# DELO: Deep Evidential LiDAR Odometry using Partial Optimal Transport

arXiv: https://arxiv.org/abs/2308.07153 · HTML: https://mlsanity.com/paper/2308.07153/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 14 Aug 2023.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [PRNet: Self-Supervised Learning for Partial-to-Partial Registration](https://mlsanity.com/paper/1910.12240/) (2019)
- [SuMa++: Efficient LiDAR-based Semantic SLAM](https://mlsanity.com/paper/2105.11320/) (2021)
- [DeepICP: An End-to-End Deep Neural Network for 3D Point Cloud Registration](https://mlsanity.com/paper/1905.04153/) (2019)
- [LCDNet: Deep Loop Closure Detection and Point Cloud Registration for LiDAR SLAM](https://mlsanity.com/paper/2103.05056/) (2021)
- [LO-Net: Deep Real-time Lidar Odometry](https://mlsanity.com/paper/1904.08242/) (2019)
- [CT-ICP: Real-time Elastic LiDAR Odometry with Loop Closure](https://mlsanity.com/paper/2109.12979/) (2021)
- [PWCLO-Net: Deep LiDAR Odometry in 3D Point Clouds Using Hierarchical Embedding Mask Optimization](https://mlsanity.com/paper/2012.00972/) (2020)
- [BALM: Bundle Adjustment for Lidar Mapping](https://mlsanity.com/paper/2010.08215/) (2020)
- [Efficient Continuous-Time SLAM for 3D Lidar-Based Online Mapping](https://mlsanity.com/paper/1810.06802/) (2018)
- [Deep Multi-Task Learning for Joint Localization, Perception, and Prediction](https://mlsanity.com/paper/2101.06720/) (2021)
- [Efficient and Robust LiDAR-Based End-to-End Navigation](https://mlsanity.com/paper/2105.09932/) (2021)
- [DMLO: Deep Matching LiDAR Odometry](https://mlsanity.com/paper/2004.03796/) (2020)
- [Self-supervised Learning of LiDAR Odometry for Robotic Applications](https://mlsanity.com/paper/2011.05418/) (2020)
- [Online LiDAR-SLAM for Legged Robots with Robust Registration and Deep-Learned Loop Closure](https://mlsanity.com/paper/2001.10249/) (2020)
- [RPSRNet: End-to-End Trainable Rigid Point Set Registration Network using Barnes-Hut 2D-Tree Representation](https://mlsanity.com/paper/2104.05328/) (2021)
- [Globally Consistent 3D LiDAR Mapping with GPU-accelerated GICP Matching Cost Factors](https://mlsanity.com/paper/2109.07073/) (2021)
- [Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations](https://mlsanity.com/paper/2009.14005/) (2020)

## Built on by (most cited first, 8 of 8)

- [DVLO: Deep Visual-LiDAR Odometry with Local-to-Global Feature Fusion and Bi-Directional Structure Alignment](https://mlsanity.com/paper/2403.18274/) (2024)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [DVLO4D: Deep Visual-Lidar Odometry with Sparse Spatial-temporal Fusion](https://mlsanity.com/paper/2509.06023/) (2025)
- [RegFormer++: An Efficient Large-Scale 3D LiDAR Point Registration Network with Projection-Aware 2D Transformer](https://mlsanity.com/paper/2603.14290/) (2026)
- [DNOI-4DRO: Deep 4D Radar Odometry with Differentiable Neural-Optimization Iterations](https://mlsanity.com/paper/2505.12310/) (2025)
- [Efficient Active Training for Deep LiDAR Odometry](https://mlsanity.com/paper/2509.03211/) (2025)
- [NeuroSymbEAD: A Large Scale Neuro-Symbolic Caption Dataset for Omni-Directional Embodied Autonomous Driving](https://mlsanity.com/paper/2609.16919/) (2026)
- [MemReg: Streaming Outdoor LiDAR Point Cloud Registration with Hybrid Memory Buffers](https://mlsanity.com/paper/2610.12624/) (2026)

## Abstract (arXiv)

Accurate, robust, and real-time LiDAR-based odometry (LO) is imperative for many applications like robot navigation, globally consistent 3D scene map reconstruction, or safe motion-planning. Though LiDAR sensor is known for its precise range measurement, the non-uniform and uncertain point sampling density induce structural inconsistencies. Hence, existing supervised and unsupervised point set registration methods fail to establish one-to-one matching correspondences between LiDAR frames. We introduce a novel deep learning-based real-time (approx. 35-40ms per frame) LO method that jointly learns accurate frame-to-frame correspondences and model's predictive uncertainty (PU) as evidence to safe-guard LO predictions. In this work, we propose (i) partial optimal transportation of LiDAR feature descriptor for robust LO estimation, (ii) joint learning of predictive uncertainty while learning odometry over driving sequences, and (iii) demonstrate how PU can serve as evidence for necessary pose-graph optimization when LO network is either under or over confident. We evaluate our method on KITTI dataset and show competitive performance, even superior generalization ability over recent state-of-the-art approaches. Source codes are available.