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TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes
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Proposes TetSphere splatting, a Lagrangian 3D shape representation that deforms collections of volumetric tetrahedral spheres under rendering loss plus bi-harmonic and non-inversion regularizers to get high-quality meshes.
Problem
Existing 3D geometry representations (Eulerian grids/neural fields and Lagrangian point clouds or surface triangles) produce poor mesh quality, with irregular triangles, non-manifoldness, and floating artifacts, which hinders downstream rendering and simulation.
Approach
Use a collection of volumetric tetrahedralized spheres as Lagrangian primitives, deformed by gradient descent under differentiable rendering loss, a bi-harmonic energy on the deformation gradient field, and a soft non-inversion penalty, so that volumetric connectivity enforces mesh regularity.
Key results
- Multi-view reconstruction: Ours achieves ALR 0.6602, manifoldness rate 100%, and CC Diff. 0.0, versus DMesh's ALR 0.1193 and MR 9.09%, while Vol. IoU reaches 0.6844 (best).
- Single-view GSO: Ours reaches Vol. IoU 0.6317 and ALR 0.3665 with CC Diff. 0.0, versus DreamGaussian's Vol. IoU 0.3476 and CC Diff. 237.4.
- Image-to-3D SDS: Ours fits batch size 120 on a 40GB A100 at 6.59 iter/s, versus DreamGaussian's 80 at 4.43 iter/s.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use multiple TetSpheres rather than a single TetSphere (ablation) | TetSphere Splatting · Multi-view reconstruction, dress and sorter | Reconstruction quality | Helped |
| Increase the number of TetSpheres (ablation) | TetSphere Splatting · Multi-view reconstruction, dress and sorter | Reconstruction quality | Helped |
| Increase the number of TetSpheres beyond 434 for the dress or 239 for the sorter (ablation) | TetSphere Splatting · Multi-view reconstruction, dress and sorter | Reconstruction quality | No clear effect |
| Increase the average number of tetrahedra per TetSphere (ablation) | TetSphere Splatting · Multi-view reconstruction | Chamfer Distance | Helped |
| Increase the number of tetrahedra per TetSphere instead of increasing the number of TetSpheres (ablation) | TetSphere Splatting · Multi-view reconstruction | Reconstruction accuracy | Mixed |
| Add volumetric regularization (ablation) | TetSphere Splatting · Sphere reconstruction inversion study | Tetrahedron inversion | Helped |
| Use TetSphere Splatting rather than the strongest reported baseline | Multi-view reconstruction · Multi-view reconstruction | Volume IoU: 0.6182 -> 0.6844 | Helped |
| Use TetSphere Splatting rather than DMesh | Multi-view reconstruction · Multi-view reconstruction | ALR: 0.1193 -> 0.6602 | Helped |
| Use TetSphere Splatting rather than DMesh | Multi-view reconstruction · Multi-view reconstruction | Chamfer Distance: 0.0136 -> 0.0184 | Hurt |
| Use TetSphere Splatting rather than Open-LRM | Single-view reconstruction · Single-view reconstruction, GSO | Volume IoU: 0.5945 -> 0.6317 | Helped |
| Use TetSphere Splatting rather than SyncDreamer | Single-view reconstruction · Single-view reconstruction, GSO | Chamfer Distance: 0.0261 -> 0.0351 | Hurt |
| Use TetSphere Splatting rather than DreamGaussian | Image-to-3D generation · Image-to-3D generation, 40GB A100 | Maximal Batch Size: 80 -> 120 | Helped |
Surprising findings
- SyncDreamer and DMesh-style baselines show lower mesh quality despite competitive Chamfer distance, indicating accuracy and mesh quality are decoupled.
- DMesh achieves the lowest Chamfer distance (0.0136) in multi-view reconstruction, beating the proposed method (0.0184).
Limitations
- Produces piecewise meshes from union of tetrahedral spheres rather than a globally consistent tetrahedral mesh.
- No strong topological guarantees; union may alter topology or manifoldness.
- Less effective on thin shells such as plant leaves, where DMesh is more accurate.
Experimental setup
Datasets: Thingi32 DeepFashion3D Objaverse Google Scanned Objects
Benchmarks: Thingi32 DeepFashion3D Objaverse Google Scanned Objects
Metrics: Chamfer Distance Volume IoU Area-Length Ratio Manifoldness Rate Connected Component Discrepancy F-Score Normal Consistency Edge Chamfer Distance Edge F-Score maximal batch size
Baselines: NIE FlexiCubes 2DGS DMesh Magic123 One-2-3-45 SyncDreamer Wonder3D Open-LRM DreamGaussian NeuS VolSDF
Builds on: Gaussian splatting DMesh Wonder3D DreamCraft3D Magic123
Closest papers by meaning
- Tetrahedron Splatting for 3D Generation (NeurIPS 2024 · similarity 0.92)
- 3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes (CVPR 2025 · similarity 0.87)
- DirectTriGS: Triplane-based Gaussian Splatting Field Representation for 3D Generation (CVPR 2025 · similarity 0.86)
- UVGS: Reimagining Unstructured 3D Gaussian Splatting using UV Mapping (CVPR 2025 · similarity 0.86)
- Geometry Field Splatting with Gaussian Surfels (CVPR 2025 · similarity 0.85)
- SplatFormer: Point Transformer for Robust 3D Gaussian Splatting (ICLR 2025 · similarity 0.85)
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