# PU-EVA: An Edge Vector based Approximation Solution for Flexible-scale Point Cloud Upsampling

arXiv: https://arxiv.org/abs/2204.10750 · HTML: https://mlsanity.com/paper/2204.10750/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 22 Apr 2022.

## Builds on (most cited first, 20 of 20)

- [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)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [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)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [Patch-based Progressive 3D Point Set Upsampling](https://mlsanity.com/paper/1811.11286/) (2018)
- [PU-GCN: Point Cloud Upsampling using Graph Convolutional Networks](https://mlsanity.com/paper/1912.03264/) (2019)
- [EC-Net: an Edge-aware Point set Consolidation Network](https://mlsanity.com/paper/1807.06010/) (2018)
- [Point Cloud Upsampling via Disentangled Refinement](https://mlsanity.com/paper/2106.04779/) (2021)
- [PUGeo-Net: A Geometry-centric Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2002.10277/) (2020)
- [Meta-PU: An Arbitrary-Scale Upsampling Network for Point Cloud](https://mlsanity.com/paper/2102.04317/) (2021)
- [Deep Magnification-Flexible Upsampling over 3D Point Clouds](https://mlsanity.com/paper/2011.12745/) (2020)
- [Point Cloud Rendering after Coding: Impacts on Subjective and Objective Quality](https://mlsanity.com/paper/1912.09137/) (2019)
- [GeoNet: Deep Geodesic Networks for Point Cloud Analysis](https://mlsanity.com/paper/1901.00680/) (2019)
- [Improving Semantic Analysis on Point Clouds via Auxiliary Supervision of Local Geometric Priors](https://mlsanity.com/paper/2001.04803/) (2020)
- [Scalable Surface Reconstruction from Point Clouds with Extreme Scale and Density Diversity](https://mlsanity.com/paper/1705.00949/) (2017)
- [CAD-PU: A Curvature-Adaptive Deep Learning Solution for Point Set Upsampling](https://mlsanity.com/paper/2009.04660/) (2020)

## Built on by (most cited first, 16 of 16)

- [Grad-PU: Arbitrary-Scale Point Cloud Upsampling via Gradient Descent with Learned Distance Functions](https://mlsanity.com/paper/2304.11846/) (2023)
- [A Conditional Denoising Diffusion Probabilistic Model for Point Cloud Upsampling](https://mlsanity.com/paper/2312.02719/) (2023)
- [Learning Continuous Implicit Field with Local Distance Indicator for Arbitrary-Scale Point Cloud Upsampling](https://mlsanity.com/paper/2312.15133/) (2023)
- [Point Cloud Upsampling via Cascaded Refinement Network](https://mlsanity.com/paper/2210.03942/) (2022)
- [PointNSP: Autoregressive 3D Point Cloud Generation with Next-Scale Level-of-Detail Prediction](https://mlsanity.com/paper/2510.05613/) (2025)
- [GET-UP: GEomeTric-aware Depth Estimation with Radar Points UPsampling](https://mlsanity.com/paper/2409.02720/) (2024)
- [Arbitrary Point Cloud Upsampling with Spherical Mixture of Gaussians](https://mlsanity.com/paper/2208.05274/) (2022)
- [Arbitrary-Scale Point Cloud Upsampling by Voxel-Based Network with Latent Geometric-Consistent Learning](https://mlsanity.com/paper/2403.05117/) (2024)
- [Deep Learning for 3D Point Cloud Enhancement: A Survey](https://mlsanity.com/paper/2411.00857/) (2024)
- [Joint Point Cloud Upsampling and Cleaning with Octree-based CNNs](https://mlsanity.com/paper/2410.17001/) (2024)
- [PU-MFA : Point Cloud Up-sampling via Multi-scale Features Attention](https://mlsanity.com/paper/2208.10968/) (2022)
- [MBPU: A Plug-and-Play State Space Model for Point Cloud Upsamping with Fast Point Rendering](https://mlsanity.com/paper/2410.15941/) (2024)
- [Representation Learning of Point Cloud Upsampling in Global and Local Inputs](https://mlsanity.com/paper/2501.07076/) (2025)
- [PU-Gaussian: Point Cloud Upsampling using 3D Gaussian Representation](https://mlsanity.com/paper/2509.20207/) (2025)
- [PointNSP: Autoregressive 3D Point Cloud Generation with Next-Scale Level-of-Detail Prediction](https://mlsanity.com/paper/2503.08594/) (2025)
- [Preserving Topological and Geometric Embeddings for Point Cloud Recovery](https://mlsanity.com/paper/2507.19121/) (2025)

## Abstract (arXiv)

High-quality point clouds have practical significance for point-based rendering, semantic understanding, and surface reconstruction. Upsampling sparse, noisy and nonuniform point clouds for a denser and more regular approximation of target objects is a desirable but challenging task. Most existing methods duplicate point features for upsampling, constraining the upsampling scales at a fixed rate. In this work, the flexible upsampling rates are achieved via edge vector based affine combinations, and a novel design of Edge Vector based Approximation for Flexible-scale Point clouds Upsampling (PU-EVA) is proposed. The edge vector based approximation encodes the neighboring connectivity via affine combinations based on edge vectors, and restricts the approximation error within the second-order term of Taylor's Expansion. The EVA upsampling decouples the upsampling scales with network architecture, achieving the flexible upsampling rates in one-time training. Qualitative and quantitative evaluations demonstrate that the proposed PU-EVA outperforms the state-of-the-art in terms of proximity-to-surface, distribution uniformity, and geometric details preservation.