# Mahalanobis k-NN: A Statistical Lens for Robust Point-Cloud Registrations

arXiv: https://arxiv.org/abs/2409.06267 · HTML: https://mlsanity.com/paper/2409.06267/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 54 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [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)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [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)
- [CrossPoint: Self-Supervised Cross-Modal Contrastive Learning for 3D Point Cloud Understanding](https://mlsanity.com/paper/2203.00680/) (2022)
- [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)
- [Deep Learning for Image and Point Cloud Fusion in Autonomous Driving: A Review](https://mlsanity.com/paper/2004.05224/) (2020)
- [Robust Point Cloud Registration Framework Based on Deep Graph Matching](https://mlsanity.com/paper/2103.04256/) (2021)
- [DeepGMR: Learning Latent Gaussian Mixture Models for Registration](https://mlsanity.com/paper/2008.09088/) (2020)
- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [3D ShapeNets: A Deep Representation for Volumetric Shapes](https://mlsanity.com/paper/1406.5670/) (2014)
- [DeepUME: Learning the Universal Manifold Embedding for Robust Point Cloud Registration](https://mlsanity.com/paper/2112.09938/) (2021)

## Abstract (arXiv)

In this paper, we discuss Mahalanobis k-NN: A Statistical Lens designed to address the challenges of feature matching in learning-based point cloud registration when confronted with an arbitrary density of point clouds. We tackle this by adopting Mahalanobis k-NN's inherent property to capture the distribution of the local neighborhood and surficial geometry. Our method can be seamlessly integrated into any local-graph-based point cloud analysis method. In this paper, we focus on two distinct methodologies: Deep Closest Point (DCP) and Deep Universal Manifold Embedding (DeepUME). Our extensive benchmarking on the ModelNet40 and FAUST datasets highlights the efficacy of the proposed method in point cloud registration tasks. Moreover, we establish for the first time that the features acquired through point cloud registration inherently can possess discriminative capabilities. This is evident by a substantial improvement of about 20% in the average accuracy observed in the point cloud few-shot classification task, benchmarked on ModelNet40 and ScanObjectNN.