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

arXiv: https://arxiv.org/abs/2512.11800 · HTML: https://mlsanity.com/paper/2512.11800/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 12 Dec 2025.

## Builds on (most cited first, 24 of 24)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks](https://mlsanity.com/paper/2103.03231/) (2021)
- [Gaussian Opacity Fields: Efficient Adaptive Surface Reconstruction in Unbounded Scenes](https://mlsanity.com/paper/2404.10772/) (2024)
- [3D Gaussian Ray Tracing: Fast Tracing of Particle Scenes](https://mlsanity.com/paper/2407.07090/) (2024)
- [Revising Densification in Gaussian Splatting](https://mlsanity.com/paper/2404.06109/) (2024)
- [StopThePop: Sorted Gaussian Splatting for View-Consistent Real-time Rendering](https://mlsanity.com/paper/2402.00525/) (2024)
- [3DGUT: Enabling Distorted Cameras and Secondary Rays in Gaussian Splatting](https://mlsanity.com/paper/2412.12507/) (2024)
- [AbsGS: Recovering Fine Details for 3D Gaussian Splatting](https://mlsanity.com/paper/2404.10484/) (2024)
- [Analytic-Splatting: Anti-Aliased 3D Gaussian Splatting via Analytic Integration](https://mlsanity.com/paper/2403.11056/) (2024)
- [EVER: Exact Volumetric Ellipsoid Rendering for Real-time View Synthesis](https://mlsanity.com/paper/2410.01804/) (2024)
- [Don't Splat your Gaussians: Volumetric Ray-Traced Primitives for Modeling and Rendering Scattering and Emissive Media](https://mlsanity.com/paper/2405.15425/) (2024)
- [Efficient Perspective-Correct 3D Gaussian Splatting Using Hybrid Transparency](https://mlsanity.com/paper/2410.08129/) (2024)
- [Sort-free Gaussian Splatting via Weighted Sum Rendering](https://mlsanity.com/paper/2410.18931/) (2024)
- [Does 3D Gaussian Splatting Need Accurate Volumetric Rendering?](https://mlsanity.com/paper/2502.19318/) (2025)
- [StochasticSplats: Stochastic Rasterization for Sorting-Free 3D Gaussian Splatting](https://mlsanity.com/paper/2503.24366/) (2025)
- [Volumetrically Consistent 3D Gaussian Rasterization](https://mlsanity.com/paper/2412.03378/) (2024)
- [RayGauss: Volumetric Gaussian-Based Ray Casting for Photorealistic Novel View Synthesis](https://mlsanity.com/paper/2408.03356/) (2024)
- [Deep and Fast Approximate Order Independent Transparency](https://mlsanity.com/paper/2305.10197/) (2023)

## Built on by (most cited first, 2 of 2)

- [VkSplat: High-Performance 3DGS Training in Vulkan Compute](https://mlsanity.com/paper/2605.00219/) (2026)
- [SteadySplats: Resampling of Low-Variance Gaussians for High-Fidelity Stochastic Rendering](https://mlsanity.com/paper/2610.05576/) (2026)

## Abstract (arXiv)

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.