RadioGS: Radiometrically Consistent Gaussian Surfels

• The paper introduces radiometric consistency by minimizing the residual between learned surfel radiance and its physically rendered counterpart.
• It leverages Gaussian surfels as surface-aligned scene representations to accurately model global illumination and indirect light transport.
• The framework achieves efficient relighting through a finetuning strategy, significantly reducing rendering times while preserving high-quality outputs.

Radiometrically Consistent Gaussian Surfels (RadioGS) is an inverse rendering framework that uses Gaussian surfels and differentiable 2D Gaussian ray tracing to enforce a physically based constraint called radiometric consistency. Its central target is a specific failure mode of Gaussian-based inverse rendering: radiance stored on primitives can fit observed camera rays while remaining incorrect along unobserved outgoing directions, which in turn corrupts indirect illumination, material decomposition, and relighting. RadioGS addresses this by minimizing the residual between each surfel’s learned outgoing radiance and its physically rendered counterpart, thereby coupling novel-view synthesis supervision with physically based rendering in a self-correcting feedback loop (Han et al., 2 Mar 2026).

1. Conceptual scope and motivating problem

RadioGS is formulated for inverse rendering under global illumination, where the goal is to recover geometry, materials, and lighting from images while accounting for indirect bounces between surfaces. The method identifies two common Gaussian-based strategies as insufficient: optimizing a learnable residual indirect-light term, and querying indirect radiance from Gaussian primitives pretrained for novel-view synthesis. The first is underconstrained; the second is supervised only toward observed camera directions, not toward the directions needed for inter-surface light transport. RadioGS therefore introduces radiometric consistency as a constraint on unobserved directions, not merely on camera rays (Han et al., 2 Mar 2026).

The paper explicitly claims three contributions: radiometric consistency as a physically based constraint enforcing consistency between surfel radiance and physically rendered radiance for unseen viewpoints; RadioGS as an inverse rendering framework that integrates this constraint using Gaussian surfels and 2D Gaussian ray tracing; and an efficient relighting method that finetunes surfel radiances under new illumination in a few minutes and renders in under 10 ms (Han et al., 2 Mar 2026).

The organizing idea is that a surfel’s stored radiance should not be a free appearance parameter. Instead, it should agree with the radiance predicted by the rendering equation under the current estimates of geometry, materials, visibility, direct light, and indirect light. The paper describes this coupling as a self-correcting feedback loop: image reconstruction constrains radiance toward camera directions, while physically rendered radiance propagates supervision toward unobserved directions (Han et al., 2 Mar 2026).

2. Gaussian surfels as the scene representation

RadioGS adopts Gaussian surfels, that is, the 2D Gaussian Splatting representation rather than generic volumetric 3D Gaussians. A surfel is represented by the transformation matrix

$$\mathbf{H} = \begin{bmatrix} s_u \mathbf{t}_u & s_v \mathbf{t}_v & \mathbf{0} & \mathbf{p} \ 0 & 0 & 0 & 1 \end{bmatrix},$$

where $\mathbf{t}_u,\mathbf{t}_v$ are principal tangential vectors, $s_u,s_v$ are tangent-plane scales, and $\mathbf{p}$ is the surfel center. Each primitive is thus a disk-like anisotropic Gaussian patch lying on a local tangent plane. In addition to geometry, each surfel has opacity $\alpha$, view-dependent radiance $c$ parameterized by spherical harmonics coefficients $\mathrm{SH}_j$, and optimizable material parameters including albedo and roughness (Han et al., 2 Mar 2026).

Rasterization follows alpha compositing over depth-sorted surfels: $$\mathcal{C}=\sum_{j=1}^{N} T_j \alpha_j c_j,\qquad T_j=\prod_{k=1}^{j-1}(1-\alpha_k),\qquad c_j=\mathrm{SH}_j(\omega_o).$$ This representation is explicitly surface-aligned. The paper’s rationale is that surfels are more suitable than unconstrained 3D Gaussian blobs for physically based inverse rendering, both because they are surface-like and because the same ray–splat intersection machinery can be used consistently in rasterization and ray tracing (Han et al., 2 Mar 2026).

