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

arXiv: https://arxiv.org/abs/2603.14974 · HTML: https://mlsanity.com/paper/2603.14974/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 29 of 29)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [NetVLAD: CNN architecture for weakly supervised place recognition](https://mlsanity.com/paper/1511.07247/) (2015)
- [Fine-tuning CNN Image Retrieval with No Human Annotation](https://mlsanity.com/paper/1711.02512/) (2017)
- [A Metric Learning Reality Check](https://mlsanity.com/paper/2003.08505/) (2020)
- [Revisiting Batch Normalization For Practical Domain Adaptation](https://mlsanity.com/paper/1603.04779/) (2016)
- [Bilinear CNNs for Fine-grained Visual Recognition](https://mlsanity.com/paper/1504.07889/) (2015)
- [PointNetVLAD: Deep Point Cloud Based Retrieval for Large-Scale Place Recognition](https://mlsanity.com/paper/1804.03492/) (2018)
- [Optimal Transport Aggregation for Visual Place Recognition](https://mlsanity.com/paper/2311.15937/) (2023)
- [MinkLoc3D: Point Cloud Based Large-Scale Place Recognition](https://mlsanity.com/paper/2011.04530/) (2020)
- [Optimal whitening and decorrelation](https://mlsanity.com/paper/1512.00809/) (2015)
- [Where is your place, Visual Place Recognition?](https://mlsanity.com/paper/2103.06443/) (2021)
- [Meta Batch-Instance Normalization for Generalizable Person Re-Identification](https://mlsanity.com/paper/2011.14670/) (2020)
- [LoGG3D-Net: Locally Guided Global Descriptor Learning for 3D Place Recognition](https://mlsanity.com/paper/2109.08336/) (2021)
- [Improving Point Cloud Based Place Recognition with Ranking-based Loss and Large Batch Training](https://mlsanity.com/paper/2203.00972/) (2022)
- [Locus: LiDAR-based Place Recognition using Spatiotemporal Higher-Order Pooling](https://mlsanity.com/paper/2011.14497/) (2020)
- [Training Deep Networks with Structured Layers by Matrix Backpropagation](https://mlsanity.com/paper/1509.07838/) (2015)
- [Improved Bilinear Pooling with CNNs](https://mlsanity.com/paper/1707.06772/) (2017)
- [TransLoc3D : Point Cloud based Large-scale Place Recognition using Adaptive Receptive Fields](https://mlsanity.com/paper/2105.11605/) (2021)
- [Backpropagation-Friendly Eigendecomposition](https://mlsanity.com/paper/1906.09023/) (2019)
- [CASSPR: Cross Attention Single Scan Place Recognition](https://mlsanity.com/paper/2211.12542/) (2022)
- [LiDAR-Based Place Recognition For Autonomous Driving: A Survey](https://mlsanity.com/paper/2306.10561/) (2023)
- [Deep Learning for Visual Localization and Mapping: A Survey](https://mlsanity.com/paper/2308.14039/) (2023)
- [A Survey on Deep Learning Methods for Robot Vision](https://mlsanity.com/paper/1803.10862/) (2018)
- [ForestLPR: LiDAR Place Recognition in Forests Attentioning Multiple BEV Density Images](https://mlsanity.com/paper/2503.04475/) (2025)
- [Voronoi-based compact image descriptors: Efficient Region-of-Interest retrieval with VLAD and deep-learning-based descriptors](https://mlsanity.com/paper/1611.08906/) (2016)
- [SelFLoc: Selective Feature Fusion for Large-scale Point Cloud-based Place Recognition](https://mlsanity.com/paper/2306.01205/) (2023)

## Abstract (arXiv)

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.