Steepest Descent Density Control for Compact 3D Gaussian Splatting
Authors: name: Peihao Wang, name: Yuehao Wang, name: Dilin Wang, name: Sreyas Mohan, name: Zhiwen Fan, name: Lemeng Wu, name: Ruisi Cai, name: Yu-Ying Yeh, name: Zhangyang Wang, name: Qiang Liu, name: Rakesh Ranjan

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.