The material model is built on the rendered surfel geometry rather than on latent volumetric appearance alone. This matters for RadioGS because radiometric consistency is enforced on surface-attached directional radiance, not on a generic appearance field. A plausible implication is that the framework treats Gaussian surfels as radiance carriers whose outgoing radiance is constrained by local reflectance and scene-level transport rather than by view synthesis alone.

3. Radiometric consistency and the rendering-equation residual

RadioGS adopts the rendering equation

$$L(x,\omega_o)=\int_{\Omega} f_r(x,\omega_o,\omega_i)L_i(x,\omega_i)(\omega_i\cdot n_x)\,d\omega_i,$$

and uses a simplified Disney BRDF

$$f_r(x,\omega_o,\omega_i)=f_d(x)+f_s(x,\omega_o,\omega_i) = \frac{a(x)}{\pi}+\frac{DFG}{4(n_x\cdot\omega_i)(n_x\cdot\omega_o)},$$

where $\mathbf{t}_u,\mathbf{t}_v$0 is diffuse albedo and $\mathbf{t}_u,\mathbf{t}_v$1 are the normal distribution, Fresnel, and geometry terms dependent on roughness $\mathbf{t}_u,\mathbf{t}_v$2. Incoming radiance is decomposed as

$\mathbf{t}_u,\mathbf{t}_v$3

with $\mathbf{t}_u,\mathbf{t}_v$4 denoting visibility, $\mathbf{t}_u,\mathbf{t}_v$5 direct light from an environment map, and $\mathbf{t}_u,\mathbf{t}_v$6 indirect illumination (Han et al., 2 Mar 2026).

The physically based outgoing radiance induced by the current surfel scene is written as

$\mathbf{t}_u,\mathbf{t}_v$7

The radiometric residual is then

$\mathbf{t}_u,\mathbf{t}_v$8

and the core loss is

$\mathbf{t}_u,\mathbf{t}_v$9

This is the defining principle of RadioGS: residual minimization of the rendering equation on the Gaussian surfels themselves, over sampled surfels and sampled outgoing directions that extend beyond observed camera rays (Han et al., 2 Mar 2026).

The paper treats this as supervision for unobserved radiative behavior. The learned surfel radiance $s_u,s_v$0 is constrained by observed-view reconstruction, while $s_u,s_v$1 propagates physically based supervision through indirect transport. This suggests that RadioGS occupies an intermediate position between view-synthesis-driven Gaussian representations and fully transport-driven inverse rendering.

4. Differentiable 2D Gaussian ray tracing and the training pipeline

To make radiometric consistency practical, RadioGS uses differentiable 2D Gaussian ray tracing. Given a ray from origin $s_u,s_v$2 in direction $s_u,s_v$3, the ray tracer returns

$s_u,s_v$4

where $s_u,s_v$5 is accumulated radiance and $s_u,s_v$6 is final transmittance, both obtained by gathering intersected Gaussian surfels and alpha-blending them exactly as in rasterization. The method then sets indirect radiance to $s_u,s_v$7 and visibility to $s_u,s_v$8. Implementation uses a CUDA/OptiX backend, a BVH built from two triangles enclosing each 2D Gaussian, an any-hit program that gathers up to $s_u,s_v$9 Gaussians per buffer chunk, depth sorting, and termination when transmittance drops below $\mathbf{p}$0. Differentiability is preserved by recasting rays to retrieve the same hit set and analytically computing gradients (Han et al., 2 Mar 2026).

The physically rendered radiance is estimated by Monte Carlo integration: $\mathbf{p}$1 with $\mathbf{p}$2 incident directions sampled uniformly over the hemisphere. The training-time residual is estimated by sampling $\mathbf{p}$3 surfels, then random outgoing directions on the hemisphere, and additionally directions toward camera viewpoints. The main implementation uses $\mathbf{p}$4, $\mathbf{p}$5, and $\mathbf{p}$6, so each iteration traces $\mathbf{p}$7 rays for radiometric consistency (Han et al., 2 Mar 2026).

