PoNQ: a Neural QEM-based Mesh Representation

1Inria, 2École polytechnique
CVPR 2024


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.

Application: Learning-based 3D Reconstruction from SDF grids

Input SDF

PoNQ (ours)

Marching Cubes

PoNQ is a learnable 3D representation. To demonstrate its potential, we applied PoNQ to surface reconstruction from Signed Distance Fields (SDF). Like in previous work, we trained a 3D CNN on the CAD shapes of the ABC dataset for this task. From a regular grid of SDF values, the networks predicts a PoNQ (consisting of Points, Normals, and Quadrics) from which a mesh can be extracted. With the same input resolution, PoNQ outperforms state-of-the-art methods and is able to reach finer details than the classical Marching Cubes algorithm.

Extension 1: Open Surfaces

The additional QEM information enables our method to recover the boundaries of open surfaces.

Extension 2: GPU-based Simplification





One can also construct, at nearly no cost, a whole hierarchy of PoNQ meshes by average pooling of predicted QEM information.


This work was supported by 3IA Côte d'Azur (ANR-19-P3IA-0002), ERC Starting Grant 758800 (EXPROTEA), ERC Consolidator Grant 101087347 (VEGA), ANR AI Chair AIGRETTE, Ansys, Adobe Research, and a Choose France Inria chair.