Neural implicit representations are known to be more compact for depicting 3D shapes than traditional discrete representations. However, the neural representations tend to round sharp corners or edges and struggle to represent surfaces with open boundaries. Moreover, they are slow to train. We present a unified neural implicit representation, called Patch-Grid, that fits to complex shapes efficiently, preserves sharp features, and effectively models surfaces with open boundaries and thin geometric features. Our superior efficiency comes from embedding each surface patch into a local latent volume and decoding it using a shared MLP decoder, which is pretrained on various local surface geometries. With this pretrained decoder fixed, fitting novel shapes and local shape updates can be done efficiently. The faithful preservation of sharp features is enabled by adopting a novel merge grid to perform local constructive solid geometry (CSG) combinations of surface patches in the cells of an adaptive Octree, yielding better robustness than using a global CSG construction as proposed in the literature. Experiments show that our Patch-Grid method faithfully captures shapes with complex sharp features, open boundaries and thin structures, and outperforms existing learning-based methods in both efficiency and quality for surface fitting and local shape updates.

翻译：神经隐式表示在描述三维形状时比传统离散表示更为紧凑。然而，神经表示往往会使尖角或边缘变得圆滑，且难以表示具有开放边界的曲面。此外，其训练速度较慢。我们提出一种统一的神经隐式表示——基于面片的网格（Patch-Grid），它能够高效拟合复杂形状、保留尖锐特征，并有效建模具有开放边界和薄几何特征的曲面。我们的高效性源于将每个曲面面片嵌入局部隐空间，并利用预训练于多种局部曲面几何的共享多层感知机解码器进行解码。在固定该预训练解码器后，拟合新形状和局部形状更新可高效完成。通过采用新型合并网格在自适应八叉树的单元中进行局部构造实体几何组合，实现了对尖锐特征的忠实保留，其鲁棒性优于文献中提出的全局构造实体几何方法。实验表明，我们的基于面片的网格方法能够忠实捕获具有复杂尖锐特征、开放边界和薄结构的形状，在曲面拟合和局部形状更新的效率与质量上均优于现有基于学习的方法。