# A Robust Loss for Point Cloud Registration

arXiv: https://arxiv.org/abs/2108.11682 · HTML: https://mlsanity.com/paper/2108.11682/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 51 references that are in the map.
- First posted on arXiv 26 Aug 2021.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [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)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [PRNet: Self-Supervised Learning for Partial-to-Partial Registration](https://mlsanity.com/paper/1910.12240/) (2019)
- [Feature-metric Registration: A Fast Semi-supervised Approach for Robust Point Cloud Registration without Correspondences](https://mlsanity.com/paper/2005.01014/) (2020)
- [Fast and Robust Iterative Closest Point](https://mlsanity.com/paper/2007.07627/) (2020)
- [SDRSAC: Semidefinite-Based Randomized Approach for Robust Point Cloud Registration without Correspondences](https://mlsanity.com/paper/1904.03483/) (2019)
- [Recurrent Multi-view Alignment Network for Unsupervised Surface Registration](https://mlsanity.com/paper/2011.12104/) (2020)
- [AA-ICP: Iterative Closest Point with Anderson Acceleration](https://mlsanity.com/paper/1709.05479/) (2017)
- [A Systematic Approach for Cross-source Point Cloud Registration by Preserving Macro and Micro Structures](https://mlsanity.com/paper/1608.05143/) (2016)
- [Correspondence Matrices are Underrated](https://mlsanity.com/paper/2010.16085/) (2020)
- [Multi-Features Guidance Network for partial-to-partial point cloud registration](https://mlsanity.com/paper/2011.12079/) (2020)

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

- [Non-Probability Sampling Network for Stochastic Human Trajectory Prediction](https://mlsanity.com/paper/2203.13471/) (2022)
- [Point Cloud Registration for LiDAR and Photogrammetric Data: a Critical Synthesis and Performance Analysis on Classic and Deep Learning Algorithms](https://mlsanity.com/paper/2302.07184/) (2023)
- [DDM: A Metric for Comparing 3D Shapes Using Directional Distance Fields](https://mlsanity.com/paper/2401.09736/) (2024)
- [FracGM: A Fast Fractional Programming Technique for Geman-McClure Robust Estimator](https://mlsanity.com/paper/2409.13978/) (2024)
- [Unleash the Potential of 3D Point Cloud Modeling with A Calibrated Local Geometry-driven Distance Metric](https://mlsanity.com/paper/2306.00552/) (2023)
- [STaR: Seamless Spatial-Temporal Aware Motion Retargeting with Penetration and Consistency Constraints](https://mlsanity.com/paper/2504.06504/) (2025)
- [DualReg: Dual-Space Filtering and Reinforcement for Rigid Registration](https://mlsanity.com/paper/2508.17034/) (2025)
- [Catalyst4D: High-Fidelity 3D-to-4D Scene Editing via Dynamic Propagation](https://mlsanity.com/paper/2603.12766/) (2026)

## Abstract (arXiv)

The performance of surface registration relies heavily on the metric used for the alignment error between the source and target shapes. Traditionally, such a metric is based on the point-to-point or point-to-plane distance from the points on the source surface to their closest points on the target surface, which is susceptible to failure due to instability of the closest-point correspondence. In this paper, we propose a novel metric based on the intersection points between the two shapes and a random straight line, which does not assume a specific correspondence. We verify the effectiveness of this metric by extensive experiments, including its direct optimization for a single registration problem as well as unsupervised learning for a set of registration problems. The results demonstrate that the algorithms utilizing our proposed metric outperforms the state-of-the-art optimization-based and unsupervised learning-based methods.