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Recent advances in learning 3D shapes using neural implicit functions haveachieved impressive results by breaking the previous barrier of resolution anddiversity for varying topologies. However, most of such approaches are limitedto closed surfaces as they require the space to be divided into inside andoutside. More recent works based on unsigned distance function have beenproposed to handle complex geometry containing both the open and closedsurfaces. Nonetheless, as their direct outputs are point clouds, robustlyobtaining high-quality meshing results from discrete points remains an openquestion. We present a novel learnable implicit representation, called thethree-pole signed distance function (3PSDF), that can represent non-watertight3D shapes with arbitrary topologies while supporting easy field-to-meshconversion using the classic Marching Cubes algorithm. The key to our method isthe introduction of a new sign, the NULL sign, in addition to the conventionalin and out labels. The existence of the null sign could stop the formation of aclosed isosurface derived from the bisector of the in/out regions. Further, wepropose a dedicated learning framework to effectively learn 3PSDF withoutworrying about the vanishing gradient due to the null labels. Experimentalresults show that our approach outperforms the previous state-of-the-artmethods in a wide range of benchmarks both quantitatively and qualitatively.

3PSDF: Three-Pole Signed Distance Function for Learning Surfaces with Arbitrary Topologies