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

2025-06-11

AI Summary

3D Gaussian Splatting (3DGS) suffers from excessive memory consumption and rendering overhead due to redundant Gaussian primitives. Method: This paper pioneers a global Gaussian mixture compression framework grounded in optimal transport theory, featuring geometric-appearance disentanglement. We formulate a composite transport divergence minimization problem over a KD-tree spatial partition, enabling provably fidelity-preserving Gaussian reduction with guaranteed global optimality; the method is plug-and-play at arbitrary training or inference stages. Contribution/Results: Our approach achieves near-lossless reconstruction—maintaining virtually identical PSNR, SSIM, and LPIPS—even when retaining only 10% of the original Gaussians—significantly outperforming existing state-of-the-art compression methods. The core innovation lies in formalizing 3DGS compression as an optimal transport problem with geometric-appearance decoupling constraints, establishing the first lightweight representation paradigm for 3DGS with theoretically guaranteed fidelity preservation.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Data Mining & Knowledge Management: Data Compression

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

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.

Problem

• Reduces redundant Gaussian primitives in 3DGS rendering
• Ensures global fidelity in Gaussian mixture reduction
• Decouples appearance from geometry for efficient rendering

Innovation

• Optimal transport for global Gaussian reduction
• KD-tree partition minimizes transport divergence
• Decouples appearance and geometry attributes