Recent advances in learning 3D shapes using neural implicit functions have achieved impressive results by breaking the previous barrier of resolution and diversity for varying topologies. However, most of such approaches are limited to closed surfaces as they require the space to be divided into inside and outside. More recent works based on unsigned distance function have been proposed to handle complex geometry containing both the open and closed surfaces. Nonetheless, as their direct outputs are point clouds, robustly obtaining high-quality meshing results from discrete points remains an open question. We present a novel learnable implicit representation, called the three-pole signed distance function (3PSDF), that can represent non-watertight 3D shapes with arbitrary topologies while supporting easy field-to-mesh conversion using the classic Marching Cubes algorithm. The key to our method is the introduction of a new sign, the NULL sign, in addition to the conventional in and out labels. The existence of the null sign could stop the formation of a closed isosurface derived from the bisector of the in/out regions. Further, we propose a dedicated learning framework to effectively learn 3PSDF without worrying about the vanishing gradient due to the null labels. Experimental results show that our approach outperforms the previous state-of-the-art methods in a wide range of benchmarks both quantitatively and qualitatively.

本文介绍了一种新的可学习的内隐表示方法称为三极符号距离函数（3PSDF），可以表示任意拓扑的非水密3D形状并使用经典的Marching Cubes算法进行易于场-网格转换。该方法引入了新符号NULL符号，支持处理开放的几何体表面。实验结果表明，该方法在定量和定性评估中都胜过以前的最先进方法。

3PSDF: 三极符号距离函数用于学习具有任意拓扑结构的表面