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

2025-12-12

AI Summary

3D Gaussian Splatting (3DGS) struggles with accurate rendering of multi-layer translucent objects due to its coarse, discrete modeling—relying on order-dependent alpha blending and density integration—which induces depth ambiguity and light-leakage artifacts. To address this, we propose a statistically grounded, continuous transmittance modeling framework based on moment representations. We analytically derive closed-form expressions for arbitrary-order moments of Gaussian densities and construct a continuous transmittance reconstruction function. Coupled with per-Gaussian ray sampling, our method enables order-independent, physically accurate volumetric light attenuation—without ray tracing or pixel sorting. This is the first approach to achieve physically consistent translucent rendering within a pure rasterization pipeline. It preserves real-time performance while significantly improving reconstruction fidelity and visual realism for complex multi-layer translucent structures.

Technology Category

• Computer Vision: Interpretability, Explainability, and Transparency
• Machine Learning: Transparent, Interpretable, Explainable ML
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

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.

Problem

• Resolves volumetric occlusion in 3D Gaussian Splatting
• Models light attenuation in translucent media accurately
• Enables order-independent transmittance without ray tracing

Innovation

• Moment-based transmittance computation without ray tracing
• Analytical per-pixel moments from 3D Gaussians for density
• Continuous transmittance function for accurate light attenuation modeling