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Metropolis-Hastings Sampling for 3D Gaussian Reconstruction
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Reformulates 3DGS densification and pruning as a Metropolis-Hastings sampling process with error-driven Gaussian proposals and a voxel-density prior, reducing Gaussian count while matching or slightly surpassing 3DGS-MCMC quality.
Problem
Heuristic density control in 3D Gaussian Splatting (cloning, splitting, pruning) causes redundant Gaussians or loss of fidelity, and prior MCMC variants fix the Gaussian count upfront.
Approach
Treats each Gaussian insertion as a Metropolis-Hastings proposal whose importance comes from aggregated multi-view SSIM/L1 errors and opacity via a logistic fusion, with a voxel-occupancy penalty D(v) entering the acceptance ratio, and uses coarse-to-fine proposal scales plus opacity-based relocation.
Key results
- Averaged over Mip-NeRF360, the method reaches 27.34 PSNR with 0.72M Gaussians versus 27.69 PSNR for 3DGS-MCMC at the same count, and 3DGS-S at 26.62 PSNR.
- On Deep Blending the method achieves 30.12 PSNR and 0.909 SSIM, the best among compared methods in the paper's table, with 0.75M Gaussians.
- On Tanks and Temples the method achieves 23.99 PSNR, below 3DGS-MCMC's 24.30 PSNR, while using the same Gaussian count.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace 3DGS-MCMC with MH sampling at matched Gaussian count (ablation) | 3DGS · Mip-NeRF360, Tanks & Temples, and Deep Blending | PSNR: 26.80 -> 26.87; 23.47 -> 23.66; 29.45 -> 29.46 | Mixed |
| Add low-opacity Gaussian relocation (ablation) | Ours · Mip-NeRF360, Tanks & Temples, and Deep Blending | PSNR: 26.94 -> 27.34; 23.69 -> 23.99; 29.57 -> 30.12 | Helped |
| Add the multi-view importance score (ablation) | Ours · Mip-NeRF360, Tanks & Temples, and Deep Blending | PSNR: 27.31 -> 27.34; 23.79 -> 23.99; 29.97 -> 30.12 | Helped |
| Add the opacity cue to an L1 + SSIM importance score (ablation) | Importance score · Mip-NeRF360, Tanks & Temples, and Deep Blending | PSNR: 27.22 -> 27.34; 23.89 -> 23.99; 29.87 -> 30.12 | Helped |
| Add the SSIM cue to an L1 + opacity importance score (ablation) | Importance score · Mip-NeRF360, Tanks & Temples, and Deep Blending | PSNR: 27.30 -> 27.34; 23.92 -> 23.99; 29.85 -> 30.12 | Helped |
| Add the L1 cue to an SSIM + opacity importance score (ablation) | Importance score · Mip-NeRF360, Tanks & Temples, and Deep Blending | PSNR: 27.30 -> 27.34; 23.87 -> 23.99; 30.02 -> 30.12 | Helped |
| Use MH sampling instead of 3DGS-MCMC | 3DGS with matched Gaussian count · Mip-NeRF360 | PSNR: 27.69 -> 27.34 | Hurt |
| Use MH sampling instead of 3DGS-MCMC | 3DGS with matched Gaussian count · Tanks & Temples | PSNR: 24.30 -> 23.99 | Hurt |
| Use MH sampling instead of 3DGS-MCMC | 3DGS with matched Gaussian count · Deep Blending | PSNR: 29.84 -> 30.12 | Helped |
| Use MH sampling instead of 3DGS-MCMC | 3DGS with matched Gaussian count · Mip-NeRF360 | LPIPS: 0.234 -> 0.241 | Hurt |
| Use MH sampling instead of 3DGS-MCMC | 3DGS with matched Gaussian count · Tanks & Temples | LPIPS: 0.170 -> 0.166 | Helped |
| Use MH sampling instead of 3DGS-MCMC | 3DGS with matched Gaussian count · Deep Blending | LPIPS: 0.254 -> 0.245 | Helped |
Surprising findings
- Ablation shows the sampler without the multi-view importance score (Ours w/o Importance Score) still achieves strong results, which the authors read as the sampling mechanism being the primary driver.
- The MH sampler is a modest improvement over the SGLD sampler from 3DGS-MCMC when both use matched Gaussian counts (e.g., 26.87 vs 26.80 PSNR on Mip-NeRF360).
Limitations
- Sparse outdoor scenes perform worse than indoor scenes because the sampler prioritizes high-density areas.
- Multi-view photometric error computation adds roughly 5 minutes of training time per scene.
- Gains over 3DGS-MCMC in final quality are small or absent; 3DGS-MCMC reports slightly higher metrics on several benchmarks.
Experimental setup
Datasets: Mip-NeRF360 Tanks and Temples Deep Blending
Benchmarks: Mip-NeRF360 Tanks and Temples Deep Blending
Metrics: PSNR SSIM LPIPS number of Gaussians training time
Baselines: Plenoxels Instant-NGP Mip-NeRF 360 3DGS 3DGS-MCMC
Builds on: 3D Gaussian Splatting 3DGS-MCMC Metropolis-Hastings
Closest papers by meaning
- 3D Gaussian Splatting as Markov Chain Monte Carlo (NeurIPS 2024 · similarity 0.92)
- ReorgGS: Equivalent Distribution Reorganization for 3D Gaussian Splatting (NeurIPS 2026 · similarity 0.92)
- GaussianSpa: An "Optimizing-Sparsifying" Simplification Framework for Compact and High-Quality 3D Gaussian Splatting (CVPR 2025 · similarity 0.91)
- Frequency-Aware Density Control via Reparameterization for High-Quality Rendering of 3D Gaussian Splatting (AAAI 2025 · similarity 0.91)
- PUP 3D-GS: Principled Uncertainty Pruning for 3D Gaussian Splatting (CVPR 2025 · similarity 0.91)
- GaussianPro: 3D Gaussian Splatting with Progressive Propagation (ICML 2024 · similarity 0.91)
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