Point cloud synthesis, i.e. the generation of novel point clouds from an input distribution, remains a challenging task, for which numerous complex machine learning models have been devised. We develop a novel method that encodes geometrical-topological characteristics of point clouds using inner products, leading to a highly-efficient point cloud representation with provable expressivity properties. Integrated into deep learning models, our encoding exhibits high quality in typical tasks like reconstruction, generation, and interpolation, with inference times orders of magnitude faster than existing methods.

翻译：点云合成，即从输入分布中生成新颖点云，仍是一项具有挑战性的任务，为此已设计出众多复杂的机器学习模型。我们提出了一种新方法，该方法利用内积对点云的几何-拓扑特征进行编码，从而得到一种具有可证明表达能力的高效点云表示。将我们的编码集成到深度学习模型中，在重建、生成和插值等典型任务中表现出高质量，且推理时间比现有方法快数个数量级。