Training is split into two stages. The initialization stage avoids full Monte Carlo transport while geometry is still unstable, and instead uses a split-sum approximation as a stable physical prior. Its objective is

$\mathbf{p}$8

The intended terms are reconstruction of learned radiance, reconstruction of physically rendered radiance via split-sum approximation, simplified radiometric consistency, depth distortion, normal-depth consistency, normal smoothing, and a mask or sparsity regularizer. Reconstruction uses a weighted $\mathbf{p}$9SSIM loss with weights $\alpha$0 and $\alpha$1. Initialization runs for 40K iterations with an environment cubemap of resolution 32; reported learning rates are $\alpha$2 for albedo, $\alpha$3 for roughness, and $\alpha$4 for the cubemap (Han et al., 2 Mar 2026).

The second stage reinitializes albedo, roughness, and cubemap, then optimizes with the full Monte Carlo radiometric-consistency objective: $\alpha$5 Here $\alpha$6 and $\alpha$7 are albedo and roughness smoothing losses, and $\alpha$8 is a light prior encouraging neutral diffuse illumination. This stage runs for 20K iterations. Total training time is about 60 minutes on an RTX 4090, roughly 30 minutes for initialization and 30 minutes for inverse rendering (Han et al., 2 Mar 2026).

5. Relighting and finetuning of surfel radiance

RadioGS includes a relighting strategy derived from the same radiometric-consistency principle. Under new illumination, previously learned surfel radiances are no longer correct. One option is to perform ray-traced physically based rendering at inference, following IRGS-style relighting: ray tracing queries normal, albedo, and roughness toward the incident direction, then uses a split-sum approximation to estimate indirect illumination. This is accurate but still incurs per-frame ray tracing and storage of incident-radiance information (Han et al., 2 Mar 2026).

To reduce rendering cost, the paper proposes finetuning-based relighting. Given a new lighting condition, everything except surfel radiances is frozen, and a few finetuning iterations are run using only $\alpha$9 under the new illumination. During this relighting finetuning, $c$0 and all other losses are discarded; the appendix states that the same learning rate is used only for the spherical harmonics coefficients. Geometry, material, and likely lighting are fixed, while only the per-surfel directional radiance is updated until it becomes consistent with the new illumination (Han et al., 2 Mar 2026).

The reported motivation is efficiency. After finetuning, relighted rendering can use direct surfel rasterization rather than repeated Monte Carlo shading. The paper reports a finetuning time of about 2 minutes and rendering cost below 10 ms per frame, specifically 5.902 ms for “Surfel finetuned” relighting on TensoIR. The relighting cost table reports 1090 ms for IRGS, 82.48 ms for SVG-IR, 38.64 ms for RadioGS PBR split-sum, 38.29 ms for RadioGS PBR finetuned, and 5.902 ms for RadioGS Surfel finetuned. The finetuned method uses 308.2 MB VRAM versus 1512.6 MB for ray tracing at $c$1, with memory increasing more for larger sample counts. The appendix notes a slight quality drop relative to ray-traced relighting because adapted surfel radiances can accumulate errors from estimated geometry and material, and because those finetuned radiances are themselves used as indirect-illumination sources (Han et al., 2 Mar 2026).

6. Empirical evidence and ablation results

RadioGS is evaluated on TensoIR and Synthetic4Relight using PSNR, SSIM, and LPIPS for novel-view synthesis, albedo, and relighting; normal MAE for geometry; and roughness MSE. On TensoIR, the reported results are 37.86 PSNR, 0.980 SSIM, and 0.027 LPIPS for NVS; 3.689 MAE for normals; 31.05 PSNR for albedo; and 32.09 PSNR, 0.953 SSIM, and 0.048 LPIPS for relighting. The finetuned relighting variant yields 31.41 PSNR, 0.948 SSIM, and 0.052 LPIPS. On Synthetic4Relight, RadioGS reports 34.98 NVS PSNR, 0.011 roughness MSE, 30.69 albedo PSNR, and 34.87 relight PSNR (Han et al., 2 Mar 2026).

