  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.
