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Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGS
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Casts 3DGS compaction as Gaussian mixture reduction under composite transport divergence, using blockwise KD-tree k-means-style GMR followed by appearance fine-tuning, retaining ~10% of Gaussians with near-vanilla quality.
Problem
3DGS produces millions of redundant Gaussians, and existing compaction methods prune per-Gaussian heuristic scores without any global fidelity guarantee.
Approach
Treats the 3DGS geometry as a Gaussian mixture and reduces it by minimizing composite transportation divergence with a cheap squared-distance cost on means and covariances, solved as a k-means-like algorithm applied blockwise over KD-tree partitions; colors and opacities are then fine-tuned separately.
Key results
- 3DGS+GHAP at 10% retention reaches 23.312 PSNR on Tanks&Temples (157 Gaussians) vs 23.785 for vanilla 3DGS (1577 Gaussians) and 21.519 for the best pruning baseline PUP-3DGS at similar count.
- MiniSplatting+GHAP achieves 27.090 PSNR on Mip-NeRF 360 with 112 Gaussians, outperforming MiniSplatting (26.022 PSNR, 111 Gaussians).
- On Mip-NeRF 360 with Mini-Splatting-D backbone at 10% retention, the compacted model (27.090 PSNR) slightly exceeds the 100% version of 3DGS-style results reported in the same table.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace Mini-Splatting pruning with GHAP | Mini-Splatting · Tanks & Temples | PSNR: 22.661 -> 23.232 | Helped |
| Replace Mini-Splatting pruning with GHAP | Mini-Splatting · Mip-NeRF 360 | PSNR: 26.022 -> 27.090 | Helped |
| Replace Mini-Splatting pruning with GHAP | Mini-Splatting · Deep Blending | PSNR: 29.395 -> 30.042 | Helped |
| Add LPIPS to the rendering loss with increased LPIPS weight (ablation) | GHAP · Tanks & Temples | LPIPS | Helped |
| Add LPIPS to the rendering loss with increased LPIPS weight (ablation) | GHAP · Tanks & Temples | PSNR | Hurt |
| Add LPIPS to the rendering loss with increased LPIPS weight (ablation) | GHAP · Tanks & Temples | SSIM | Hurt |
| Use multiple compaction stages instead of one at iteration 15001 (ablation) | GHAP · Tanks & Temples | SSIM: 0.817; 0.817; 0.811 | No clear effect |
| Use multiple compaction stages instead of one at iteration 15001 (ablation) | GHAP · Tanks & Temples | PSNR: 23.313; 23.44; 23.359 | Mixed |
| Use multiple compaction stages instead of one at iteration 15001 (ablation) | GHAP · Tanks & Temples | LPIPS: 0.242; 0.247; 0.255 | Hurt |
| Add appearance optimization after geometric compaction (ablation) | GHAP · Tanks & Temples | PSNR | Helped |
| Replace GHAP geometric compaction with random subsampling (ablation) | GHAP · Tanks & Temples | PSNR | Hurt |
| Increase KD-tree depth (ablation) | GHAP · NeRF-Synthetic mic | PSNR | Mixed |
Surprising findings
- Compacted Mini-Splatting-D models sometimes exceed the quality of the uncompacted backbone, which the authors attribute to global regularization of over-saturated Gaussian sets.
- Multi-stage compaction (repeated geometry reduction at several iterations) did not improve over single-stage compaction in the appendix ablation.
Limitations
- Performance is bounded by the quality of the input backbone; artifacts from the backbone (e.g., AtomGS on Bicycle) persist after compaction.
- LPIPS is slightly worse than some baselines (e.g., MesonGS, PUP-3DGS) at comparable Gaussian counts for the 3DGS backbone.
Experimental setup
Datasets: Tanks & Temples Mip-NeRF 360 Deep Blending NeRF-Synthetic
Benchmarks: Tanks & Temples Mip-NeRF 360 Deep Blending NeRF-Synthetic
Metrics: PSNR SSIM LPIPS number of Gaussians runtime memory
Baselines: LightGaussian PUP-3DGS Trimming the Fat MesonGS Mini-Splatting 3DGS-MCMC LocoGS AtomGS
Builds on: 3D Gaussian Splatting composite transportation divergence Mini-Splatting AtomGS LightGaussian
Closest papers by meaning
- Compact 3D Gaussian Representation for Radiance Field (CVPR 2024 · similarity 0.93)
- GaussianSpa: An "Optimizing-Sparsifying" Simplification Framework for Compact and High-Quality 3D Gaussian Splatting (CVPR 2025 · similarity 0.92)
- GaussianPro: 3D Gaussian Splatting with Progressive Propagation (ICML 2024 · similarity 0.92)
- Locality-aware Gaussian Compression for Fast and High-quality Rendering (ICLR 2025 · similarity 0.92)
- Steepest Descent Density Control for Compact 3D Gaussian Splatting (CVPR 2025 · similarity 0.92)
- Optimized Minimal 3D Gaussian Splatting (NeurIPS 2025 · similarity 0.91)
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