In large-scale metric localization, an incorrect result during retrieval will lead to an incorrect pose estimate or loop closure. Re-ranking methods propose to take into account all the top retrieval candidates and re-order them to increase the likelihood of the top candidate being correct. However, state-of-the-art re-ranking methods are inefficient when re-ranking many potential candidates due to their need for resource intensive point cloud registration between the query and each candidate. In this work, we propose an efficient spectral method for geometric verification (named SpectralGV) that does not require registration. We demonstrate how the optimal inter-cluster score of the correspondence compatibility graph of two point clouds represents a robust fitness score measuring their spatial consistency. This score takes into account the subtle geometric differences between structurally similar point clouds and therefore can be used to identify the correct candidate among potential matches retrieved by global similarity search. SpectralGV is deterministic, robust to outlier correspondences, and can be computed in parallel for all potential candidates. We conduct extensive experiments on 5 large-scale datasets to demonstrate that SpectralGV outperforms other state-of-the-art re-ranking methods and show that it consistently improves the recall and pose estimation of 3 state-of-the-art metric localization architectures while having a negligible effect on their runtime. The open-source implementation and trained models are available at: https://github.com/csiro-robotics/SpectralGV.

翻译：在大规模度量定位中，检索阶段的错误结果将导致错误的位姿估计或闭环检测。重排序方法通过综合考虑所有顶级检索候选并重新排序，提高首位候选正确的概率。然而，现有最先进的重排序方法因需要在查询点云与每个候选点云之间进行资源密集型的点云配准，导致其在处理大量候选时效率低下。本文提出一种无需配准的高效谱几何验证方法（命名为SpectralGV）。我们证明了两个点云对应兼容性图的簇间最优得分可作为衡量其空间一致性的鲁棒拟合分数。该分数能捕捉结构相似点云间的细微几何差异，因此可用于识别全局相似搜索返回的潜在匹配中的正确候选。SpectralGV具有确定性、对异常对应具有鲁棒性，且可对所有候选进行并行计算。通过在五个大规模数据集上的大量实验，我们证明SpectralGV优于其他最先进的重排序方法，并表明其能持续提升三种最先进度量定位架构的召回率和位姿估计精度，同时对运行时影响可忽略不计。开源实现与预训练模型可通过以下链接获取：https://github.com/csiro-robotics/SpectralGV。