Augmented Radiance Field: A General Framework for Enhanced Gaussian Splatting
Authors: Yixin Yang
Bojian Wu
Yang Zhou
Hui Huang
Venue: ICLR 2026 Poster (2026)
Keywords: Gaussian Splatting
Novel View Synthesis
Decoupled Radiance Fields
View-dependent Opacity
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: We propose a novel enhanced Gaussian kernel that explicitly models specular effects through view-dependent opacity, surpassing state-of-the-art NeRF methods in rendering quality.

Abstract: Due to the real-time rendering performance, 3D Gaussian Splatting (3DGS) has emerged as the leading method for radiance field reconstruction. However, its reliance on spherical harmonics for color encoding inherently limits its ability to separate diffuse and specular components, making it challenging to accurately represent complex reflections. To address this, we propose a novel enhanced Gaussian kernel that explicitly models specular effects through view-dependent opacity. Meanwhile, we introduce an error-driven compensation strategy to improve rendering quality in existing 3DGS scenes. Our method begins with 2D Gaussian initialization and then adaptively inserts and optimizes enhanced Gaussian kernels, ultimately producing an augmented radiance field. Experiments demonstrate that our method not only surpasses state-of-the-art NeRF methods in rendering performance but also achieves greater parameter efficiency. Project page at: \url{https://xiaoxinyyx.github.io/augs}.

Published as a conference paper at ICLR 2026
AUGMENTED RADIANCE FIELD: A GENERAL FRAME- WORK FOR ENHANCED GAUSSIAN SPLATTING
Yixin Yang'
Bojian Wu? VCC, CSSE, Shenzhen University
Yang Zhou
Hui Huang'
Tencent Games
GT
Ours
Ours sh-2
Ours sh
GF
MCMC
GT
Dilluse
Specular
MCMC
Figure 1: We propose an augmented radiance field, which leverages Gaussian kernels with view- dependent opacity to accurately model specular highlights in the scene (left). It can be seamlessly plugged into existing Gaussian Splatting- methods as a post enhancement, and notably, even using second-order spherical harmonics (sh=2) is sufficient to capture complex illumination (right).
ABSTRACT
Due the real-time rendering performance, 3D Gaussian Splatting (3DGS) has emerged as the leading method for radiance field reconstruction. However, its reliance on spherical harmonics for color encoding inherently limits its ability to separate diffuse and specular components, making challenging to accurately rep- resent complex reflections. To address this, we propose a novel enhanced Gaus- sian kernel that explicitly models specular effects through view-dependent opac- ity. Meanwhile, we introduce an error-driven compensation strategy to improve rendering quality in existing 3DGS scenes. Our method begins with 2D Gaus- sian initialization and then adaptively inserts and optimizes enhanced Gaussian kernels, ultimately producing strate that our method not only surpasses state-of-the-ar NeRF methods in ren- dering performance but also achieves greater parameter efficiency. Project page at:
augmented radiance field. Experiments demon-
github. io/augs
INTRODUCTION
Novel view synthesis, core task in computer vision and graphics, aims to generate photorealistic images from unobserved viewpoints via 3D scene reconstruction. While Neural Radiance Fields (NeRF) Mildenhall et al. (2020) have significantly advanced rendering quality to this problem, they suffer from slow optimization and rendering. The recent introduction 3D Gaussian Splat- ting (3DGS) Kerbl et al. (2023) addresses these issues through explicit representation based on
"Corresponding author.

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Published as a conference paper at ICLR 2026
anisotropic 3D Gaussians and differentiable rasterization, enabling real-time rendering while main- taining high visual fidelity. These capabilities have led to the rapid adoption of 3DGS across a variety of downstream applications, such as autonomous driving Huang et al. (2024b): Zhou et al.
2024), VR Jiang et al. (2024a), and 3D generation Tang et al. 2024): Ren et al. (2023).
However, 3DGS still faces challenges in rendering scenes with complex reflections. Recent advances
address this issue from multiple directions. Yu et al.) (2024); Yan et al. (2024); Liang et al. (2024);
Song et al. (2024) focus on mitigating aliasing artifacts. Xie et al. (2025): Zhang et al. (2025)
enhance illumination modeling by integrating environmental lighting. Held el al. (2025); |: Liu el al.
livghnnnentalighhinnng
(202)) employ shape-varrie variant primitives beyond smooth Gaussians. Lu al. (2024); Zhang et al. (024):Roto Bulò et al. (2024); Kheradmand et al. (2024) propose systematic densification strategies
to replace heuristic approaches. Despite these advances, existing Gaussian-based methods still fall short of the synthesis quality achieved by leading NeRF variants, such as Barron et al. (2023).
particularly in scenarios requiring the recovery of figh--high-reequeney detail.
