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.

翻译：量化两个非结构化三维点云之间的差异是一项具有挑战性的任务，现有度量通常依赖于测量对应点之间的距离，这种方法要么效率低下，要么效果不佳。本文提出了一种新颖的距离度量，称为校准局部几何距离（CLGD），该度量通过一组参考点计算校准和诱导的底层三维曲面之间的差异。通过计算每个参考点到两个给定点云的方向距离，将其与两个点云相关联，同一参考点的方向距离差异刻画了两个点云典型局部区域间的几何差异。最终，CLGD通过对所有参考点的方向距离差异取平均得到。我们在各种优化和无监督学习任务中评估CLGD，包括形状重建、刚性配准、场景流估计和特征表示。大量实验表明，与现有度量相比，CLGD在所有任务中以内存和计算高效的方式实现了显著更高的精度。作为一种通用度量，CLGD具有推动三维点云建模发展的潜力。源代码已公开于 https://github.com/rsy6318/CLGD。