最陡下降密度控制用於緊湊型3D高斯潑濺

摘要

三維高斯潑濺（3DGS）已成為實現實時、高分辨率新視角合成的強大技術。通過將場景表示為高斯基元的混合體，3DGS利用GPU光柵化管線進行高效的渲染與重建。為優化場景覆蓋並捕捉細微細節，3DGS採用了一種密集化算法來生成額外的點。然而，這一過程往往導致冗餘的點雲，造成過高的內存使用、性能下降及巨大的存儲需求，這對在資源受限設備上的部署構成了重大挑戰。為解決這一限制，我們提出了一個理論框架，旨在揭示並改進3DGS中的密度控制。我們的分析表明，分割對於逃離鞍點至關重要。通過優化理論的方法，我們確立了密集化的必要條件，確定了最小子代高斯數目，找出了最優參數更新方向，並提供了子代不透明度歸一化的解析解。基於這些洞見，我們引入了SteepGS，它融合了最陡密度控制，這是一種在保持點雲緊湊的同時最小化損失的原則性策略。SteepGS在不影響渲染質量的前提下，實現了高斯點數約50%的減少，顯著提升了效率與可擴展性。

English

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for real-time, high-resolution novel view synthesis. By representing scenes as a mixture of Gaussian primitives, 3DGS leverages GPU rasterization pipelines for efficient rendering and reconstruction. To optimize scene coverage and capture fine details, 3DGS employs a densification algorithm to generate additional points. However, this process often leads to redundant point clouds, resulting in excessive memory usage, slower performance, and substantial storage demands - posing significant challenges for deployment on resource-constrained devices. To address this limitation, we propose a theoretical framework that demystifies and improves density control in 3DGS. Our analysis reveals that splitting is crucial for escaping saddle points. Through an optimization-theoretic approach, we establish the necessary conditions for densification, determine the minimal number of offspring Gaussians, identify the optimal parameter update direction, and provide an analytical solution for normalizing off-spring opacity. Building on these insights, we introduce SteepGS, incorporating steepest density control, a principled strategy that minimizes loss while maintaining a compact point cloud. SteepGS achieves a ~50% reduction in Gaussian points without compromising rendering quality, significantly enhancing both efficiency and scalability.

最陡下降密度控制用於緊湊型3D高斯潑濺

Steepest Descent Density Control for Compact 3D Gaussian Splatting

摘要

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