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NDT-Transformer: Large-Scale 3D Point Cloud Localisation using the Normal Distribution Transform Representation

Zhicheng Zhou, Cheng Zhao, Daniel Adolfsson, Songzhi Su, Yang Gao, Tom Duckett, Li Sun

arXiv:2103.12292v1cs.ROcs.CV

TL;DR

Point-cloud localisation is needed in GPS-challenged settings, but large-scale systems face scalability and generalisation challenges. NDT-Transformer represents point clouds with geometric NDT cells and learns contextual global descriptors; on Oxford Robotcar, it improves average recall over LPD-Net.

  • Problem

    Point-cloud localisation is needed in GPS-challenged environments, while current systems face generality and scalability challenges.

    Source: §I · p. 1

  • Method

    NDT-Transformer encodes compact NDT cells with a residual transformer to aggregate contextual cues into a global place descriptor.

    Source: B. 3D NDT Representation · p. 3, C. NDT-Transformer Network · p. 4

  • Results

    7.52% improvement for top 1(@1) average recall and 2.73% improvement for top 1% (@1%) average recall over LPD-Net.

    Source: C. Performance Evaluation · p. 5

  • Takeaways & Limitations

    The system balances state-of-the-art performance with run-time performance as a potential real-time SLAM module and supplement to NDT-based SLAM approaches.

    Source: §V · p. 6

Abstract

from arXiv · show

3D point cloud-based place recognition is highly demanded by autonomous driving in GPS-challenged environments and serves as an essential component (i.e. loop-closure detection) in lidar-based SLAM systems. This paper proposes a novel approach, named NDT-Transformer, for realtime and large-scale place recognition using 3D point clouds. Specifically, a 3D Normal Distribution Transform (NDT) representation is employed to condense the raw, dense 3D point cloud as probabilistic distributions (NDT cells) to provide the geometrical shape description. Then a novel NDT-Transformer network learns a global descriptor from a set of 3D NDT cell representations. Benefiting from the NDT representation and NDT-Transformer network, the learned global descriptors are enriched with both geometrical and contextual information. Finally, descriptor retrieval is achieved using a query-database for place recognition. Compared to the state-of-the-art methods, the proposed approach achieves an improvement of 7.52% on average top 1 recall and 2.73% on average top 1% recall on the Oxford Robotcar benchmark.

I. INTRODUCTION

The paper targets point-cloud localisation and loop closure in GPS-challenged settings, where conventional methods face scalability and generalisation challenges. It proposes NDT-Transformer to retrieve place descriptors from geometry-enriched NDT cells.

  • The approach addresses demand for robust point-cloud localisation and loop-closure detection where GPS is unavailable or unreliable.Source: §I · p. 1
  • Large-scale localisation remains challenging because conventional registration and particle-filtering methods do not scale, while regression-based methods do not generalise to novel environments.Source: §I · p. 1
  • NDT-Transformer learns place descriptors from geometry-enriched NDT cells, with query descriptors computed online and database descriptors precomputed offline.Source: §I · p. 1
  • The paper reports state-of-the-art performance for point-cloud place recognition and positions the method as a supplement for NDT-based SLAM and Monte-Carlo localisation.Source: §I · p. 2

II. RELATED WORK

Prior point-cloud localisation methods span regression, intermediate representations, and global features. Their trade-offs include limited generalisation, computational costs, loss of local geometry through downsampling, and difficulty extracting contextual information.

A. Point cloud-based global localisation

B. NDT-based localisation

NDT represents point clouds through Gaussian cell distributions that encode geometric structure and support memory-efficient localisation. The paper formulates loop closure as nearest-neighbour retrieval of a query submap descriptor from a database.

B. NDT-based localisation

  • NDT represents point clouds as multivariate Gaussian distributions whose cell parameters implicitly encode map structure and geometry, supporting memory-efficient localisation.Source: B. NDT-based localisation · p. 2

A. Problem Formulation

  • Robot trajectories are divided into fixed-range submaps, represented as sampled NDT cells, and encoded as fixed-size global descriptors for similarity comparison.Source: A. Problem Formulation · p. 2
  • Loop closure is formulated as finding the database submap whose descriptor has the smallest Euclidean distance to the query descriptor.Source: A. Problem Formulation · pp. 2–3
  • For place recognition, the system matches a query point cloud from another run against stored place descriptors, computing the query descriptor online and database descriptors offline.Source: A. Problem Formulation · p. 3

B. 3D NDT Representation

The representation replaces fixed-count point downsampling with compact NDT cells that retain local geometric shape. Spatially distributed sampling selects a fixed number of cells while aiming to preserve structural information.

