紧凑型3D高斯溅射的最速下降密度控制

摘要

三维高斯泼溅（3DGS）作为一种强大的技术，在实时高分辨率新视角合成领域崭露头角。通过将场景表示为高斯基元的混合体，3DGS利用GPU光栅化管线实现高效的渲染与重建。为了优化场景覆盖并捕捉精细细节，3DGS采用了一种密集化算法来生成额外点云。然而，这一过程常导致点云冗余，引发内存占用过高、性能下降及存储需求激增等问题，对资源受限设备的部署构成了重大挑战。针对这一局限，我们提出了一套理论框架，旨在阐明并改进3DGS中的密度控制机制。我们的分析表明，分裂操作对于逃离鞍点至关重要。通过优化理论方法，我们确立了密集化的必要条件，确定了最小子代高斯数量，找出了最优参数更新方向，并提供了子代不透明度归一化的解析解。基于这些洞见，我们引入了SteepGS，它融入了最陡密度控制这一原则性策略，在保持点云紧凑的同时最小化损失。SteepGS实现了约50%的高斯点减少，且不牺牲渲染质量，显著提升了效率与可扩展性。

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.

紧凑型3D高斯溅射的最速下降密度控制

Steepest Descent Density Control for Compact 3D Gaussian Splatting

摘要

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