# Arbitrary Point Cloud Upsampling with Spherical Mixture of Gaussians

arXiv: https://arxiv.org/abs/2208.05274 · HTML: https://mlsanity.com/paper/2208.05274/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 41 references that are in the map.
- First posted on arXiv 10 Aug 2022.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (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)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [An End-to-End Transformer Model for 3D Object Detection](https://mlsanity.com/paper/2109.08141/) (2021)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [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)
- [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)
- [LCDNet: Deep Loop Closure Detection and Point Cloud Registration for LiDAR SLAM](https://mlsanity.com/paper/2103.05056/) (2021)
- [Neural Points: Point Cloud Representation with Neural Fields for Arbitrary Upsampling](https://mlsanity.com/paper/2112.04148/) (2021)
- [Self-Supervised Pillar Motion Learning for Autonomous Driving](https://mlsanity.com/paper/2104.08683/) (2021)
- [Meta-PU: An Arbitrary-Scale Upsampling Network for Point Cloud](https://mlsanity.com/paper/2102.04317/) (2021)
- [PU-Transformer: Point Cloud Upsampling Transformer](https://mlsanity.com/paper/2111.12242/) (2021)
- [Deep Magnification-Flexible Upsampling over 3D Point Clouds](https://mlsanity.com/paper/2011.12745/) (2020)
- [Cloud Transformers: A Universal Approach To Point Cloud Processing Tasks](https://mlsanity.com/paper/2007.11679/) (2020)
- [TearingNet: Point Cloud Autoencoder to Learn Topology-Friendly Representations](https://mlsanity.com/paper/2006.10187/) (2020)
- [Learning 3D Dense Correspondence via Canonical Point Autoencoder](https://mlsanity.com/paper/2107.04867/) (2021)

## Built on by (most cited first, 6 of 6)

- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Learning Continuous Implicit Field with Local Distance Indicator for Arbitrary-Scale Point Cloud Upsampling](https://mlsanity.com/paper/2312.15133/) (2023)
- [iPUNet:Iterative Cross Field Guided Point Cloud Upsampling](https://mlsanity.com/paper/2310.09092/) (2023)
- [Deep Learning for 3D Point Cloud Enhancement: A Survey](https://mlsanity.com/paper/2411.00857/) (2024)
- [ModelNet-O: A Large-Scale Synthetic Dataset for Occlusion-Aware Point Cloud Classification](https://mlsanity.com/paper/2401.08210/) (2024)
- [PU-Gaussian: Point Cloud Upsampling using 3D Gaussian Representation](https://mlsanity.com/paper/2509.20207/) (2025)

## Abstract (arXiv)

Generating dense point clouds from sparse raw data benefits downstream 3D understanding tasks, but existing models are limited to a fixed upsampling ratio or to a short range of integer values. In this paper, we present APU-SMOG, a Transformer-based model for Arbitrary Point cloud Upsampling (APU). The sparse input is firstly mapped to a Spherical Mixture of Gaussians (SMOG) distribution, from which an arbitrary number of points can be sampled. Then, these samples are fed as queries to the Transformer decoder, which maps them back to the target surface. Extensive qualitative and quantitative evaluations show that APU-SMOG outperforms state-of-the-art fixed-ratio methods, while effectively enabling upsampling with any scaling factor, including non-integer values, with a single trained model. The code is available at https://github.com/apusmog/apusmog/