# Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGS

arXiv: https://arxiv.org/abs/2506.09534 · HTML: https://mlsanity.com/paper/2506.09534/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 43 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 30 of 33)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [DreamGaussian: Generative Gaussian Splatting for Efficient 3D Content Creation](https://mlsanity.com/paper/2309.16653/) (2023)
- [LightGaussian: Unbounded 3D Gaussian Compression with 15x Reduction and 200+ FPS](https://mlsanity.com/paper/2311.17245/) (2023)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [DrivingGaussian: Composite Gaussian Splatting for Surrounding Dynamic Autonomous Driving Scenes](https://mlsanity.com/paper/2312.07920/) (2023)
- [GaussianEditor: Swift and Controllable 3D Editing with Gaussian Splatting](https://mlsanity.com/paper/2311.14521/) (2023)
- [Octree-GS: Towards Consistent Real-time Rendering with LOD-Structured 3D Gaussians](https://mlsanity.com/paper/2403.17898/) (2024)
- [A Survey on 3D Gaussian Splatting](https://mlsanity.com/paper/2401.03890/) (2024)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [Mini-Splatting: Representing Scenes with a Constrained Number of Gaussians](https://mlsanity.com/paper/2403.14166/) (2024)
- [HAC: Hash-grid Assisted Context for 3D Gaussian Splatting Compression](https://mlsanity.com/paper/2403.14530/) (2024)
- [Taming 3DGS: High-Quality Radiance Fields with Limited Resources](https://mlsanity.com/paper/2406.15643/) (2024)
- [GaussianPro: 3D Gaussian Splatting with Progressive Propagation](https://mlsanity.com/paper/2402.14650/) (2024)
- [GPS-Gaussian: Generalizable Pixel-wise 3D Gaussian Splatting for Real-time Human Novel View Synthesis](https://mlsanity.com/paper/2312.02155/) (2023)
- [GauHuman: Articulated Gaussian Splatting from Monocular Human Videos](https://mlsanity.com/paper/2312.02973/) (2023)
- [High-quality Surface Reconstruction using Gaussian Surfels](https://mlsanity.com/paper/2404.17774/) (2024)
- [RadSplat: Radiance Field-Informed Gaussian Splatting for Robust Real-Time Rendering with 900+ FPS](https://mlsanity.com/paper/2403.13806/) (2024)
- [3D Gaussian as a New Era: A Survey](https://mlsanity.com/paper/2402.07181/) (2024)
- [PUP 3D-GS: Principled Uncertainty Pruning for 3D Gaussian Splatting](https://mlsanity.com/paper/2406.10219/) (2024)
- [3D Gaussian Splatting: Survey, Technologies, Challenges, and Opportunities](https://mlsanity.com/paper/2407.17418/) (2024)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [3DGS.zip: A survey on 3D Gaussian Splatting Compression Methods](https://mlsanity.com/paper/2407.09510/) (2024)
- [MesonGS: Post-training Compression of 3D Gaussians via Efficient Attribute Transformation](https://mlsanity.com/paper/2409.09756/) (2024)
- [LP-3DGS: Learning to Prune 3D Gaussian Splatting](https://mlsanity.com/paper/2405.18784/) (2024)
- [Trimming the Fat: Efficient Compression of 3D Gaussian Splats through Pruning](https://mlsanity.com/paper/2406.18214/) (2024)
- [Optimal transport for Gaussian mixture models](https://mlsanity.com/paper/1710.07876/) (2017)
- [Locality-aware Gaussian Compression for Fast and High-quality Rendering](https://mlsanity.com/paper/2501.05757/) (2025)

## Built on by (most cited first, 9 of 9)

- [REFINE: Super-efficient 3D Gaussian Splatting Pruning via Rendering-Free Primitive Importance](https://mlsanity.com/paper/2606.09074/) (2026)
- [SUCCESS-GS: Survey of Compactness and Compression for Efficient Static and Dynamic Gaussian Splatting](https://mlsanity.com/paper/2512.07197/) (2025)
- [NanoGS: Training-Free Gaussian Splat Simplification](https://mlsanity.com/paper/2603.16103/) (2026)
- [Provable Pruning for Efficient 3D Gaussian Splatting via Coresets](https://mlsanity.com/paper/2607.02721/) (2026)
- [SPARE-GS: Structural Parsimony and Resource Efficiency for 3D Gaussian Splatting](https://mlsanity.com/paper/2607.16624/) (2026)
- [MMGS: 10× Compressed 3DGS through Optimal Transport Aggregation based on Multi-view Ranking](https://mlsanity.com/paper/2605.19304/) (2026)
- [SRRM: Improving Recursive Transport Surrogates in the Small-Discrepancy Regime](https://mlsanity.com/paper/2603.18781/) (2026)
- [CVT-GS: Learning to Simplify 3D Gaussian Splatting with Centroidal Voronoi Tessellation](https://mlsanity.com/paper/2609.08730/) (2026)
- [SplatQ: Interaction-Aware Pruning of 3D Gaussian Splatting via Quadratic Selection](https://mlsanity.com/paper/2610.13503/) (2026)

## Abstract (arXiv)

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for radiance field rendering, but it typically requires millions of redundant Gaussian primitives, overwhelming memory and rendering budgets. Existing compaction approaches address this by pruning Gaussians based on heuristic importance scores, without global fidelity guarantee. To bridge this gap, we propose a novel optimal transport perspective that casts 3DGS compaction as global Gaussian mixture reduction. Specifically, we first minimize the composite transport divergence over a KD-tree partition to produce a compact geometric representation, and then decouple appearance from geometry by fine-tuning color and opacity attributes with far fewer Gaussian primitives. Experiments on benchmark datasets show that our method (i) yields negligible loss in rendering quality (PSNR, SSIM, LPIPS) compared to vanilla 3DGS with only 10% Gaussians; and (ii) consistently outperforms state-of-the-art 3DGS compaction techniques. Notably, our method is applicable to any stage of vanilla or accelerated 3DGS pipelines, providing an efficient and agnostic pathway to lightweight neural rendering. The code is publicly available at https://github.com/DrunkenPoet/GHAP