# (Just) A Spoonful of Refinements Helps the Registration Error Go Down

arXiv: https://arxiv.org/abs/2108.03257 · HTML: https://mlsanity.com/paper/2108.03257/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 6 Aug 2021.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Frustum PointNets for 3D Object Detection from RGB-D Data](https://mlsanity.com/paper/1711.08488/) (2017)
- [Video Instance Segmentation](https://mlsanity.com/paper/1905.04804/) (2019)
- [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)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [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)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [Learning to Find Good Correspondences](https://mlsanity.com/paper/1711.05971/) (2017)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [3DFeat-Net: Weakly Supervised Local 3D Features for Point Cloud Registration](https://mlsanity.com/paper/1807.09413/) (2018)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [Robust Multi-Modality Multi-Object Tracking](https://mlsanity.com/paper/1909.03850/) (2019)
- [Learning Compact Geometric Features](https://mlsanity.com/paper/1709.05056/) (2017)
- [PointGMM: a Neural GMM Network for Point Clouds](https://mlsanity.com/paper/2003.13326/) (2020)
- [Weakly-supervised 3D Shape Completion in the Wild](https://mlsanity.com/paper/2008.09110/) (2020)
- [Learning to Localize Using a LiDAR Intensity Map](https://mlsanity.com/paper/2012.10902/) (2020)
- [SDRSAC: Semidefinite-Based Randomized Approach for Robust Point Cloud Registration without Correspondences](https://mlsanity.com/paper/1904.03483/) (2019)
- [3D Local Features for Direct Pairwise Registration](https://mlsanity.com/paper/1904.04281/) (2019)
- [High-dimensional Convolutional Networks for Geometric Pattern Recognition](https://mlsanity.com/paper/2005.08144/) (2020)
- [AlignNet-3D: Fast Point Cloud Registration of Partially Observed Objects](https://mlsanity.com/paper/1910.04668/) (2019)

## Built on by (most cited first, 2 of 2)

- [Regularizing Self-supervised 3D Scene Flows with Surface Awareness and Cyclic Consistency](https://mlsanity.com/paper/2312.08879/) (2023)
- [SoloPose: One-Shot Kinematic 3D Human Pose Estimation with Video Data Augmentation](https://mlsanity.com/paper/2312.10195/) (2023)

## Abstract (arXiv)

We tackle data-driven 3D point cloud registration. Given point correspondences, the standard Kabsch algorithm provides an optimal rotation estimate. This allows to train registration models in an end-to-end manner by differentiating the SVD operation. However, given the initial rotation estimate supplied by Kabsch, we show we can improve point correspondence learning during model training by extending the original optimization problem. In particular, we linearize the governing constraints of the rotation matrix and solve the resulting linear system of equations. We then iteratively produce new solutions by updating the initial estimate. Our experiments show that, by plugging our differentiable layer to existing learning-based registration methods, we improve the correspondence matching quality. This yields up to a 7% decrease in rotation error for correspondence-based data-driven registration methods.