# Adaptive Hierarchical Down-Sampling for Point Cloud Classification

arXiv: https://arxiv.org/abs/1904.08506 · HTML: https://mlsanity.com/paper/1904.08506/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2019.

## Built on by (most cited first, 30 of 40)

- [Taming 3DGS: High-Quality Radiance Fields with Limited Resources](https://mlsanity.com/paper/2406.15643/) (2024)
- [Surface Representation for Point Clouds](https://mlsanity.com/paper/2205.05740/) (2022)
- [Contrastive Boundary Learning for Point Cloud Segmentation](https://mlsanity.com/paper/2203.05272/) (2022)
- [PnP-DETR: Towards Efficient Visual Analysis with Transformers](https://mlsanity.com/paper/2109.07036/) (2021)
- [SASA: Semantics-Augmented Set Abstraction for Point-based 3D Object Detection](https://mlsanity.com/paper/2201.01976/) (2022)
- [RBGNet: Ray-based Grouping for 3D Object Detection](https://mlsanity.com/paper/2204.02251/) (2022)
- [Attention-based Point Cloud Edge Sampling](https://mlsanity.com/paper/2302.14673/) (2023)
- [FESTA: Flow Estimation via Spatial-Temporal Attention for Scene Point Clouds](https://mlsanity.com/paper/2104.00798/) (2021)
- [Learning Inner-Group Relations on Point Clouds](https://mlsanity.com/paper/2108.12468/) (2021)
- [Dual Transformer for Point Cloud Analysis](https://mlsanity.com/paper/2104.13044/) (2021)
- [Centroid Transformers: Learning to Abstract with Attention](https://mlsanity.com/paper/2102.08606/) (2021)
- [Point Cloud Learning with Transformer](https://mlsanity.com/paper/2104.13636/) (2021)
- [PointMCD: Boosting Deep Point Cloud Encoders via Multi-view Cross-modal Distillation for 3D Shape Recognition](https://mlsanity.com/paper/2207.03128/) (2022)
- [Predicting the generalization gap in neural networks using topological data analysis](https://mlsanity.com/paper/2203.12330/) (2022)
- [RPSRNet: End-to-End Trainable Rigid Point Set Registration Network using Barnes-Hut 2D-Tree Representation](https://mlsanity.com/paper/2104.05328/) (2021)
- [LighTN: Light-weight Transformer Network for Performance-overhead Tradeoff in Point Cloud Downsampling](https://mlsanity.com/paper/2202.06263/) (2022)
- [PSNet: Fast Data Structuring for Hierarchical Deep Learning on Point Cloud](https://mlsanity.com/paper/2205.14965/) (2022)
- [Meta-Sampler: Almost-Universal yet Task-Oriented Sampling for Point Clouds](https://mlsanity.com/paper/2203.16001/) (2022)
- [A Correct-and-Certify Approach to Self-Supervise Object Pose Estimators via Ensemble Self-Training](https://mlsanity.com/paper/2302.06019/) (2023)
- [D-Net: Learning for Distinctive Point Clouds by Self-Attentive Point Searching and Learnable Feature Fusion](https://mlsanity.com/paper/2305.05842/) (2023)
- [MICAS: Multi-grained In-Context Adaptive Sampling for 3D Point Cloud Processing](https://mlsanity.com/paper/2411.16773/) (2024)
- [PointLIE: Locally Invertible Embedding for Point Cloud Sampling and Recovery](https://mlsanity.com/paper/2104.14769/) (2021)
- [Supervised Contrastive Learning with Structure Inference for Graph Classification](https://mlsanity.com/paper/2203.07691/) (2022)
- [On-the-fly Point Feature Representation for Point Clouds Analysis](https://mlsanity.com/paper/2407.21335/) (2024)
- [Adaptive LiDAR Scanning: Harnessing Temporal Cues for Efficient 3D Object Detection via Multi-Modal Fusion](https://mlsanity.com/paper/2508.01562/) (2025)
- [Cross-Level Cross-Scale Cross-Attention Network for Point Cloud Representation](https://mlsanity.com/paper/2104.13053/) (2021)
- [Deep Point Cloud Simplification for High-quality Surface Reconstruction](https://mlsanity.com/paper/2203.09088/) (2022)
- [Local region-learning modules for point cloud classification](https://mlsanity.com/paper/2303.17338/) (2023)
- [Hierarchical Adaptive Voxel-guided Sampling for Real-time Applications in Large-scale Point Clouds](https://mlsanity.com/paper/2305.14306/) (2023)
- [Curvature Informed Furthest Point Sampling](https://mlsanity.com/paper/2411.16995/) (2024)

## Abstract (arXiv)

While several convolution-like operators have recently been proposed for extracting features out of point clouds, down-sampling an unordered point cloud in a deep neural network has not been rigorously studied. Existing methods down-sample the points regardless of their importance for the output. As a result, some important points in the point cloud may be removed, while less valuable points may be passed to the next layers. In contrast, adaptive down-sampling methods sample the points by taking into account the importance of each point, which varies based on the application, task and training data. In this paper, we propose a permutation-invariant learning-based adaptive down-sampling layer, called Critical Points Layer (CPL), which reduces the number of points in an unordered point cloud while retaining the important points. Unlike most graph-based point cloud down-sampling methods that use k-NN search algorithm to find the neighbouring points, CPL is a global down-sampling method, rendering it computationally very efficient. The proposed layer can be used along with any graph-based point cloud convolution layer to form a convolutional neural network, dubbed CP-Net in this paper. We introduce a CP-Net for 3D object classification that achieves the best accuracy for the ModelNet40 dataset among point cloud-based methods, which validates the effectiveness of the CPL.