Emission-Aware Gaussians and Path Tracing

• The paper introduces a novel method that fuses Gaussian and surfel primitives with explicit emission modeling to achieve unbiased multi-bounce global illumination.
• EAG-PT employs closed-form transmittance and efficient ray sampling to enable precise, editable scene reconstruction and physically coherent lighting.
• Experimental results demonstrate that EAG-PT outperforms NeRF and mesh-based methods in metrics such as PSNR and LPIPS, providing more accurate relighting and global illumination.

Emission-Aware Gaussians and Path Tracing (EAG-PT) encompasses a class of algorithms and representations that enable physically based, editable reconstruction and rendering of complex scenes by combining Gaussian (and related kernel) volumetric or surfel proxies with explicit emission modeling and path tracing. EAG-PT provides a compact alternative to mesh or voxel grids for both forward and inverse rendering, supporting multi-bounce global illumination, scattering, relighting, and consistent radiometric scene editing. The approach leverages closed-form solutions for ray transmittance, efficient sampling strategies, and differentiated treatment of emissive and non-emissive elements, facilitating physically coherent light transport directly on data-derived Gaussian representations.

1. Volumetric and Surfel-Based Scene Primitives

EAG-PT models a scene as a set of Gaussian or related kernel-based primitives. In the volumetric rendition, each primitive $i$ is defined by:

• Mean location $\boldsymbol\mu_i \in \mathbb{R}^3$
• Full-rank covariance $\Sigma_i \in \mathbb{R}^{3\times3}$
• Scalar weight $w_i$
• Single-scattering albedo $\alpha_i$
• Emissive coefficient $\varepsilon_i$

Density kernels include:

• 3D Gaussian:

$$K_i(\mathbf x) = \frac{1}{(2\pi)^{3/2}|\Sigma_i|^{1/2}} \exp\left(-\frac{1}{2} (\mathbf x - \mu_i)^\top \Sigma_i^{-1} (\mathbf x - \mu_i)\right)$$

• Epanechnikov Kernel (for compact support):

$$K_i(\mathbf x) = \begin{cases} c (1-u) |\Sigma_i|^{-1/2}, & u \leq 1\ 0, & u > 1 \end{cases}$$

with $$u = (\mathbf x - \mu_i)^\top \Sigma_i^{-1} (\mathbf x - \mu_i)$$, $c = \frac{d+2}{2V_d}$, $\boldsymbol\mu_i \in \mathbb{R}^3$0.

The extinction, scattering, and emission fields are then, respectively,

$\boldsymbol\mu_i \in \mathbb{R}^3$1

$\boldsymbol\mu_i \in \mathbb{R}^3$2

In surfel-based variants (Yang et al., 30 Jan 2026), each primitive is a 2D Gaussian patch (center $\boldsymbol\mu_i \in \mathbb{R}^3$3, tangent axes, covariance in local $\boldsymbol\mu_i \in \mathbb{R}^3$4 plane) with attached appearance attributes (emissive mask $\boldsymbol\mu_i \in \mathbb{R}^3$5, cached radiance $\boldsymbol\mu_i \in \mathbb{R}^3$6, diffuse albedo $\boldsymbol\mu_i \in \mathbb{R}^3$7).

2. Closed-Form Transmittance and Ray Sampling

Transmittance along a ray $\boldsymbol\mu_i \in \mathbb{R}^3$8 is given by

$\boldsymbol\mu_i \in \mathbb{R}^3$9

with $\Sigma_i \in \mathbb{R}^{3\times3}$0. For a Gaussian, analytic expressions are obtained via error functions and Mahalanobis geometry.

Sampling the free-flight distance $\Sigma_i \in \mathbb{R}^{3\times3}$1 obeys PDF $\Sigma_i \in \mathbb{R}^{3\times3}$2, with inverse-CDF sampling (for mixtures, Newton–Raphson solution): $\Sigma_i \in \mathbb{R}^{3\times3}$3

These closed-form expressions permit exact, unbiased volumetric event sampling, crucial for unbiased path tracing and inverse rendering (Condor et al., 2024).

3. Explicit Emission Modeling and Component Separation

A defining feature of EAG-PT is the explicit identification and modeling of scene emitters at the kernel/surfel level. During the initial scene reconstruction, each primitive carries both a radiance value and an emissive probability or mask ($\Sigma_i \in \mathbb{R}^{3\times3}$4), learned or imposed via 2D user-provided masks $\Sigma_i \in \mathbb{R}^{3\times3}$5 and supervised accordingly: $\Sigma_i \in \mathbb{R}^{3\times3}$6 where $\Sigma_i \in \mathbb{R}^{3\times3}$7 is the accumulated emissive component along the view ray for pixel $\Sigma_i \in \mathbb{R}^{3\times3}$8. Emitters ($\Sigma_i \in \mathbb{R}^{3\times3}$9) never reflect light in subsequent optimization, while non-emitters ($w_i$0) support albedo reconstruction and indirect illumination (Yang et al., 30 Jan 2026).

