Research map / 3D vision / Face and shape
PoNQ: a Neural QEM-based Mesh Representation
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Introduces PoNQ, a learnable mesh representation of points, normals and QEM matrices from which watertight, self-intersection-free meshes are extracted via Delaunay tetrahedralization and graph-cut tagging, evaluated on SDF-to-mesh reconstruction.
Problem
Learning-based mesh prediction needs representations that capture sharp features and thin structures while guaranteeing watertight, non-self-intersecting output meshes; existing explicit and implicit methods lack these properties or rely on regular grids.
Approach
Represent a shape by a set of learned points, each with an averaged normal and a QEM matrix encoding local tangent-plane geometry; extract the mesh from the QEM-optimal vertices using Delaunay tetrahedralization with inside/outside tagging (circumcenter criterion plus min-cut), so output is watertight and intersection-free by design.
Key results
- On ABC at 643 resolution, PoNQ reaches CD 0.886e-5 and NC 0.980 versus VoroMesh's 1.219e-5 and 0.966, with 100% watertight, intersection-free outputs.
- On Thingi30 at 1283, PoNQ achieves ECD 0.123 and EF1 0.592 while NMC and NDC are not watertight (0% and 0%).
- PoNQ-lite (single QEM per cell) outperforms NDC at equal element count on ABC, e.g., CD 1.514 vs 66.004 at 323 for PoNQ vs NDC.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PoNQ instead of the strongest baseline for surface reconstruction from SDF | ABC reconstruction model · ABC | CD: 1.069 -> 0.920 (×10−5) | Helped |
| Use PoNQ instead of the strongest baseline for edge reconstruction from SDF | ABC reconstruction model · ABC | ECD: 0.095 -> 0.191 | Hurt |
| Use PoNQ instead of the strongest baseline for edge F-score | ABC reconstruction model · ABC | EF1: 0.947 -> 0.878 | Hurt |
| Use PoNQ instead of NMC for surface reconstruction | Thingi30 reconstruction model · Thingi30 | CD: 0.642 -> 0.641 (×10−5) | Helped |
| Use PoNQ instead of PoNQ-lite (four predicted points per cell rather than one pooled point) (ablation) | PoNQ · Thingi30 | ECD: 0.055 -> 0.123 | Hurt |
| Use PoNQ instead of PoNQ-lite (four predicted points per cell rather than one pooled point) (ablation) | PoNQ · Thingi30 | EF1: 0.699 -> 0.592 | Hurt |
| Use four predicted points per cell instead of pooling to one PoNQ-lite point (ablation) | PoNQ · ABC | ECD: 0.043 -> 0.191 | Hurt |
| Use four predicted points per cell instead of pooling to one PoNQ-lite point (ablation) | PoNQ · ABC | EF1: 0.933 -> 0.878 | Hurt |
| Remove the image-based loss from DPF training | DPF · Thingi30 optimization | CD: 0.644 -> 0.644 | No clear effect |
| Remove the image-based loss from DPF training | DPF · Thingi30 optimization | optimization time: 71.0 -> 17.7 s | Helped |
Surprising findings
- VoroMesh has the best raw surface-fitting scores (CD) at low resolutions in optimization tests, while PoNQ wins on normal consistency and sharp-edge metrics.
- PoNQ-lite slightly beats full PoNQ on ECD and EF1 on Thingi30 at 1283 resolution.
Limitations
- Meshing of open boundaries relies on a score-based triangle culling step that can be brittle.
- PoNQ extraction may create non-manifold vertices or edges despite being watertight.
- Boundary variant cannot handle special cases like a single square sheet and no longer bounds a volume.
Experimental setup
Datasets: ABC Thingi10k Thingi30
Benchmarks: ABC Thingi30
Metrics: chamfer distance F1 score normal consistency edge chamfer distance edge F1 watertightness number of vertices and faces
Baselines: NMC NDC VoroMesh SAP DPF DPFchamfer
Builds on: NDC VoroMesh Crust Garland-Heckbert QEM
Closest papers by meaning
- PolyGen: An Autoregressive Generative Model of 3D Meshes (ICML 2020 · similarity 0.87)
- Neural Parts: Learning Expressive 3D Shape Abstractions With Invertible Neural Networks (CVPR 2021 · similarity 0.87)
- Polyhedral Complex Derivation from Piecewise Trilinear Networks (NeurIPS 2024 · similarity 0.86)
- MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers (CVPR 2024 · similarity 0.86)
- Flatten Anything: Unsupervised Neural Surface Parameterization (NeurIPS 2024 · similarity 0.86)
- CoFie: Learning Compact Neural Surface Representations with Coordinate Fields (NeurIPS 2024 · similarity 0.85)
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