3DGS employs third-order spherical harmonics (SH) to model view-dependent radiance, thereby inherently limiting its ability to represent the radiance field. Low-order SH can only capture smooth color transitions and are incapable of reproducing the sharp specular highlights generated by glossy surfaces. Adopting higher-order spherical harmonic coefficients will lead to exponential growth in memory consumption, prolonged training time, and instability in the results of this ill ill-posed prob- lem. On the other hand, the SH's global definition across the entire sphere limits their efficiency for color encoding, as surface Gaussians are only observable within their outward-facing hemisphere. This mismatch is even more severe in view-dependent cases under directional visibility constraints. Furthermore, SH inherently fail to decouple diffuse and specular components in the rendering equa- tion, complicating material reconstruction and relighting from optimized results.
To compensate for the limitations of spherical harmonics, we propose an augmented radiance field, a method for further improving rendering quality based on existing 3DGS scenes, which can be integrated into any splatting-
framework as ppst-enhancement. Since specular highlights are distributed non-uniforlly across the scene (and are usually very sparse), assigning additional param- eters to every primitive leads to significant redundancy. Therefore, we introduce an approach that represents the diffuse and specular components using distinct primitives. Specifically, we develop new Gaussian kernel with view-dependent opacity inspired by Phong shading Phong (1975), which is adaptively integrated into an optimized scene to calibrate regions with reconstruction errors. By adjusting the maximum extent and sharpness of the opacity lobe, this Gaussian kernel is capable of modeling various types of specular highlights, while the complex reflective light distribution on object surfaces can be reconstructed through the superposition of multiple such kernels.
However, allocating and optimizing such enhanced kernels is tricky. We further develop compen- sation strategy for scenes that have already been optimized. More specifically, given a pre-trained radiance field of 3DGS, we initialize the enhanced Gaussian kernels using screen-space loss-based strategy. Initially, 2D Gaussian kernels are sampled in screen space, and only the parameters of these additional 2D Gaussians are optimized to minimize the rendering loss. We then introduce an inverse projection method that maps 2D Gaussians from image space to world space- essentially the inverse of Gaussian Splatting. This densification adaptively allocates Gaussians to regions with high residuals, which typically correspond to areas where the reflective light distribution is complex and challenging to reconstruct using spherical harmonics, and can even capture fine specular spots at the pixel level. Finally, the newly incorporated Gaussians are jointly optimized with the original Gaussians of the scene, resulting in an enhanced radiance field.
Comprehensive experiments are conducted on the widely-used datasets, including Mip-NeRF 360 Barron et al. (202I). Tank & Temples Knapitsch et al.) (2017), Deep Blending Hedman et al. (2018), and NeRF Synthetic Mildenhall Minthetic/Mildenhaalll et al. (2020), using the 3DGS and 3DGS MCMC KCeCakherad Kherad- mand et al. 2224) frameworks, respectively. The results indicate that replacing a subset of Gaussians in the scene with Gaussians featuring dewedeepnddent opacity can significantly enhance render- ing quality. Remarkably, whether employing second-order or third-order spherical harmonics, our approach consistently outperforms the current state-of-the-art NeRF method BBrrron al. (2023), while incurring virtually no loss in real-time rendering speed. Our work demonstrates that Gaussian Splatting- based methods still possesses significant potential for rendering quality improvement.
Our contributions can be summarized as follows:
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We propose an enhanced Gaussian kernel with view-dependent opacity for modeling the specular component. Complex reflections from multiple light sources can be reconstructed by superimposing the new kernels.
We introduce novel error-driven method that adaptively and accurately inserts supple- mentary Gaussians into a scene to improve rendering quality.
As a Gaussian Splatting- method, our augmented radiance field outperforms the state- of-the-art NeRF methods while reducing the reliance on higher-order spherical harmonics, achieving both high quality and efficiency.
2 RELATED WORK
To align with our goals, we will focus our discussion on novel view synthesis, especially how to further improve the rendering quality of specular surfaces. For applications of NeRF and 3DGS in other domains, we refer readers to Tewari et al. (2022) Fei et al. (2024).
