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.

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