The paper also introduces an additional indirect-illumination dataset rendered from Blender scenes using Cycles at 256 spp plus denoising, because existing benchmarks lack ground-truth indirect illumination. On this evaluation, IRGS obtains 24.22 indirect PSNR, SVG-IR 30.97, RadioGS without $c$2 30.10, and RadioGS 32.88. This directly supports the paper’s main thesis that the gains are not limited to final image metrics but extend to indirect transport itself (Han et al., 2 Mar 2026).

Ablations are closely aligned with the method’s central claim. Setting $c$3 degrades NVS from 37.86 to 35.82, albedo from 31.05 to 30.82, and relighting from 32.09 to 31.69. Detaching gradients from either $c$4 or $c$5 reduces performance, which the paper interprets as evidence that both the physically rendered branch and the learned-radiance branch are necessary. Replacing the proposed physically guided initialization with ordinary NVS initialization yields 37.43 NVS PSNR, 30.34 albedo PSNR, and 31.66 relight PSNR, all below the full method. Appendix ablations comparing split-sum only, RT precompute, RT without differentiability, and the full method show the full method performs best, supporting the need for dynamic differentiable ray tracing. Under scarce-view supervision, reducing training views to 25% causes RadioGS indirect PSNR to drop only from 32.88 to 32.71, whereas RadioGS without $c$6 drops from 30.10 to 27.89. The paper presents this as direct evidence that radiometric consistency adds supervision unavailable from view-based reconstruction alone (Han et al., 2 Mar 2026).

7. Position within Gaussian-surfel research and stated limitations

RadioGS builds on a broader shift from volumetric Gaussian ellipsoids to surface-aligned Gaussian surfels. “High-quality Surface Reconstruction using Gaussian Surfels” introduced an explicit Gaussian-surface representation by flattening 3D Gaussian points into 2D ellipses and focused on surface alignment, depth-normal consistency, and volumetric cutting, but not on radiometric consistency (Dai et al., 2024). “GauS-SLAM” used 2D Gaussian surfels for dense RGB-D SLAM and emphasized multi-view geometric consistency, surface-aware depth rendering, and local-map visibility isolation; its consistency machinery is primarily geometric and only includes a simple per-frame linear exposure compensation $c$7 (Su et al., 3 May 2025).

Other neighboring works move toward physics-based surfel rendering through different routes. “Differentiable Light Transport with Gaussian Surfels via Adapted Radiosity for Efficient Relighting and Geometry Reconstruction” formulates an adapted radiosity system over Gaussian surfels in spherical-harmonics coefficient space, with soft visibility and semi-opaque transport, which suggests a related but distinct approach to physically constrained surfel radiance (Jiang et al., 23 Sep 2025). “GOGS” combines 2D Gaussian surfels with a Disney BRDF, split-sum approximation, Monte Carlo importance sampling, differentiable 2D Gaussian ray tracing, and a learned specular compensation term for glossy inverse rendering, but it does not present explicit radiometric calibration or a rendering-equation residual on surfel radiance as RadioGS does (Yang et al., 20 Aug 2025). This suggests that RadioGS occupies a specific niche within Gaussian-surfel research: it is neither a purely geometric surfel method nor a full coefficient-space radiosity solver, but an inverse rendering framework centered on residual minimization between learned and physically rendered surfel radiance.

The paper’s clearest stated limitation is that the current method supports mostly dielectric materials. Its BRDF assumes diffuse albedo plus a Disney-style specular lobe parameterized by roughness, and the conclusion points to anisotropic or highly reflective materials as future work. Additional limitations are also explicit or implicit: finetuned relighting exhibits a slight quality drop relative to ray-traced relighting; the physically based estimate is based on single-step Monte Carlo sampling with a finite number of secondary directions; accuracy depends on estimated geometry and material quality; and the method still requires a substantial optimization process, although much less than many NeRF-based approaches (Han et al., 2 Mar 2026).