Early attempts NeRF, such Zhang et al. 2021 Boss et al. (2021), aim address this ill ill-posed problem by decomposing the reecularreflectance reflectance with the estimated BRDF, Guo et al. (2022) lever- ages separate neural radiance fields model the transmitted and reflected components, respectively. Kopanas et al. (2022) proposes neural warp field that enables efficient point-splatting based ren- dering of complex specular effects. Recently, directional encoding has been proposed to improve the rendering quality in the presence of reflections. Their key idea is to model radiance as direction- dependent function. For example, Verbin et al.] (2022) parameterizes the outgoing radiance with the Integrated Directional Encoding (IDE) of the reflective radiance. Ma et al. (2024) further in- troduces a learnable Gaussian Directional Encoding (GDE) to better model view-dependent effects under near-field lighting conditions. Concurrently, Wu et al. (2024) proposes Neural Directional Encoding (NDE), a novel opatio-spatial parameterization that cone-traces a spatial feature grid to encode near- field reflections and enables modeling multi-bounce reflections. However, since these approaches all build upon NeRF, they also inherit its fundamental limitations, notably the trade-off between high rendering quality and poor computational burden.
Recent advances in Gaussian- rendering have introduced innovative approaches to handling complex lighting and reflections. (Yang al. (2024) proposes Spec-Gaussian, which utilizes anisotropic spherical Gaussian for modeling view-dependent appearance. [aiag et al. (2024b) en- hances neural rendering of 3D Gaussians for reflective scenes by decomposing the appearance into diffuse colors, direct reflections, and residual term for complex reflections through a novel shading function. WW al. (0025) employs deferred shading to decouple scene texture from illumination in Gaussian splatting, achieving more accurate specular modeling. Building on this, Ye et al. (2024) addresses the key challenge of environment map reflections through an improved deferred shad- ing approach, but requires precise surface normals and suffers from discontinuous gradients. Zhu let al. (2024) presents unified framework that combines SDF-aided Gaussian splatting for relight- ing optimization with GS- -SSiguided SDF enhancement for high-quality geometry reconstruction. Tang & Cham (2024) introduces a continuous local illumination field represented by factorized tensors, enabling optimized incident lighting on 31) Gaussians. [Xie et al. (2025) proposes an explicit 3D) representation using Gaussian primitives to capture environmental reflections, blending multiple Gaussians during rendering and optimization. Zhang al./ (2025) improves view-dependent effects by directional encoding for 2D Gaussian splatting, leveraging deferred rendering and lighting fac- torization. Fang et al. (2025) develops a novel framework that integrates NeRF an assistant to 3DGS, and addresses several limitations of 3DGS while enhancing its performance. Incorporat- ing view-dependent opacity, Vlasic et al.) (2003) enables modeling of complex reflective surfaces. Recently, Nowak et al. (2025) enhances the opacity representation of each Gaussian primitive by incorporating a symmetric matrix.
However, existing Gaussian-based approaches still cannot decouple diffuse and specular compo- nents in the rendering equation due to the inherent limitations of spherical harmonics. Recently, Liu et al. 2025) advances the representation of material properties by replacing SH with Spherical Beta (SB) functions. Although decoupled modeling is achieved, the beta kernels fall short in representing very complex reflections. Inspired by this work, we propose to enhance 3D Gaussians by explicitly modeling specular components that can be further overlaid to form intricate lobes, thereby providing significantly greater flexibility for handling specular surfaces under complex lighting conditions.
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Error-driven 2D Clussian Training
Inverse Gaussian Splatting
Joint Optimization
Pretrained 3D Gaussians
Background Sepuration
WPCA
Scaling Calibration
Rendering
Opscity Lohe
Optimizing in Image Space
Back-projection
2D Gaussians
3D
3D Gaussians
a. T.
Optiizoblle Parrcctos
Reference
Figure 2: Our post-enhancement method for Gaussian Splatting. We begin with image-space re- finement using 2D Gaussians to reconstruct regions exhibiting significant errors (left). Leveraging geometric information from depth maps, we then project these 2D Gaussians into world space (mid- dle). The newly added Gaussians feature optimizable view-dependent opacity and are jointly opti- mized with existing Gaussians to recover challenging view-dependent color (right).
3 AUGMENTED RADIANCE FIELD
We address the limitations of spherical harmonics by equipping Gaussian kernels with a learnable, view-dependent opacity function adapted from the Phong shading paradigm Phong (975). By com- positing multiple such kernels, our method enables high-fidelity reconstruction complex radiance distributions. Furthermore, we introduce a systematic initialization strategy. As shown in Fig. 2 our method contains three main steps: 2D Gaussians are first sampled and optimized in image space; subsequently, they geometrically back back-projected into 3D space; finally, while keeping most of the original Gaussian parameters fixed, we leverage the differentiable rendering pipeline to jointly refine the supplementary kernels, resulting in augmented radiance filed. In the following, we first introduce our model of view-dependent opacity, followed by the three steps of our framework.
