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.

翻译：近年来，神经网络已成为大多数点云上采样方法中的主导模型。尽管这些方法取得了良好效果，但存在可解释性不足和数据依赖性等缺陷。此外，它们必须在与测试数据相似的数据集上训练才能表现良好。为避免这些缺点，我们提出基于面片频率叠加的点云上采样方法（PUtPFS）——一种基于优化的方法，通过选取点子集并利用空间频率叠加技术估计该子集的曲面，继而在该曲面上生成新点。通过逐步选取点云中最稀疏区域的点，可实现均匀上采样。该方法在通用点面距离指标上超越当前最优上采样结果，同时在基于优化的方法中取得最佳Chamfer距离和Hausdorff距离。作为额外优势，本方法无需任何训练数据且具有数学可解释性。