# PointLIE: Locally Invertible Embedding for Point Cloud Sampling and Recovery

arXiv: https://arxiv.org/abs/2104.14769 · HTML: https://mlsanity.com/paper/2104.14769/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 30 Apr 2021.

## Builds on (most cited first, 21 of 21)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [PointASNL: Robust Point Clouds Processing using Nonlocal Neural Networks with Adaptive Sampling](https://mlsanity.com/paper/2003.00492/) (2020)
- [Sparse Single Sweep LiDAR Point Cloud Segmentation via Learning Contextual Shape Priors from Scene Completion](https://mlsanity.com/paper/2012.03762/) (2020)
- [The Reversible Residual Network: Backpropagation Without Storing Activations](https://mlsanity.com/paper/1707.04585/) (2017)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [Modeling Point Clouds with Self-Attention and Gumbel Subset Sampling](https://mlsanity.com/paper/1904.03375/) (2019)
- [i-RevNet: Deep Invertible Networks](https://mlsanity.com/paper/1802.07088/) (2018)
- [Patch-based Progressive 3D Point Set Upsampling](https://mlsanity.com/paper/1811.11286/) (2018)
- [SampleNet: Differentiable Point Cloud Sampling](https://mlsanity.com/paper/1912.03663/) (2019)
- [PUGeo-Net: A Geometry-centric Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2002.10277/) (2020)
- [Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds](https://mlsanity.com/paper/1806.01759/) (2018)
- [Adaptive Hierarchical Down-Sampling for Point Cloud Classification](https://mlsanity.com/paper/1904.08506/) (2019)

## Built on by (most cited first, 3 of 3)

- [Point Set Self-Embedding](https://mlsanity.com/paper/2202.13577/) (2022)
- [Temporal Visual Semantics-Induced Human Motion Understanding with Large Language Models](https://mlsanity.com/paper/2512.22249/) (2025)
- [DualGenerator: Information Interaction-based Generative Network for Point Cloud Completion](https://mlsanity.com/paper/2305.09132/) (2023)

## Abstract (arXiv)

Point Cloud Sampling and Recovery (PCSR) is critical for massive real-time point cloud collection and processing since raw data usually requires large storage and computation. In this paper, we address a fundamental problem in PCSR: How to downsample the dense point cloud with arbitrary scales while preserving the local topology of discarding points in a case-agnostic manner (i.e. without additional storage for point relationship)? We propose a novel Locally Invertible Embedding for point cloud adaptive sampling and recovery (PointLIE). Instead of learning to predict the underlying geometry details in a seemingly plausible manner, PointLIE unifies point cloud sampling and upsampling to one single framework through bi-directional learning. Specifically, PointLIE recursively samples and adjusts neighboring points on each scale. Then it encodes the neighboring offsets of sampled points to a latent space and thus decouples the sampled points and the corresponding local geometric relationship. Once the latent space is determined and that the deep model is optimized, the recovery process could be conducted by passing the recover-pleasing sampled points and a randomly-drawn embedding to the same network through an invertible operation. Such a scheme could guarantee the fidelity of dense point recovery from sampled points. Extensive experiments demonstrate that the proposed PointLIE outperforms state-of-the-arts both quantitatively and qualitatively. Our code is released through https://github.com/zwb0/PointLIE.