Research map / 3D vision / NeRF and radiance fields
LinPrim: Linear Primitives for Differentiable Volumetric Rendering
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Introduces LinPrim, a differentiable volumetric rendering method using octahedron and tetrahedron polyhedral primitives with a GPU rasterizer based on ray-triangle intersections, matching 3DGS-style quality with fewer primitives.
Problem
Novel view synthesis currently relies on NeRFs (implicit, expensive) and 3D Gaussians; the paper explores whether simple bounded homogeneous polyhedral primitives can achieve comparable fidelity and real-time rendering.
Approach
Replace Gaussian kernels with homogeneous-density convex polyhedra (octahedra, tetrahedra) bounded by triangular faces; compute opacity from the distance between Möller-Trumbore ray-triangle intersection points, and backpropagate image errors through these intersections to the polyhedron geometry, with 3DGS-style optimization and population control.
Key results
- On ScanNet++ v2 LinPrim reaches 24.04 mean PSNR with 255k primitives vs 24.09 for 3DGS with 738k primitives.
- On Mip-NeRF 360 LinPrim reaches 26.63 PSNR with 1.79M primitives vs 27.43 for 3DGS with 3.32M primitives.
- LinPrim + MCMC achieves 24.41 mean PSNR on ScanNet++ at 255k primitives, versus 24.50 for GS-MCMC at 255k.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MCMC-based densification (ablation) | LinPrim · ScanNet++ v2 | PSNR: 24.04 -> 24.41 | Helped |
| Use MCMC-based densification (ablation) | LinPrim · Mip-NeRF 360 | PSNR: 26.63 -> 27.04 | Helped |
| Replace octahedra with tetrahedra (ablation) | LinPrim · ScanNet++ v2 | PSNR: 24.04 -> 24.05 | No clear effect |
| Replace octahedra with tetrahedra (ablation) | LinPrim · Mip-NeRF 360 | PSNR: 26.63 -> 25.96 | Hurt |
| Add the 2D anti-aliasing filter (ablation) | LinPrim · Bonsai | PSNR: 30.84 -> 30.96 | Helped |
| Add the 3D anti-aliasing filter (ablation) | LinPrim · Bonsai | PSNR: 30.84 -> 30.97 | Helped |
| Add both anti-aliasing filters (ablation) | LinPrim · Bonsai | PSNR: 30.84 -> 31.21 | Helped |
| Add both anti-aliasing filters (ablation) | LinPrim · dc263dfbf0 | PSNR: 22.46 -> 22.67 | Helped |
| Remove the ray-space approximation (ablation) | LinPrim + MCMC · ScanNet++ v2 | PSNR: 24.41 -> 24.50 | Helped |
| Remove the ray-space approximation (ablation) | LinPrim + MCMC · ScanNet++ v2 scene 39f36d | Rendering time: 15.87ms -> 29.15ms | Hurt |
| Optimize unnormalized density directly instead of opacity (ablation) | LinPrim · Novel view synthesis | Performance | No clear effect |
Surprising findings
- Linear primitives produce roughly 5-10% of the ray intersections of Gaussians, yet remain competitive in quality.
- Rendering speed is slower than 3DGS (68 fps on ScanNet++ vs. 3DGS at ~175 fps), despite fewer primitives.
Limitations
- Bounded primitives create hard, segment-like artifacts in poorly observed regions.
- Population control and MCMC were designed for Gaussians and are not fully optimal for polyhedra.
- Rendering efficiency is below the optimized Gaussian rasterizer.
Experimental setup
Datasets: Mip-NeRF 360 ScanNet++ v2 NeRF synthetic
Benchmarks: Mip-NeRF 360 ScanNet++ v2 NeRF synthetic
Metrics: PSNR SSIM LPIPS rendering speed (ms/fps) Chamfer distance L1/L2 depth error
Baselines: 3DGS Mip-Splatting 3D Convex Splatting GS-MCMC Zip-NeRF
Builds on: 3D Gaussian Splatting Mip-Splatting EVER GS-MCMC EWA Splatting
Closest papers by meaning
- Volumetric Surfaces: Representing Fuzzy Geometries with Layered Meshes (CVPR 2025 · similarity 0.87)
- UniGS: Unified Geometry-Aware Gaussian Splatting for Multimodal Rendering (NeurIPS 2026 · similarity 0.87)
- CompactSplat: Spatially Adaptive Gaussian Distribution for Feedforward Scene Reconstruction (NeurIPS 2026 · similarity 0.86)
- DNGaussian: Optimizing Sparse-View 3D Gaussian Radiance Fields with Global-Local Depth Normalization (CVPR 2024 · similarity 0.86)
- Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGS (NeurIPS 2025 · similarity 0.86)
- HybridNeRF: Efficient Neural Rendering via Adaptive Volumetric Surfaces (CVPR 2024 · similarity 0.86)
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