3D correspondence, i.e., a pair of 3D points, is a fundamental concept in computer vision. A set of 3D correspondences, when equipped with compatibility edges, forms a correspondence graph. This graph is a critical component in several state-of-the-art 3D point cloud registration approaches, e.g., the one based on maximal cliques (MAC). However, its properties have not been well understood. So we present the first study that introduces graph signal processing into the domain of correspondence graph. We exploit the generalized degree signal on correspondence graph and pursue sampling strategies that preserve high-frequency components of this signal. To address time-consuming singular value decomposition in deterministic sampling, we resort to a stochastic approximate sampling strategy. As such, the core of our method is the stochastic spectral sampling of correspondence graph. As an application, we build a complete 3D registration algorithm termed as FastMAC, that reaches real-time speed while leading to little to none performance drop. Through extensive experiments, we validate that FastMAC works for both indoor and outdoor benchmarks. For example, FastMAC can accelerate MAC by 80 times while maintaining high registration success rate on KITTI. Codes are publicly available at https://github.com/Forrest-110/FastMAC.

翻译：三维对应点（即一对三维点）是计算机视觉中的基本概念。一组三维对应点在配备兼容性边后构成对应图，该图是多种先进三维点云配准方法（例如基于最大团的方法MAC）的关键组成部分。然而，其特性尚未被充分理解。为此，我们首次将图信号处理引入对应图领域，利用对应图上的广义度信号，并研究保留该信号高频分量的采样策略。为解决确定性采样中耗时的奇异值分解问题，我们采用随机近似采样策略，由此形成方法的本质——对应图的随机谱采样。作为应用，我们构建了完整的配准算法FastMAC，该算法在实现实时速度的同时几乎不损失性能。通过大量实验，我们验证了FastMAC在室内和室外基准测试中的有效性。例如，在KITTI数据集上，FastMAC可将MAC加速80倍，同时保持高配准成功率。代码已开源至https://github.com/Forrest-110/FastMAC。