PoNQ: a Neural QEM-based Mesh Representation
<|reference_start|>PoNQ: a Neural QEM-based Mesh Representation: 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.<|reference_end|>
@article{maruani2024ponq:,
    title={PoNQ: a Neural QEM-based Mesh Representation},
    author={Nissim Maruani, Maks Ovsjanikov, Pierre Alliez, Mathieu Desbrun},
    journal={arXiv preprint arXiv:2403.12870},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.12870},
    primaryClass={cs.CV}
}