A New Split Algorithm for 3D Gaussian Splatting

TL;DR

A new 3D Gaussian splitting algorithm is proposed, which can produce a more uniform and surface-bounded 3D Gaussian splatting model and ensures consistency of mathematical characteristics and similarity of appearance, allowing resulting 3D Gaussian splatting models to be more uniform and a better fit to the underlying surface.

Abstract

3D Gaussian splatting models, as a novel explicit 3D representation, have been applied in many domains recently, such as explicit geometric editing and geometry generation. Progress has been rapid. However, due to their mixed scales and cluttered shapes, 3D Gaussian splatting models can produce a blurred or needle-like effect near the surface. At the same time, 3D Gaussian splatting models tend to flatten large untextured regions, yielding a very sparse point cloud. These problems are caused by the non-uniform nature of 3D Gaussian splatting models, so in this paper, we propose a new 3D Gaussian splitting algorithm, which can produce a more uniform and surface-bounded 3D Gaussian splatting model. Our algorithm splits an $N$-dimensional Gaussian into two N-dimensional Gaussians. It ensures consistency of mathematical characteristics and similarity of appearance, allowing resulting 3D Gaussian splatting models to be more uniform and a better fit to the underlying surface, and thus more suitable for explicit editing, point cloud extraction and other tasks. Meanwhile, our 3D Gaussian splitting approach has a very simple closed-form solution, making it readily applicable to any 3D Gaussian model.

Figures (9)

• Figure 1: Structural (above) and scale (below) inhomogeneities (2D examples). If an editing operation is performed, here shown as cutting at a plane and pulling apart, the results will include parts crossing the plane: blurring and needle-like bulges will occur. Small circles represent more homogeneous Gaussians.
• Figure 2: 2D illustration of the Gaussian splitting process. Three conservation rules are used to ensure visual consistency.
• Figure 3: The first three examples split the chair into two pieces directly along a randomly chosen plane passing through the origin with $\mathbf{n} = [0.5401,0.8316,0.0963]^T$; the last two remove a triangular model from the chair's back. We compare our method to three other baselines: the move solution which moves any Gaussians directly, the remove solution which removes any Gaussians in the gap, and the filter solution which removes any Gaussian whose position is inside the bounding box or the closed curve. We execute our algorithm twice and 3 times in different situations for better results. The move solution results visible components in the gap while the remove solution leads to many holes. The filter solution produces many artifacts. Our solution produces the cleanest boundaries near the cuts.
• Figure 4: We integrate our splitting algorithm into the training of 3D Gaussian with different splitting thresholds $Th_{\gamma}$. Our method removes most of the inhomogeneous Gaussians and achieves better results.
• Figure 5: Our splitting algorithm helps to extract more uniform and denser point clouds from a well-trained 3D Gaussian model for the chair object.