ParaPoint: Learning Global Free-Boundary Surface Parameterization of 3D Point Clouds

TL;DR

ParaPoint tackles UV unwrapping of unstructured 3D point clouds by learning a global, free-boundary surface parameterization without meshes. It introduces a bi-directional cycle mapping framework built from five interpretable sub-networks (Deform-Net, Cut-Net, Stitch-Net, Wrap-Net, Unwrap-Net) and optimized with losses including unwrapping, wrapping (Chamfer), cycle consistency, and differential geometric constraints (conformal/isometric) plus anti-flipping. The method automatically discovers cutting seams and adaptively deforms the 2D UV domain to minimize distortion, enabling smooth per-point UVs and texture mapping directly on point clouds. This neural parameterization approach broadens UV mapping capabilities beyond traditional mesh-based pipelines, reducing preprocessing and enabling flexible texture applications on diverse 3D data.

Abstract

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.

Figures (8)

• Figure 1: Illustration of the bi-directional cycle mapping pipeline, which is composed of (a) the 3D$\rightarrow$2D$\rightarrow$3D cycle mapping branch, and (b) the 2D$\rightarrow$3D$\rightarrow$2D cycle mapping branch. The input is an unoriented 3D point cloud containing $4096$ points. (c) visualizes the corresponding texture mapping. (d) shows the learned cutting seams. The colors of 2D UV coordinates $\mathbf{Q}$, $\hat{\mathbf{Q}}$, and $\hat{\mathbf{Q}}_\mathrm{cycle}$ represent point-wise normal directions.
• Figure 2: Display of various selected testing shapes, where we also present the mesh edges to facilitate showing the shape structure. Note that the inputs to our approach are only 3D point coordinates (without normals) sampled from the target surfaces.
• Figure 3: Illustration of neural parameterization results produced by ParaPoint. (a) Input 3D point cloud; (b) 2D UV coordinates; (c) Texture mapping from the checkerboard; (d) The automatically learned cutting seams (points marked in green).
• Figure 4: Neural parameterization for complex 3D shapes, where the weight for the $\ell_\mathrm{conf}$ is decreased from the default $1e^{-2}$ to $1e^{-4}$ for relaxing the conformal constraint.
• Figure 5: Ablation results in terms of distortion optimization objectives and bi-directional mapping branches. (a) and (b) compare the effects of constraining conformal and isometric losses. (c) and (d) show the UV unwrapping results of the "eight" model produced by only preserving the 2D$\rightarrow$3D$\rightarrow$2D branch and the 3D$\rightarrow$2D$\rightarrow$3D branch, respectively.