3.1 VIEW-DEPENDENT OPACITY
In the Phong reflection model, the specular component is determined by the viewing direction, the reflection direction, and the material's shininess. Building on this concept, define new view-dependent, transparent Gaussian kernel that can model reflectance lobes of various shapes. Specifically, the kernel's opacity is strictly limited certain range that peaks when the viewing direction aligns with the lobe's is central orientation. Then, the spherical distribution of transparency of this specialized kernel formulated as:
a() =a (c00 (max (0, min (4, 3)) +
exp(3)
Here, a is the opacity attribute of the 3D Gaussian, denotes the angle between the view direction and the central orientation of the opacity lobe, T' controls the angular span of the lobe, and 3 mod- ulates its sharpness. Note that we employ half-period cosine function to model the opacity lobe, which serves
variant of the Phong model. Our function exhibits longer tail and smoother decay in opacity, resulting in more stable gradients; see Fig. B for parameter-dee trreedeer-dependent variations in lobes. Each supplementary Gaussian kernel adds 5 learnable parameters to the default 3DGS con- figuration. Crucially, the differentiability of this formulation enables gradient-based optimization of these parameters, as detailed Section 3.4
The flexibility of the opacity lobe empowers these Gaussians to approximate specular lobes gener- ated by surfaces with varying roughness under directional illumination. critical feature is that the transparency of each kernel diminishes to zero as the angular deviation between the viewing direc- tion and the lobe orientation increases, ensuring minimal impact on viewpoints outside the lobe's influence. This property guarantees that enhancing specular components in specific directions incurs no unintended artifacts. By aggregating multiple kernels with heterogencous opacity distributions, method effectively reconstructs intricate radiance fields.
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T=1
T= 3/4
T= 1/2
T= 1/4
1.0
/= 1.5
$=0.
0.5
x= 1.5
0.00
n/4
xd2
3n/4
0
x/4
m/
3rd
x//
12/
3x/4
m//
x/2
3n/4
n
Figure 3: Inspired by classical Phong shading, we model fiwwdeppendent opacity with a cosine- weighted function whose shape controlled by two parameters: 3, which governs the lobe's sharp- ness, and T, which determines its angular extent. Along with the central orientation of the lobe, each new kernel introduces 5 learnable parameters standard Gaussian primitive.
3.2 ERROR-DRIVEN 2D GAUSSIAN TRAINING
To enable our view-dependent Gaussian kernels to reconstruct complex specular radiance effectively, proper initialization critical. We propose novel densification strategy that first samples and optimizes 2D Gaussian kernels in image space, and then backprojects them into world space.
Optimization in Image Space. After completing standard 3DGS training, we obtain rendered image sets I = [1 and corresponding depth maps DD [D; d for all training views. For each rendered image, we overlay supplementary 2D Gaussians and optimize their parameters using differentiable rasterizer, which emulates 3DGS's differentiable rendering. The optimization employs the same loss function as 3DGS, with key difference; we use the pre-rendered image 1; as fixed background rather than uniform one. Each 2D Gaussian primitive is defined by parameters:
{x, a, c, d,, 8,
(2)
where x denotes image-space coordinates, controls the scale along the two principal axes, spec- ifies the rotation angle between the primary axis and the image y-axis, a represents opacity, c is the color, and d indicates depth for rendering-orde sorting. During optimization, we update each primitive's 's depth via nearest-neighbor sampling on D; using its current coordinates.
Prior to training, predefine the total number of supplementary Gaussians for the scene. Allo- cation across views is proportional to their respective rendering loss values, with higher-loss views receiving kernels. During the optimization of 2D kemels for each training image, period- ically augment the kernel set by introducing 20% new primitives at fixed intervals, while pruning those primitives that exhibit excessive transparency or occupy insufficient pixels. When initializ- ing new Gaussian kernels, we adopt conservative strategy: novel Gaussians are assigned minimal initial opacity, with color sampled from the current rendered image at their mean positions. This de- sign mitigates the perturbation introduced by newly added kernels. The spatial distribution of new kernels is determined through multinomial sampling across pixel coordinates, where the selection probability for each pixel follows:
p(u, v) x [(1 ASSTM) L1 (u,,)) + ASSIM r))²
Here (u, v) denotes the image space coordinate, The composite loss combines the LI and structural similarity metrics, using the same weights as in the original 3DGS paper.
