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arXiv · 2403.12870

PoNQ: a Neural QEM-based Mesh Representation

Nissim Maruani·Maks Ovsjanikov·Pierre Alliez·Mathieu Desbrun
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Abstract

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.

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Nissim Maruani, Maks Ovsjanikov, Pierre Alliez, Mathieu Desbrun. 2024-03-19. PoNQ: a Neural QEM-based Mesh Representation. https://arxiv.org/abs/2403.12870

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