A Structure-Aware Triangular Mesh Simplification Based on Graph Neural Network (GNN)-Guided Quadric Error Metrics (QEM)

Triangular mesh is one of the most widely used representations for 3D surfaces. However, high-resolution mesh models often contain a large number of triangles, leading to significant burdens in storage, transmission, and real-time rendering. Mesh simplification aims to reduce model complexity while preserving geometric fidelity and structural features. Classical methods, such as quadric error metrics (QEM), rely solely on local geometric errors, making them difficult to distinguish between redundant regions and structurally important features, often resulting in feature loss and topological degradation. To address these limitations, this study proposes a structure-aware triangular mesh simplification framework based on graph neural networks (GNNs)-guided QEM. GNNs are employed as a structural importance estimator to predict geometric saliencies of mesh edges. The predicted importances are incorporated into the classical QEM edge collapse cost through a soft modulation mechanism. Furthermore, a geometry-saliency-driven dynamic cost modulation strategy is designed, enabling the simplification process to prioritize critical features in early stages and gradually transition to global error minimization in later stages, without compromising the geometric optimality of QEM. In terms of model design, hybrid structural representation GNNs are constructed by integrating spectral geometry and a dual-branch architecture. Laplacian positional encoding is introduced to capture global topological information, while 1-hop and 2-hop message passing branches enable multi-scale representation of complex geometric structures. In addition, a staged inference strategy is adopted to dynamically update graph structural features during simplification, effectively mitigating topological drift. Experimental results on the TOSCA dataset demonstrate that the proposed method achieves stable performance across various simplification ratios. It consistently outperforms FQMS and QEM in terms of geometric error (\({P_{CD}}\)) and normal consistency (\({P_{NE}}\)). For structural preservation (\({P_{LE}}\)), the method shows advantages, with win-rates generally exceeding 90%. Moreover, it significantly improves the preservation of local geometric details at low to moderate simplification ratios. In summary, the proposed method effectively enhances local structural preservation while maintaining global geometric topology, providing an interpretable and practical solution for integrating learning-based structural awareness with classical geometric optimization in mesh simplification.