Research map / 3D vision / Face and shape
DMesh: A Differentiable Mesh Representation
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Proposes DMesh, a differentiable representation of general 3D triangle meshes built on differentiable weighted Delaunay triangulation, enabling gradient-based optimization of both geometry and connectivity.
Problem
Existing differentiable mesh methods fix topology or rely on iso-surface extraction producing dense meshes; a differentiable representation that handles varying topology and connectivity is lacking.
Approach
Select triangular faces from a weighted Delaunay triangulation of weighted points and define each face's existence probability differentiably via power diagram distances (dual-form to reduced power cell signed distance) times a per-point real-value term, extending a 2D differentiable WDT to 3D with near-linear cost.
Key results
- Mesh-to-DMesh conversion recovers 99.78% (Bunny), 99.72% (Dragon), 99.64% (Buddha) of faces with 0.00-0.84% false positives.
- Point cloud reconstruction with normals achieves CD 3.364e-5, F1 0.886, NC 0.952 with 3.56K vertices, versus PSR at CD 690e-5 and 159K vertices.
- Multi-view reconstruction achieves CD 34.6e-5 and F1 0.685 vs FlexiCube CD 273e-5 and F1 0.591, with 4.19K vertices; the WDT probability computation scales near-linearly, versus quadratic for prior method.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use point normals during point-cloud reconstruction (ablation) | DMesh · Point cloud reconstruction (11-model average) | CD (× 10^-5): 3.726 -> 3.364 | Helped |
| Use point normals during point-cloud reconstruction (ablation) | DMesh · Point cloud reconstruction (11-model average) | F1: 0.866 -> 0.886 | Helped |
| Use point normals during point-cloud reconstruction (ablation) | DMesh · Point cloud reconstruction (11-model average) | ECD: 0.067 -> 0.141 | Hurt |
| Use point normals during point-cloud reconstruction (ablation) | DMesh · Point cloud reconstruction (11-model average) | EF1: 0.342 -> 0.438 | Helped |
| Use point normals during point-cloud reconstruction (ablation) | DMesh · Point cloud reconstruction (11-model average) | # Verts: 3.87K -> 3.56K | Helped |
| Use point normals during point-cloud reconstruction (ablation) | DMesh · Point cloud reconstruction (11-model average) | Time (sec): 775 -> 743 | Helped |
| Use point normals during point-cloud reconstruction (ablation) | DMesh · Point cloud reconstruction (11-model average) | NC: 0.936 -> 0.952 | Helped |
| Use DMesh rather than the strongest listed baseline | DMesh · Point cloud reconstruction (11-model average) | CD (× 10^-5): 3.611 -> 3.364 | Helped |
| Use DMesh rather than the strongest listed baseline | DMesh · Point cloud reconstruction (11-model average) | ECD: 0.022 -> 0.141 | Hurt |
| Use DMesh rather than the strongest listed baseline | DMesh · Multi-view reconstruction (11-model average) | CD (× 10^-5): 273 -> 34.6 | Helped |
| Use DMesh rather than the strongest listed baseline | DMesh · Multi-view reconstruction (11-model average) | ECD: 0.039 -> 0.094 | Hurt |
| Use DMesh rather than the strongest listed baseline | DMesh · Multi-view reconstruction (11-model average) | # Verts: 10.9K -> 4.19K | Helped |
Surprising findings
- Non-manifold edges are prevalent: 5.50% of edges for point cloud and 6.62% for multi-view reconstruction.
- Edge-quality metrics (ECD, EF1) are weaker than baselines such as NDC and FlexiCubes despite better mesh compactness.
Limitations
- Resolution limited by WDT construction cost; meshes over 100K vertices are challenging.
- Non-manifold edges and vertices appear in outputs, and ECD/EF1 edge quality lags baselines.
- Mesh-level fine detail is weaker than volumetric approaches for closed surfaces.
Experimental setup
Datasets: Stanford 3D Scanning Repository Thingi32 DeepFashion3D Objaverse Adobe Stock
Benchmarks: Stanford Bunny Dragon Buddha Thingi32 DeepFashion3D Objaverse Adobe Stock
Metrics: Chamfer Distance F1 normal consistency edge chamfer distance edge F1 recovery ratio false positive ratio number of vertices and faces time
Baselines: Screened Poisson Surface Reconstruction VoroMesh Neural Dual Contouring FlexiCubes Neural Implicit Evolution
Builds on: Rakotosaona et al. 2021 differentiable WDT reduced power cell Chamfer distance FlexiCubes
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