This explicit split ensures that scene edits (moving or recoloring lights) yield unambiguous, physically meaningful relighting with correct global transport, unattainable in NeRF/3DGS radiance-only baselines that bake all illumination.

4. Optimization and Inverse Rendering Algorithms

EAG-PT typically employs a two-stage optimization protocol:

Stage 0: Radiant Scene Reconstruction

• Each Gaussian primitive is optimized to reproduce the input radiance images and associated geometry (normals, depth), embedding both radiance and emissive mask fields via direct supervision.

Stage 1: Material Parameter Recovery (Single-Bounce Fitting)

• With emissive/non-emissive identities fixed, per-primitive diffuse albedos $w_i$1 are estimated using 1-bounce physically based rendering:

$w_i$2

with MC integration and Monte Carlo color matching loss $w_i$3.

After scene editing (moving, recoloring light Gaussians), the pipeline discards the outdated radiance cache on non-emitters and employs full multi-bounce path tracing for forward or inverse rendering.

5. Path Tracing and Light Transport Implementation

Rendering leverages a GPU-accelerated OptiX-based path tracer, with all primitives stored as 2D or 3D Gaussians. Key algorithmic points include:

• Storage of all primitives in a spatial BVH, typically over ellipsoidal bounding shells for efficient culling (Condor et al., 2024, Byrski et al., 31 Jan 2025)
• Ray traversal resolves per-ray Gaussian intersections using robust quadratic solvers and collects all relevant attributes (normal, depth, emission, albedo).
• For emission, only emissive Gaussians ($w_i$4) contribute source terms at the termination of MC paths.
• Scattering and indirect illumination are recursively accumulated using cosine-weighted hemisphere sampling; non-emitters act as classical Lambertian or general BRDF surfaces.
• After pixel-level MC sampling, output is fed to a learned denoiser.

Performance optimizations include kernel pruning, clustering (merging similar Gaussians via KL divergence), early ray termination, and customized adjoints for efficient inverse/gradient-based rendering (Condor et al., 2024).

6. Comparison to Baselines and Empirical Results

EAG-PT produces edited and relit results with physically plausible global-illumination changes, robust shadows, and indirect lighting. In contrast:

• NeRF/3DGS: Relightings fail to propagate changes, as all transport is pre-integrated into the radiance field.
• 1-Bounce Methods: Only direct reflections are modified after edits; indirect effects remain incorrect.
• Mesh-based Inverse Path Tracing: While physically correct, mesh-based approaches suffer geometric artifacts (bleeding, faceting) and struggle to capture thin or complex structures that Gaussian proxies handle robustly (Yang et al., 30 Jan 2026).

On controlled synthetic benchmarks:

• Path tracing (EAG-PT) achieves PSNR ≈ 29 dB (vs. 16–19 dB for naïve/1-bounce), LPIPS ≈ 0.08, FLIP ≈ 0.18 after relighting.
• On real indoor scenes, EAG-PT attains PSNR ≈ 28.6 dB (vs. 26.4 dB for mesh path tracing) and lower perceptual error metrics; qualitative improvements include preservation of geometric detail and physically accurate scene edits (Yang et al., 30 Jan 2026).

7. Broader Context and Connections

The EAG-PT methodology generalizes prior Gaussian and kernel-based representations for both radiance fields (Condor et al., 2024, Byrski et al., 31 Jan 2025) and bidirectional scene/light transport modeling. By incorporating the emission channel and supporting full MC path tracing, it reconciles the strengths of neural scene representation (editability, compactness, lack of mesh artifacts) with those of physically based rendering (multi-bounce, variance reduction, correct indirect illumination).

Spatio-directional mixture models (Dodik et al., 2021) further elaborate on the statistical path guiding side, exploiting Gaussians in 5D for advanced direction-sampling strategies and emission-aware variance reduction. These approaches, when combined with explicit emission tagging, efficiently handle complex illumination, localized light sources, and high-correlation transport regimes.

A plausible implication is that EAG-PT's proxy model can serve not only for static scene relighting but also for XR content generation, rapid scene edits in design, and embodied AI tasks that require consistent physical interaction with lighting changes. Future research may extend kernel sets, path-guiding schemes, and neural optimization to further unify volume, surface, and transport modeling within a single emission-aware Gaussian proxy framework.

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Key References:

• "EAG-PT: Emission-Aware Gaussians and Path Tracing for Indoor Scene Reconstruction and Editing" (Yang et al., 30 Jan 2026)
• "Don't Splat your Gaussians: Volumetric Ray-Traced Primitives for Modeling and Rendering Scattering and Emissive Media" (Condor et al., 2024)
• "RaySplats: Ray Tracing based Gaussian Splatting" (Byrski et al., 31 Jan 2025)
• "Path Guiding Using Spatio-Directional Mixture Models" (Dodik et al., 2021)