A New Split Algorithm for 3D Gaussian Splatting

Abstract

3DGS, 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 , 3DGS can produce a blurred or needle-like effect near the surface. At the same time, 3DGS tend to flatten large untextured regions , yielding a very sparse point cloud. These problems are caused by the non-uniform nature of 3DGS.

In this paper, we propose a new 3D Gaussiansplitting algorithm, which can produce a more uniform and surface-bounded 3DGS.

Our algorithm splits an 𝑁-dimensional Gaussian into two 𝑁 -dimensional Gaussians. It ensures consistency of mathematical characteristics and similarity of appearance , allowing resulting 3DGS 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 Gaussiansplitting approach has a very simple closed-form solution , making it readily applicable to any 3D Gaussian model.

Figure

Figure 1

Benefiting from our new Gaussian splitting algorithm, we can produce more uniform, surface-bounded 3DGS, enabling their explicit editing to produce clearer surfaces and the extraction of denser point clouds for untextured regions. Our splitting method also benefits 3D Gaussian learning, rendering views of higher quality.

Figure 2

_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 3

2D illustration of theGaussian splitting process. Three conservation rules are used to ensure visual consistency.

Figure 4

The first three examples split the chair into two pieces directly along a randomly chosen plane passing through the origin with ;

thelast 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 5

We integrate our splitting algorithm into the training of 3D Gaussian with different splitting thresholds . Our method removes most of the inhomogeneous Gaussians and achieves better results.

Figure 6

Our splitting algorithm helps to extract more uniform and denser point clouds from a well-trained 3D Gaussian model for the chair object.

Figure 7

Various planesplit results , which show the differences between splitting algorithms more clearly. The remove solution leads to more holes, and the move solution leads to more adhesion, while ours clearly separates the two parts with a clear boundary.

Figure 8

Incorporating our algorithm reduces blurring and needles compared to the standard 3D Gaussian splatting model training.

Figure 9

Various editing examplesremoving certain shapes from a 3D Gaussian splatting model. The filter solution of deleting the Gaussians within the shape directly produces more irregular boundaries than our methods, and leaves material in the hole left by removal.

Figure 10

Example showing that our algorithm can help to extract a more uniform point cloud.

CONCLUSION AND FUTURE WORK

In this paper, we model the problem of how to split an 𝑁-dimensional Gaussian into two independent 𝑁-dimensional Gaussians and present a closed-form solution for this problem. This enables our splitting algorithm to be readily used with any 3D Gaussian model processing and helps to produce more uniformly distributed Gaussian.

In this way, blurring and needle-like artifacts can be significantlyreduced , benefiting various downstream applications.

In the future, we hope to apply our work to conversions between 3DGS and other 3D representations, improvement of rendering quality, GS editing , and some othergeometric applications of GS. Moreover, there is an inverse to our method, to merge Gaussians, which can be used to greatly decrease storage requirements.