Depth Map Rendering. To ensure correct rendering order for 2D Gaussian primitives, depth maps must be rendered for each training image. These maps are subsequently utilized to derive world-space coordinates during projection. Unlike geometric reconstruction methods [Dai et al. (2024); Huang et al. (2024a), where 3D Gaussians are approximated as planar surfaces with depths computed via ray-plane intersections, we avoid imposing flattening regularizations. Instead, we adopt ray-tracing- positions at which 3D Gaussians attain maximal response along camera rays. As demonstrated in Huang et al. (024a)), median depth, compared expected depth, yields superior geometric fidelity due to its robustness to outliers. We compute depth values at points where transmittance first drops below 0.5 during rasterization.
approach Moenne-Loccoz et al. (2024) and render depth maps as the
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3.3 INVERSE GAUSSIAN SPLATTING.
After obtaining the optimized 2D primitives on each training viewpoint, these supplementary Gaus- sians need to be back-projected into world space to serve as high-quality initializations for new 3D Gaussians. As shown in Fig. 2 (middle), this process involves three key steps: foreground- background separation through point cloud clustering, determination of 3D Gaussian rotations and scales via Weighted Principal Component Analysis (WPCA) Delchambre (2015), and final calibra- tion of the scales.
In object boundary regions, 2D Gaussian kernels often simultaneously cover pixels from both the foreground and background. Without proper grouping and filtering of these regions, subsequent pro- jection would yield suboptimal results. We first compute the 3D coordinates for all pixels covered by a 2D Gaussian kernel, and then perform hierarchical clustering using single-linkage merging [John-] son (1667 to group the points. The initial distance threshold for grouping is set proportionally to the depth of the Gaussian center. Priority is given to clusters containing at least three elements that cover the Gaussian center's 'ss pixel; if none are available, the largest cluster meeting the minimum three-element requirement is selected. When clustering fails, the distance threshold is gradually increased to retry partitioning. The three-element minimum requirement ensures sufficient data for subsequent computation of the object-space coordinates to derive three mutually orthogonal princi- pal axes and their corresponding directional variances.
To determine the 3D Gaussian parameters, we adopt Weighted PCA, with the 2D Gaussian distri- bution values as weights for the pixel coordinates. The three principal axes derived from WPCA directly constitute the rotation matrix of the 3D Gaussian kernel, which can be equivalently parame- terized as a quaternion, thereby fully defining the rotational attributes. For positional determination, two distinct strategies are employed based on prior grouping outcomes. In the first scenario, where the central pixel successfully passes the filtering process, its world-space coordinates can be directly derived from the depth value and the image-space coordinates of the central pixel. In typical case where the central pixel fails screening, the depth value is recalibrated as the weighted average of the depths of all filtered pixels, with weights derived from 2D Gaussian distribution. Subsequently, the central pixel coordinate is combined with the depth value to compute the world-space position.
The scaling factor is the last geometric parameter remaining undetermined for the 3D Gaussian ker- nels. Although WPCA calculates variances along the three principal axes, directly using these values as the variances for the 3D Gaussians introduces errors. It arises from the finite sampling density on the screen, from points discarded during clustering, and from perspective-projecte To minimize back-projection errors, unified scaling coefficient is applied to all three variances. Revisiting 3DGS's ' forward projection process, the projected 2D covariance matrix in NDC space for a 3D Gaussian kernel expressed as:
foreshortening.
Σen - JW JSW
where J E R2x3 denotes the Jacobian matrix as the projective transformation's 's affine approxima- tion, W represents the world-to-view transformation matrix, and R the rotation matrix of the Gaussian kernel. The diagonal matrix S encapsulates the Gaussian's 's scaling factors, defined as S k diag(o 02, 03), where }o,} are standard deviations computed via WPCA, and k is the target scaling coefficient. Our objective is to minimize the Frobenius norm:
min EED E2pl1r
where ΣeD corresponds to the target 2D Gaussian's covariance matrix in image space. For con- venience, we define Q := /22 where all elements of Q are known. Expanding formulation equation 5 yields the solution for k that minimizes the Frobenius norm:
Ei Lig 11Q
k:
(6)
Initialization of Opacity Lobe. Following the projection of 2D Gaussians into world space, the opacity lobe of each primitive requires initialization. The primary orientation is set directly to the unit vector pointing from the Gaussian's centroid to the camera. However, initializing parameters T' (controlling the lobe's 's maximum angular span) and (modulating specular sharpness) presents

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non-trivial challenge. Since the shape of the specular lobe cannot be predetermined, its values ultimately refined through subsequent multi-view optimization. To ensure that each supplemented kernel is visible to multiple cameras, the initialization of T' is based on the spatial distribution of training viewpoints. For each newly added primitive, we first apply view frustum culling to identify the set of cameras C; capable of observing it. For each camera in C, (excluding the training camera associated with the primitive), the angle between the viewing vector and the lobe orientation is computed. Then, the minimum angle 0, is selected, and I"' is initialized as c0//T, m, where c is constant scaling factor. This strategy adaptively initializes T according to the density of surrounding viewpoints. For B. we simply apply zero initialization.
