FastMAC: Stochastic Spectral Sampling of Correspondence Graph

TL;DR

This paper builds a complete 3D registration algorithm termed as FastMAC, that reaches real-time speed while leading to little to none performance drop, and exploits the generalized degree signal on correspondence graph and pursue sampling strategies that preserve highfrequency components of this signal.

Abstract

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.

Figures (9)

• Figure 1: LEFT: FastMAC can accelerate MAC zhang20233d by 80 times, while preserving similarly high registration success rate (denoted by registration recall). This is achieved by sampling 5% nodes on the correspondence graph, through a stochastic spectral formulation. Other sampling ratios are also shown, and FastMAC achieves real-time when the ratio is lower than 20%. MIDDLE: Time profiling comparison between vanilla MAC and FastMAC with different sampling ratios. FastMAC significantly accelerates all stages of MAC. RIGHT: A detailed runtime breakdown for each component in MAC and FastMAC. Maximal clique search is no longer a bottleneck.
• Figure 2: Pipeline of FastMAC. In the top-right panel, we show the the procedure of constructing a correspondence graph from input correspondences. The graph is mathematically represented by an adjacency matrix. High values in this matrix mean high compatibility between two correspondences. In the bottom panel, we define generalized degree signal on the graph as the aggregation of compatibility scores on edges connecting with a node. We pass the signal through a Laplacian high-pass graph filter (constructed from the adjacency matrix) to get its high-frequency component. As mentioned in the text, after filtering, nodes with high response are named as high-frequency nodes. In the top-left panel, we derive a stochastic sampling strategy in which the sampling probability of a node is proportional to the response magnitude. This sampling strategy is a fast approximation of the optimal (but slow) deterministic sampling strategy that recovers a signal of interest. Lastly but not shown in this figure, we use the MAC registration algorithm on output correspondences.
• Figure 3: Response of the degree signal to a high-pass filter on connected-caveman graphs. Node size represents the response magnitude. This shows why high-pass filter is suited for MAC.
• Figure 4: Sampling performance on KITTI. Each column represents a metric in TE,RE and RR and each row represents a setting composed of datasets and descriptors. Shaded areas represent variance from multiple runs.
• Figure 5: Sampling performance on 3DMatch. Each column represents a metric in TE,RE and RR and each row represents a setting composed of datasets and descriptors.