# Point Cloud Upsampling through Patch-based Frequency Superposition

arXiv: https://arxiv.org/abs/2606.14355 · HTML: https://mlsanity.com/paper/2606.14355/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 8 of 8)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (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)
- [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)
- [SPU-Net: Self-Supervised Point Cloud Upsampling by Coarse-to-Fine Reconstruction with Self-Projection Optimization](https://mlsanity.com/paper/2012.04439/) (2020)
- [Resampling Images to a Regular Grid from a Non-Regular Subset of Pixel Positions Using Frequency Selective Reconstruction](https://mlsanity.com/paper/2204.12873/) (2022)
- [Frequency-Selective Geometry Upsampling of Point Clouds](https://mlsanity.com/paper/2205.01458/) (2022)

## Abstract (arXiv)

In recent years, neural networks have become the dominant models in most point cloud upsampling methods. Although these approaches are achieving good results, they do have drawbacks, such as a lack of interpretability and data dependency. Moreover, they have to be trained on a dataset that is similar to the test data in order to perform well. To avoid these disadvantages, we propose Point Cloud Upsampling through Patch-based Frequency Superposition (PUtPFS), an optimization-based approach that selects subsets of points and estimates the surface of this set through superpositioning spatial frequencies. Then, new points are placed on this surface. By successively selecting points in the least dense regions of the point cloud, a uniform upsampling can be reached. With this method, we surpass the current best upsampling results in the commonly considered point-to-surface distance. Furthermore, we achieve the best Chamfer and Hausdorff distance among the optimization-based approaches. As an additional advantage, our method does not need any training data and is mathematically interpretable.