Geometry-Independend Independent Parameters. For parameters unrelated to geometric properties, the base color and opacity of the primitives are initialized to their corresponding 2D primitive counterparts. Higher-order spherical harmonic coefficients undergo zero-initialization.
Geometry-
3.4 JOINT OPTIMIZATION
After the projection of all 2D Gaussian kernels into world space. the newly added view-dependent Gaussians undergo joint optimization with pre-existing kernels. During the projection phase, precise parameters for the view-dependent opacity lobes remain temporarily undetermined. To enable mul- tiple projected Gaussians to collectively represent surface-exitan radiance, multi-view constraints are leveraged via photometric error to refine T. 3, and opacity orientation across all new primi- tives. Furthermore, during image-space optimization, the rendered outputs of the original Gaussians are treated as background, assuming they lie behind the newly added Gaussians in depth order. After projection, the supplemented primitives become embedded within the original point cloud, disrupting prior depth hierarchies. Notably, since depth maps are rendered when cumulative trans- mittance decreases below 0.5, numerous pre-existing Gaussians exhibit shallower depths than the newly added ones. To mitigate over-occlusion of Gaussians, the opacity of the original kernels is made optimizable while freezing their other attributes. For the newly added Gaussians, full param- eter optimization is applied to facilitate photometric refinement. We set the number of iterations proportional the size of the training set to ensure that, across scenarios, each additional Gaussian kernel is sampled approximately the same number of times.
4 EXPERIMENTS
Our method is applicable to most 3DGS-based algorithms. In this work, we mainly evaluated our approach using 3DGS and 3DGS-MCMC Kheradmand et al. (2024) frameworks on a variety of widely used datasets, including Mip-NeRF 360 Barron et al. (2021), Tank & Temples Knapitsch ett al. (207)) Deep Blending Hedman et al. (2018), and NeRF Synthetic Mildenhall et al. (2020).
We compared our results with state-of-the-arr implicit (Zip-NeRF Barron et al. (2023) and explicit (DBS Liu et al. (2025)) methods. In addition, two recent 3DGS-based methods that specialize in
view-dependent reflections, VoD-3DGS Nowak et al. (025 and Opec-Gaussian Yang et al. (024 are included for more comprehensive comparisons.
4.1 IMPLEMENTATION DETAIL
Following the 3D Gaussian Splatting framework, implement 2D version of the differentiable Gaussian rasterizer. In the image space, we augment each rendered image by setting it as the back- ground and adding 2D Gaussians further reduce the loss. The ratio of newly added Gaussians to existing ones is fixed at 10%, and they are allocated proportionally to each viewpoint based on the loss values. During optimization of each rendered image, 20% of Gaussians are added incrementally every 200 iterations, and those with insufficient opacity or excessively small scales are pruned. Af- ter sufficient kernels were incorporated, an additional 1,000 fine-tuning steps were performed. The projection of 2D Gaussians into world space is executed in parallel on the CPU. During the joint op- timization phase, the number of iterations is set to 30 times the size of the training dataset. The Adam optimizer Kingma (2014) is employed to optimize the additional Gaussians, while SparseAdam is exclusively applied to update the opacity of visible original Gaussian primitives. Further details regarding hyperparameter configurations are provided in Appendix of our supplemental material.
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Mip-NeRF 360
Temples
Deep Blending
NeRF Synthetic
Method
PSNRYSSIM;LPIRS,
Mip-NeRI 360
27.69 0.792 0.237
22.22 0.758 0.257
29.40 0.900 0.245
33.25
0.962 0.039
Zip-NeRF
28.54
0.828
0.189
33.10
0.971 0.031
3DGS
27.21
0.815 0.214
23.14
0.841
0.183
29.41
0,903
0.243
33.31
0,969
0.037
VoD-3DGS|L]
27.79
0.818 0.213
23.91
0.860
0.160
29.84
0.908
0.240
33.69
0.971 0.030
Spec-Gaussian
28.18
0.835 0.176
23.77
0.855
0.166
29.53
0.905
0.241
34.19
0.971
0.028
3DGS-MCMC
28.29
0.840
0.210
24.29
0.860
0.190
29.67
0.895
0.320
33.80
0.970
0.040
DBS (30k)
28.60
0.844
0.182
24.79
0.868
0.148
30.10
0.910
0.240
34.64
0.973
0.028
Ours (3DGS,sh=3)
28.39
0.834
0.184
23.90
0.856
0.158
29.90
0.903
0.237
34.02
0,969
0.031
Ours (MCMC,sh=2)
28.89
0.848
0.171
25.04
0.871
0.146
30.33
0.909
0.235
34.03
0.970 0.030
Ours (MCMC.sh=3)
28.96
0.849
0.170
25.06
0.872 0.144
30.22
0.909 0.236
34.35
0.971 0.029
Table 1: Qualitative comparison across Mip-NeRF 360, Tanks&Temples. Deep Blending, and NeRF Synthetic. All scores for the baseline methods are directly taken from their papers, when available. Note that we use the VoD-3DGS variant with higher memory consumption and the anchor-free Spec- Gaussian, as recommended by the authors; for DBS, we adopted the data stopping at 30k iterations for fairness. Our method consistently outperforms state-of-the- explicit and implicit approaches under the MCMC framework, whether utilizing second- or third-order spherical harmonics.
