Moment-Based 3D Gaussian Splatting: Resolving Volumetric Occlusion with Order-Independent Transmittance

TL;DR

This paper introduces a moment-based, order-independent transmittance method for 3D Gaussian Splatting that improves rendering of semi-transparent objects without ray tracing, enhancing quality and efficiency.

Contribution

It develops a novel, analytical approach to compute per-ray moments for high-fidelity transmittance in 3D Gaussian rendering, avoiding ray tracing and sorting.

Findings

Improves rendering quality of semi-transparent objects.

Enables order-independent, physically plausible transparency.

Achieves real-time rendering with higher fidelity.

Abstract

The recent success of 3D Gaussian Splatting (3DGS) has reshaped novel view synthesis by enabling fast optimization and real-time rendering of high-quality radiance fields. However, it relies on simplified, order-dependent alpha blending and coarse approximations of the density integral within the rasterizer, thereby limiting its ability to render complex, overlapping semi-transparent objects. In this paper, we extend rasterization-based rendering of 3D Gaussian representations with a novel method for high-fidelity transmittance computation, entirely avoiding the need for ray tracing or per-pixel sample sorting. Building on prior work in moment-based order-independent transparency, our key idea is to characterize the density distribution along each camera ray with a compact and continuous representation based on statistical moments. To this end, we analytically derive and compute a set of per-pixel moments from all contributing 3D Gaussians. From these moments, a continuous transmittance function is reconstructed for each ray, which is then independently sampled within each Gaussian. As a result, our method bridges the gap between rasterization and physical accuracy by modeling light attenuation in complex translucent media, significantly improving overall reconstruction and rendering quality.