Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

通过本文，我们引入了一种新型的可学习网格表示方法，通过一组局部三维样本点、法线和二次误差度量（QEM）相对于底层形状的获取，我们将其称为PoNQ。我们通过高效地利用局部二次误差的知识，直接从PoNQ中获取全局网格，并确保了拓扑和几何特性，使PoNQ网格不自相交且始终是一个边界体积。值得注意的是，我们的表示方法不依赖于正规网格，仅由目标表面进行监督，并且还能处理具有边界和/或锐利特征的开放表面。通过从SDF网格进行基于学习的网格预测，我们展示了PoNQ的有效性，并且在表面和边缘相关指标上超过了最近研究中的先进技术。

PoNQ: 基于神经量化嵌网的网格表示