Unleash the Potential of 3D Point Cloud Modeling with A Calibrated Local
  Geometry-driven Distance Metric
Siyu Ren Junhui Hou
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.