B. 3D NDT Representation

  • 3D NDT represents point-cloud submaps as compact spherical cell structures that preserve local geometric shape while reducing memory complexity.Source: B. 3D NDT Representation · p. 3
  • Spatially distributed sampling generates evenly distributed NDT cells, mapping a variable-size submap to a fixed number of cells.Source: B. 3D NDT Representation · p. 3
  • Sampling downsamples to an oversampled point set, estimates each cell from nearby original points, then removes cells with highest mutual information until k remain.Mutual information is computed using symmetric Kullback–Leibler divergence; the method states that this preserves structural information.Source: B. 3D NDT Representation · p. 3
  • Figure 2 contrasts dense point clouds with their NDT cells and shows the cells within the dense cloud.Source: Figure 2 · p. 3

C. NDT-Transformer Network

The network maps a 3D NDT submap to a global descriptor through point transformation, contextual encoding, and descriptor aggregation.

C. NDT-Transformer Network

  • The pipeline feeds the NDT representation into the NDT-Transformer network to obtain a submap descriptor.The network comprises NDT representation, a residual transformer encoder, and NetVLAD.Source: C. NDT-Transformer Network · p. 3
  • A submap’s NDT representation is transformed for rotational invariance, with the learned point transform also propagating uncertainty.The Transform Net learns its transition matrix from the NDT mean vectors.Source: C. NDT-Transformer Network · p. 3
  • A residual transformer encoder aggregates contextual cues across NDT cells to make their representations more distinctive.This addresses the lack of context between individual NDT representations and contrasts with kNN-based grouping.Source: C. NDT-Transformer Network · pp. 3–4
  • Three transformer encoder stacks use multi-head self-attention, feed-forward networks, and layer normalization to learn co-contextual information.The implementation uses four attention heads, which connect a cell with other salient cells.Source: C. NDT-Transformer Network · p. 4
  • NetVLAD aggregates the NDT-cell descriptors into a fixed-size global descriptor, followed by an MLP.Its assignment parameters are learned end-to-end, and it is used instead of max pooling to improve permutation invariance.Source: C. NDT-Transformer Network · p. 4

D. Metric Learning

Metric learning trains the global descriptors to distinguish query places from nearby positives and more distant negatives.

D. Metric Learning

  • The Lazy Quadruplet loss trains query descriptors against positive, negative, and hard-negative descriptors sampled from other locations.The paper follows PointNetVLAD in using this loss for metric learning.Source: D. Metric Learning · p. 4
  • The loss pulls query and positive descriptors together, separates query from negative descriptors, and maintains distance between negative and hard-negative descriptors.It uses constant margins α and β and Euclidean distance.Source: D. Metric Learning · p. 4

A. Dataset Benchmark

The Oxford RobotCar dataset provides the long-term, multi-session data used to evaluate the method.

A. Dataset Benchmark

  • The evaluation uses Oxford RobotCar long-term, multi-session data collected with a rear-mounted Sick LMS-151 2D lidar.The scans support construction of a dense point-cloud map.Source: A. Dataset Benchmark · p. 4
  • The map is built from 2D lidar scans transformed using an accurate 6 DOF trajectory fused from GPS-RTK and visual-inertial sensors.Places are spaced at 10 m for training and 20 m for evaluation, and submaps use 20 m trajectory segments.Source: A. Dataset Benchmark · p. 5
  • Training and testing use 44 and 22 runs, respectively, yielding 21,898 training submaps and 3,071 test submaps.Evaluation inputs use 2,000 NDT cells at 0.8 m resolution; places within 10 m are positives and those beyond 50 m are negatives.Source: A. Dataset Benchmark · p. 5

B. Neural Network Training

The network uses transformer and NetVLAD settings alongside a metric-learning training schedule.

B. Neural Network Training

  • The network uses three four-head transformer encoders with 256-dimensional input and output, a 1,024-dimensional feed-forward layer, and 0.1 dropout.The shared linear stacks use hidden sizes 256 and 1,024, while NetVLAD uses 64 clusters and maps 1,024 dimensions to 256.Source: B. Neural Network Training · p. 5
  • Training runs for 20 epochs with batch size 2, using one query, two positives, 18 negatives, and one hard negative per batch.The schedule decays the 1e-5 learning rate by 0.1 at epochs 9 and 15, with momentum 0.9.Source: B. Neural Network Training · p. 5

C. Performance Evaluation

On the Oxford Robotcar benchmark, NDT-Transformer outperforms the compared methods on the reported recall metrics. Evaluation also examines component ablations and retrieval on previously unseen streets.

C. Performance Evaluation

V. CONCLUSION

NDT-Transformer turns point-cloud submaps into location descriptors using NDT representations and a transformer encoder. On Oxford Robotcar, it improves on the state-of-the-art method at both reported recall measures and is proposed as a supplement to real-time SLAM.

V. CONCLUSION

  • NDT-Transformer represents dense point-cloud submaps as discriminative location descriptors for large-scale topological localization through place recognition and retrieval.Source: §V · p. 6
  • The NDT representation and transformer encoder summarize geometric and contextual information without handcrafted features, hierarchically aggregating and strengthening local features.Source: §V · p. 6
  • On Oxford Robotcar, the method improves average recall over the state-of-the-art by 7.52% at top 1 and 2.73% at top 1%; it is proposed as a real-time SLAM module and supplement to NDT-based SLAM.Source: §V · p. 6
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