Flatten Anything：无监督神经曲面参数化
Flatten Anything: Unsupervised Neural Surface Parameterization
AI总结：
本文提出无监督神经模型FAM，通过双向循环映射和可解释子网络学习3D点到自适应UV坐标的映射，实现无需预切割、支持点云和复杂拓扑的自动曲面参数化。
摘要：
曲面参数化在众多计算机图形学和几何处理应用中发挥着重要作用。传统参数化方法是为专业3D建模师精心创建的高质量网格设计的，因此无法满足当前海量普通3D数据的处理需求。此外，它们的工作机制通常局限于某些简单拓扑，因而依赖繁琐的人工操作（例如曲面切割、部件分割）进行预处理。本文提出 Flatten Anything Model（FAM），这是一种无监督神经架构，通过学习目标几何曲面上的3D点与二维参数域内自适应变形的UV坐标之间的逐点映射，实现全局自由边界曲面参数化。为模拟实际物理过程，我们巧妙构建了具有几何可解释性的子网络，分别承担曲面切割、UV变形、展开和包裹的特定功能，并将其组合成双向循环映射框架。与以往方法相比，FAM直接作用于离散曲面点，无需利用连接性信息，因此显著降低了对网格质量的严格要求，甚至适用于非结构化点云数据。更重要的是，FAM完全自动化，无需预切割，并能够处理高度复杂的拓扑，因为其学习过程会自适应地找到合理的切割缝和UV边界。大量实验证明了我们提出的神经曲面参数化范式的通用性、优越性和令人鼓舞的潜力。代码位于 https://github.com/keeganhk/FlattenAnything。
英文摘要：
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. Our code is available at https://github.com/keeganhk/FlattenAnything.
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