Surface Simpliﬁcation Using Quadric Error Metrics

By F. Baumann. 2018

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Citations in the corpus

Generating 3D faces using Convolutional Mesh Autoencoders (2018, methodology): “The down-sampling is obtained by contracting vertex pairs iteratively that maintain surface error approximations using quadric matrices [20].”
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence (2017, methodology): “For increased efﬁciency, we down-sample the input shapes to 15K vertices by edge contraction [19]; in case the input mesh has a smaller amount of vertices, it is kept at full resolution.”
Articulation-Aware Canonical Surface Mapping (2020, methodology): “They have been pre-processed to have 642 vertices and 1280 faces using Meshlab’s [6] quadratic vertex decimation [11].”
SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering (2023, methodology): “We perform Poisson reconstruction with depth 10 and apply mesh simpliﬁcation using quadric error metrics [9] to decrease the resolution of the meshes.”
ABC: A Big CAD Model Dataset for Geometric Deep Learning (2018, methodology): “We provide tools to ﬁlter our meshes depending on quality or number of patches, to compute mesh statistics, and to resample the generated surfaces to match a desired number of vertices [25].”
Learning to Dress 3D People in Generative Clothing (2019, unknown): “Most relevant here, Ranjan et al. [41] learn a convolutional autoencoder using graph convolutions [11] with mesh down-and up-sampling layers [13].”
CNN-GCN Aggregation Enabled Boundary Regression for Biomedical Image Segmentation (2020, methodology): “Q d is obtained by iteratively contracting vertex pairs, which uses a quadratic matrix to maintain surface error approximations [9].”
Weakly-Supervised Mesh-Convolutional Hand Reconstruction in the Wild (2020, methodology): “We contract vertex pairs based on quadric error metrics [15] that allow the coarse vertices to be a subset of the denser mesh.”
Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes (2021, methodology): “Classic methods [15, 20] do this by greedily removing mesh elements with the smallest impact on geometric accuracy.”