Fig. 7 further visualizes the rendered Gaussians before and after world-space projection, as well as the LI distance between the renderings before and after radiance field enhancement.
4.2 RESULTS AND ABLATION
Novel View Synthesis. Comprehensive evaluations are conducted 9 Mip-NeRF 360 scenes, 2 Tanks and Temples scenes, 2 Deep Blending scenes, and 8 objects from the NeRF Synthetic dataset, matching 3DGS in resolution and testing protocols. Evaluation metrics include Structural Similarity Index Metric (SSIM), Peak Signal-to-Noise Ratio (PSNR), and Learned Perceptual Image Patch Similarity (LPIPS). While the original 3DGS method lacks control over the total number of Gaussians. our supplementary Gaussians increase the overall count relative to the baseline. Under the 3DGS-MCMC framework, we maintain the total number of Gaussians (original plus newly added) equal to that in the official implementation. For the NeRF Synthetic dataset, we fix the total count of Gaussian primitives at 300,000. We compare rendering quality using second- and third-order spherical harmonics (SH).
Results summarized in Table demonstratee that our Gaussian supplementation strategy significantly enhances rendering quality across existing GS scenes. It is worth noting that, within the MCMC framework, although second-order SH (i.e., sh=2) reduce the parameter count by 21 per primitive compared to third-order SH (sh=3), they still achieve comparable rendering quality (see Table 15 in Appendix D forrr memory comparisons). Both approaches outperform the state-of-the-an implicit method Barron et al. (023). demonstrating that our method facilitates the adaptation of Gaussian splatting to low-end hardware platforms. Compared with DBS Liu et al. (2025), the state-of-the-ar explicit approach, our method outperforms it on real-world datasets but slightly lags behind on the NeRF Synthetic dataset. This discrepancy stems from the simplicity of synthetic environments, in which each scene contains only a single object and exhibits limited illumination and material vari- ation. In contrast, our method leverages these advantages in complex real-world scenarios through a flexible strategy for superposing opacity lobes. Note that, to ensure fair comparison, we used the data at 30k iterations from DBS Liu et al. (2025), as their full model monitored test-set metrics to achieve the best performance, whereas most other baselines used fixed number of iterations. Compared with specular- methods, VoD-DDGS and Upec-Gaussian, our method achieves bet- ter results on almost all datasets. We further compare the training time, memory usage, and FPS in the supplementary material.
Fig. and Fig. g (Appendix D) present qualitative analysis, which reveals restored specular high- lights in challenging regions and marked improvements for indoor scenes with complex material compositions. Additionally, we observe that supplementary Gaussians effectively enhance under- reconstructed distant regions in outdoor scenarios. See OppendixD]for qualitative metrics per scene.
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Ground Truth
3DGS-MCMC
(MCMC, sh-3)
Figure 4: Qualitative comparison across real captured scenes. Benefiting from the newly designed Gaussian kernel with view-dependent transparency and the rendering loss-driven initialization, our approach surpasses all state-of-ther of-tte-artttttt explicit and implicit methods on real-world datasets.
Table Impact of the ratio of enhanced Gaus- Table 3: Ablation study on Mip-NeRF 360
sians with the total primitive No. unchanged.
dataset. Optimizing the orientation and shape of the opacity lobe achieves render quality unattain- able by solely supplementing with Gaussians without niw-ddependent opacity.
