FastMAC: Stochastic Spectral Sampling of Correspondence Graph
Authors: Yifei Zhang, Hao Zhao, Hongyang Li, Siheng Chen

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.