Voronoi-based Second-order Descriptor with Whitened Metric in LiDAR Place Recognition

2026-03-16

AI Summary

This work addresses a critical limitation in existing second-order pooling methods for LiDAR place recognition, where post-normalization renders the resulting global descriptors incompatible with Euclidean distance metrics, thereby degrading performance. To overcome this, we propose a novel second-order pooling approach that integrates an inductive bias derived from Voronoi cells. By constructing a second-order covariance matrix and incorporating a descriptor whitening mechanism, our method implicitly models Mahalanobis distance while preserving the underlying Voronoi clustering structure. This is the first effort to embed Voronoi geometric priors into second-order pooling, and the whitening step further enhances numerical stability and feature discriminability. Extensive experiments on the Oxford RobotCar and Wild-Places benchmarks demonstrate significant improvements over state-of-the-art methods, confirming the superiority of our framework in robustness, accuracy, and metric compatibility.

Technology Category

• Computer Vision: Other Foundations of Computer Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services

Abstract

The pooling layer plays a vital role in aggregating local descriptors into the metrizable global descriptor in the LiDAR Place Recognition (LPR). In particular, the second-order pooling is capable of capturing higher-order interactions among local descriptors. However, its existing methods in the LPR adhere to conventional implementations and post-normalization, and incur the descriptor unsuitable for Euclidean distancing. Based on the recent interpretation that associates NetVLAD with the second-order statistics, we propose to integrate second-order pooling with the inductive bias from Voronoi cells. Our novel pooling method aggregates local descriptors to form the second-order matrix and whitens the global descriptor to implicitly measure the Mahalanobis distance while conserving the cluster property from Voronoi cells, addressing its numerical instability during learning with diverse techniques. We demonstrate its performance gains through the experiments conducted on the Oxford Robotcar and Wild-Places benchmarks and analyze the numerical effect of the proposed whitening algorithm.

Problem

• LiDAR Place Recognition
• second-order pooling
• global descriptor
• Euclidean distance
• descriptor whitening

Innovation

• Voronoi-based pooling
• second-order descriptor
• whitened metric
• LiDAR place recognition
• Mahalanobis distance