# PointTree: Transformation-Robust Point Cloud Encoder with Relaxed K-D Trees

arXiv: https://arxiv.org/abs/2208.05962 · HTML: https://mlsanity.com/paper/2208.05962/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 39 references that are in the map.
- First posted on arXiv 11 Aug 2022.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Joint 2D-3D-Semantic Data for Indoor Scene Understanding](https://mlsanity.com/paper/1702.01105/) (2017)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [Walk in the Cloud: Learning Curves for Point Clouds Shape Analysis](https://mlsanity.com/paper/2105.01288/) (2021)
- [Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models](https://mlsanity.com/paper/1704.01222/) (2017)
- [DensePoint: Learning Densely Contextual Representation for Efficient Point Cloud Processing](https://mlsanity.com/paper/1909.03669/) (2019)
- [Multiresolution Tree Networks for 3D Point Cloud Processing](https://mlsanity.com/paper/1807.03520/) (2018)
- [Benchmarking Robustness of 3D Point Cloud Recognition Against Common Corruptions](https://mlsanity.com/paper/2201.12296/) (2022)
- [Learning Geometry-Disentangled Representation for Complementary Understanding of 3D Object Point Cloud](https://mlsanity.com/paper/2012.10921/) (2020)
- [A Rotation-Invariant Framework for Deep Point Cloud Analysis](https://mlsanity.com/paper/2003.07238/) (2020)
- [VoxelContext-Net: An Octree based Framework for Point Cloud Compression](https://mlsanity.com/paper/2105.02158/) (2021)
- [Octree guided CNN with Spherical Kernels for 3D Point Clouds](https://mlsanity.com/paper/1903.00343/) (2019)
- [A Graph-CNN for 3D Point Cloud Classification](https://mlsanity.com/paper/1812.01711/) (2018)
- [3D-Rotation-Equivariant Quaternion Neural Networks](https://mlsanity.com/paper/1911.09040/) (2019)
- [3D ShapeNets: A Deep Representation for Volumetric Shapes](https://mlsanity.com/paper/1406.5670/) (2014)
- [Large-Scale 3D Shape Reconstruction and Segmentation from ShapeNet Core55](https://mlsanity.com/paper/1710.06104/) (2017)
- [Iterative Transformer Network for 3D Point Cloud](https://mlsanity.com/paper/1811.11209/) (2018)
- [Rotation Invariant Point Cloud Classification: Where Local Geometry Meets Global Topology](https://mlsanity.com/paper/1911.00195/) (2019)
- [Geometric Back-projection Network for Point Cloud Classification](https://mlsanity.com/paper/1911.12885/) (2019)

## Built on by (most cited first, 1 of 1)

- [ProxyFormer: Proxy Alignment Assisted Point Cloud Completion with Missing Part Sensitive Transformer](https://mlsanity.com/paper/2302.14435/) (2023)

## Abstract (arXiv)

Being able to learn an effective semantic representation directly on raw point clouds has become a central topic in 3D understanding. Despite rapid progress, state-of-the-art encoders are restrictive to canonicalized point clouds, and have weaker than necessary performance when encountering geometric transformation distortions. To overcome this challenge, we propose PointTree, a general-purpose point cloud encoder that is robust to transformations based on relaxed K-D trees. Key to our approach is the design of the division rule in K-D trees by using principal component analysis (PCA). We use the structure of the relaxed K-D tree as our computational graph, and model the features as border descriptors which are merged with pointwise-maximum operation. In addition to this novel architecture design, we further improve the robustness by introducing pre-alignment -- a simple yet effective PCA-based normalization scheme. Our PointTree encoder combined with pre-alignment consistently outperforms state-of-the-art methods by large margins, for applications from object classification to semantic segmentation on various transformed versions of the widely-benchmarked datasets. Code and pre-trained models are available at https://github.com/immortalCO/PointTree.