Surface parameterization is a fundamental geometry processing problem with rich downstream applications. Traditional approaches are designed to operate on well-behaved mesh models with high-quality triangulations that are laboriously produced by specialized 3D modelers, and thus unable to meet the processing demand for the current explosion of ordinary 3D data. In this paper, we seek to perform UV unwrapping on unstructured 3D point clouds. Technically, we propose ParaPoint, an unsupervised neural learning pipeline for achieving global free-boundary surface parameterization by building point-wise mappings between given 3D points and 2D UV coordinates with adaptively deformed boundaries. We ingeniously construct several geometrically meaningful sub-networks with specific functionalities, and assemble them into a bi-directional cycle mapping framework. We also design effective loss functions and auxiliary differential geometric constraints for the optimization of the neural mapping process. To the best of our knowledge, this work makes the first attempt to investigate neural point cloud parameterization that pursues both global mappings and free boundaries. Experiments demonstrate the effectiveness and inspiring potential of our proposed learning paradigm. The code will be publicly available.

翻译：曲面参数化是一个基础的几何处理问题，具有丰富的下游应用。传统方法设计用于处理具有高质量三角剖分的良好网格模型，这些模型由专业的三维建模者精心制作，因此无法满足当前普通三维数据爆炸式增长的处理需求。在本文中，我们尝试对非结构化的三维点云进行UV展开。技术上，我们提出了ParaPoint，一种无监督的神经学习流水线，通过构建给定三维点与二维UV坐标之间的逐点映射（并带有自适应变形边界），实现全局自由边界曲面参数化。我们巧妙构建了多个具有特定功能的几何上有意义的子网络，并将其组装成一个双向循环映射框架。我们还设计了有效的损失函数和辅助微分几何约束，以优化神经映射过程。据我们所知，这项工作首次尝试研究追求全局映射和自由边界的神经点云参数化。实验证明了我们提出的学习范式的有效性和鼓舞人心的潜力。代码将公开提供。