PoNQ: a Neural QEM-based Mesh Representation
Authors: Nissim Maruani, Maks Ovsjanikov, Pierre Alliez, Mathieu Desbrun

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.