Point Cloud Upsampling through Patch-based Frequency Superposition

2026-06-12

AI Summary

Existing neural network–based point cloud upsampling methods suffer from poor interpretability, strong dependence on training data, and limited generalization. This work proposes a training-free optimization framework that, for the first time, introduces the concept of spatial frequency superposition to point cloud upsampling. By adaptively selecting local point patches in sparse regions and reconstructing local surfaces through frequency superposition, the method generates new points on these reconstructed surfaces to achieve uniform upsampling. An iterative density equalization strategy is further integrated to significantly enhance point distribution uniformity. The proposed approach outperforms state-of-the-art methods in terms of point-to-surface distance and achieves the best performance among optimization-based techniques on both Chamfer and Hausdorff distance metrics, offering strong mathematical interpretability and complete independence from training data.

Abstract

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.

Problem

• point cloud upsampling
• interpretability
• data dependency
• optimization-based approach

Innovation

• point cloud upsampling
• frequency superposition
• optimization-based
• data-free
• surface reconstruction