Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGS
This addresses memory and rendering budget issues in 3DGS for neural rendering applications, offering an incremental improvement over existing compaction methods.
The paper tackles the problem of redundant Gaussian primitives in 3D Gaussian Splatting (3DGS) by proposing a novel optimal transport perspective for global Gaussian mixture reduction, resulting in negligible loss in rendering quality with only 10% of the Gaussians and outperforming state-of-the-art compaction techniques.
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