用分布建模几何，无需假设表面拓扑，可精准捕捉细粒度结构。
Geometry Distributions
- 将几何视为点分布，通过扩散模型学习表面点的生成规律。
- 在多种物体类型上实现高保真度重建，尤其擅长处理薄结构和非封闭面。
- 适用于纹理网格、表面压缩、动态建模等场景，适合3D生成与学习研究者。
基于坐标神经网络的3D数据表示已在多个应用中广泛采用，尤其用于建模标量或向量场。然而，这类方法在处理细长结构和非封闭几何时存在固有局限，限制了其灵活性与精度。本文提出一种新型几何表示方法，将几何建模为分布，该表示不依赖于表面的拓扑类型、连通性或边界条件。我们采用具有新颖网络架构的扩散模型，学习表面点的分布，从而捕捉精细几何细节。我们在多种物体类型上进行了定性和定量评估，验证了该表示在实现高几何保真度方面的有效性。此外，我们探索了该表示在纹理网格表示、神经表面压缩、动态物体建模及渲染等任务中的应用，展示了其在推进3D几何学习方面的潜力。
原文摘要 · Abstract (English)
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.
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