Surface parameterization plays an essential role in numerous computer
graphics and geometry processing applications. Traditional parameterization
approaches are designed for high-quality meshes laboriously created by
specialized 3D modelers, thus unable to meet the processing demand for the
current explosion of ordinary 3D data. Moreover, their working mechanisms are
typically restricted to certain simple topologies, thus relying on cumbersome
manual efforts (e.g., surface cutting, part segmentation) for pre-processing.
In this paper, we introduce the Flatten Anything Model (FAM), an unsupervised
neural architecture to achieve global free-boundary surface parameterization
via learning point-wise mappings between 3D points on the target geometric
surface and adaptively-deformed UV coordinates within the 2D parameter domain.
To mimic the actual physical procedures, we ingeniously construct
geometrically-interpretable sub-networks with specific functionalities of
surface cutting, UV deforming, unwrapping, and wrapping, which are assembled
into a bi-directional cycle mapping framework. Compared with previous methods,
our FAM directly operates on discrete surface points without utilizing
connectivity information, thus significantly reducing the strict requirements
for mesh quality and even applicable to unstructured point cloud data. More
importantly, our FAM is fully-automated without the need for pre-cutting and
can deal with highly-complex topologies, since its learning process adaptively
finds reasonable cutting seams and UV boundaries. Extensive experiments
demonstrate the universality, superiority, and inspiring potential of our
proposed neural surface parameterization paradigm. The code will be publicly
available.

通过学习目标几何表面上的三维点与二维参数域内的自适应变形的 UV 坐标之间的逐点映射，我们引入了全局自由边界表面参数化的非监督神经网络架构 (称为 Flatten Anything Model - FAM)。与先前的方法相比，在不利用连接信息的情况下，FAM 基于离散表面点直接操作，从而显著降低了对网格质量的严格要求，甚至适用于无结构点云数据。此外，FAM 是全自动的，无需预切割，并且能处理高度复杂的拓扑结构，因为其学习过程能自适应找到合理的切割接缝和 UV 边界。广泛的实验证明了我们提出的神经表面参数化范式的普适性、优越性和激发潜力。

将任何东西展平：无监督神经表面参数化

Flatten Anything: Unsupervised Neural Surface Parameterization

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.

本文提出了 ParaPoint，一种无监督的神经学习管道，通过在不规则的三维点云上建立 3D 点与 2D UV 坐标之间的点对点映射，实现全局自由边界表面参数化。我们构建了几个具有特定功能的几何意义的子网络，并将它们组装成双向循环映射框架。通过设计有效的损失函数和辅助微分几何约束，优化了神经映射过程。实验证明了我们提出的学习范式的有效性和激发潜力。