PointTriNet: Learned Triangulation of 3D Point Sets

Abstract

This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D learning pipelines. The method iteratively applies two neural networks to generate a triangulation: a classification network predicts whether a candidate triangle should appear in the triangulation, while a proposal network suggests additional candidates. Both networks are structured as PointNets over nearby points and triangles, using a novel triangle-relative input encoding. Since these learning problems operate on local geometric data, our method scales effectively to large input sets and unseen shape categories, and we can train the networks in an unsupervised manner from a collection of shapes represented as meshes or point clouds. We demonstrate the effectiveness of this approach for classical meshing tasks, robustness to outliers, and as a component in end-to-end learning systems.

Point2Skeleton: Learning Skeletal Representations from Point Clouds

“…Scan2Mesh [13] learns to explicitly generate vertices, edges and faces using graph neural networks. PointTriNet [33] explicitly learns the triangulation of a given point set to form the mesh.…”

Learning Delaunay Surface Elements for Mesh Reconstruction

“…Most closely related to ours are two very recent approaches aimed directly to address the point set triangulation problem. The first method PointTriNet [41] works on point clouds and, similarly to ours, uses a local patchbased network for predicting connectivity. However, this technique processes triangles independently and only promotes watertight and manifold structure through soft penalties.…”

“…In contrast to both of these approaches [41,33], we formulate the meshing problem as learning of (local) Delaunay triangulations. Starting from the restricted Voronoi diagram based formulation proposed in [10] we use data-driven priors to directly learn local projections to create local Delaunay patches.…”

“…PointTriNet [41] and IER meshing [33] We compare our method to two recent learning based methods for triangulating point clouds. We retrain PointTriNet on our dataset.…”

“…Most of such techniques focus on robustly predicting a signed distance field or simply an occupancy map, from which a mesh is subsequently extracted using volumetric triangulation [12,22,39]. Only two recent methods [41,33] produce a triangulation while respecting the original point set, but they ignore the quality of the triangles or have trouble reconstructing sharp features.…”