NegGS: Negative Gaussian Splatting

Abstract

One of the key strengths of 3D rendering lies in its ability to simulate intricate scenes with high fidelity. Among the recent advancements, Gaussian Splatting has gained prominence for its fast training and inference capabilities.

At its core, Gaussian Splatting encodes 3D scene information using a collection of Gaussian distributions, each contributing to a continuous, differentiable 3D representation—akin to traditional meshes but more flexible. However, the standard approach is limited by the inherently linear nature of Gaussian functions, making it less effective in modeling highly nonlinear structures common in real-world objects.

A conventional workaround involves increasing the number of Gaussian components to capture these complexities. Yet, this leads to significant computational overhead.

In this paper, we propose Negative Gaussians, interpreted as components with negative color contributions. Inspired by the density distributions resulting from dividing two Gaussian probability density functions (PDFs)—which we term Diff-Gaussians—this method allows the representation of non-trivial structures such as donut or moon-shaped geometries.

Our experiments demonstrate that the use of Negative Gaussians:

• Enhances modeling of high-frequency details and rapid color transitions,
• Improves the realism of shadow representations,
• Offers a more expressive alternative to purely additive Gaussian approaches.

To the best of our knowledge, this is the first work to extend the basic ellipsoidal representation in Gaussian Splatting to encompass complex, nonlinear forms.

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