This paper presents a novel approach to learn compact channel correlation representation for LiDAR place recognition, called C3R, aimed at reducing the computational burden and dimensionality associated with traditional covariance pooling methods for place recognition tasks. Our method partitions the feature matrix into smaller groups, computes group-wise covariance matrices, and aggregates them via a learnable aggregation strategy. Matrix power normalization is applied to ensure stability. Theoretical analyses are also given to demonstrate the effectiveness of the proposed method, including its ability to preserve permutation invariance and maintain high mutual information between the original features and the aggregated representation. We conduct extensive experiments on four large-scale, public LiDAR place recognition datasets including Oxford RobotCar, In-house, MulRan, and WildPlaces datasets to validate our approach's superiority in accuracy, and robustness. Furthermore, we provide the quantitative results of our approach for a deeper understanding. The code will be released upon acceptance.

翻译：本文提出了一种新颖的方法，用于学习激光雷达地点识别的紧凑通道相关性表示，称为C3R，旨在降低传统协方差池化方法在地点识别任务中带来的计算负担和维度问题。我们的方法将特征矩阵划分为较小的组，计算组内协方差矩阵，并通过可学习的聚合策略进行聚合。应用矩阵幂归一化以确保稳定性。同时提供了理论分析，以证明所提方法的有效性，包括其保持置换不变性的能力以及在原始特征与聚合表示之间维持高互信息的能力。我们在四个大规模公开激光雷达地点识别数据集上进行了广泛实验，包括Oxford RobotCar、In-house、MulRan和WildPlaces数据集，以验证我们方法在准确性和鲁棒性方面的优越性。此外，我们提供了该方法的定量结果以便更深入理解。代码将在论文被接受后发布。