modeling with A Calibrated Local Geometry-driven Distance Metric

Quantifying the dissimilarity between two unstructured 3D point clouds is a challenging task, with existing metrics often relying on measuring the distance between corresponding points that can be either inefficient or ineffective. In this paper, we propose a novel distance metric called Calibrated Local Geometry Distance (CLGD), which computes the difference between the underlying 3D surfaces calibrated and induced by a set of reference points. By associating each reference point with two given point clouds through computing its directional distances to them, the difference in directional distances of an identical reference point characterizes the geometric difference between a typical local region of the two point clouds. Finally, CLGD is obtained by averaging the directional distance differences of all reference points. We evaluate CLGD on various optimization and unsupervised learning-based tasks, including shape reconstruction, rigid registration, scene flow estimation, and feature representation. Extensive experiments show that CLGD achieves significantly higher accuracy under all tasks in a memory and computationally efficient manner, compared with existing metrics. As a generic metric, CLGD has the potential to advance 3D point cloud modeling. The source code is publicly available at https://github.com/rsy6318/CLGD.