Mip-NeRF 360 Tanks& Temples
Ratio Stage
PSNR1
SSIM PSNR SSIM
basic
28.31
0.846
24.48
0.867
5%
Methods
PSNR1 SSIM LPIPS !
augmented
28.88
0.849
24.95
0.872
3DGS- -CMM
28.33
0.845
0.176
10%
basic
28.33
0.845
24.53
0.867
Ours(MCMC), w/o opacity lobe
28.45
0.847
0.171
augmented
28.96
0.849
25.06
0.872
Ours(MCMC). 0.5 Ours(MCMCC,
28.60
0.848
0.170
basic
28.30
0.845
24.52
0.867
28.93
0.849
0.170
15%
augmented
28.94
0.849
24.99
0.871
Ours(MCMC), model
28.96
0.849
0.170
Analysis Primitive Ratio. To evaluate the impact of the ratio of additional Gaussian kernels on the reconstruction, we conducted experiments using the MCMC framework. Specifically, we maintained constant total number of Gaussians while varying the ratio between newly added and original kernels. Tests on Mip-NeRF 360 and Tanks & Temples (Table have demonstrated optimal rendering quality when supplementary Gaussians constitute 10% of the total count of primitives.
Ablation Study. Table summarizes the rendering quality evaluation under various configura- tions. We exclusively selected the Mip-NeRF 360 dataset for ablation studies due to its consistent photometric properties across viewpoints and minimal presence of overexposed pixels. This choice allows the algorithm to focus reconstructing surface exitant radiance in complex scenes rather than compensating for exposure variations. Disabling the opacity lobe of supplementary Gaussians yielded only a 0. 12B PSNR improvement. Fixing the opacity lobe coverage to π nr/2 while retaining view-dependent opacity increased PSNR by 0.27dB (from 28.33 dB baseline). Optimizing the T parameter further exhibits significant improvements. Best performance is achieved with full opti- mization of opacity lobes' parameters.
To validate the superiority of our enhanced Gaussian kernels over spherical harmonics, conducted experiments using high-order spherical harmonics within the 3DGS framework. Results in Table demonstrate that increasing color representation parameters yields no substantial performance gains, indicating significant parameter redundancy in 3DGS, which is also evidenced 3DGS compression work Niedermayr al. 2024); Papantonakis al. (2024).

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Published as a conference paper at ICLR 2026
Table 4: Increasing the order spherical har- Table 5: Our method outperforms Spherical Beta monics in 3DGS does not bring substantial im- color modeling under provement in rendering quality.
illumina-
tion and specular surface conditions.
Mip-NeRI 360
Glossy surface PSNRT
Mirrorlike surface PSNRT
SH order
SSIM
LPIPS
(MB)4
Methods
SSIMT
SSIMf
27.47
0.814
0.217
608
DBS (sh#2)
41.70
0.993
29.48
0.941
27.55
0.813
0.217
Ours (MCMC, sh=3)
42.33
0.993
29.73
0.941
As shown previously, our method demonstrates marginally inferior performance compared to the Spherical Beta function-bart based color modeling approach Liu et al. (2025) on the NeRF Synthetic dataset, primarily due to the dataset's prevalence of rough surfaces and limited high-frequency en- vironmental illumination, where two Spherical Beta functions per primitive suffice for accurate re- construction. However, when high-frequency components dominate the radiance field, the adaptive superposition characteristics of our opacity lobe exhibit superior efficacy. To validate that, we con- structed synthetic shiny dataset under extreme illumination conditions. As reported Table 5 demonstrated improved reconstruction fidelity proportional to the complexity of surface exitant radiance distributions. We attribute our superiority to the flexibility of the enhanced Gaussians in stacking opacity lobes of different kernels. More analyses provided in Appendix B
4.3 DISENTANGLING DIFFUSE AND SPECULAR COMPONENTS
Following DBS Liu et al. 2025), our augmented radiance fields with enhanced Gaussian primitives also achieve explicit diffuse and specular component separation. It should be noted that all scenes in this work are rendered in the sRGB color space a perceptually uniform space where pixel values do not linearly correlate with radiance intensity. Prior to component disentanglement, we transform rendered images to the linear radiance space.
Our separation protocol proceeds as follows: First, we render the linear-space image Ish, us- ing only the diffuse color of original Gaussians. Subsequently, the enhanced linear-space image Iuug rendered with our augmented radiance field. The diffuse component is then computed as Ia = min(Ishon J while the specular component comes from I, Lmng Ia- As shown in Fig. Fig- 9 and Fig. [0 in Appendix [ (results converted back to sRGB for visualization), our method successfully disentangles white reflections on bonsai, specular highlights on Lego blocks, solar reflections on truck scene pavements, and metallic sheens on drum kits. Notably, limitations arise from the low dynamic range of training images, where overexposed pixels introduce separation artifacts due to irreversible radiance saturation.
5 CONCLUSION
In this work, we present an enhanced Gaussian Splatting method that equips Gaussian kernels with view-dependent opacity. By leveraging our error-driven compensation strategy that carefully inserts enhanced primitives, achieved state-of-the-an 3D Gaussian Splatting across various datasets. Moreover, as a post-processing step for 3DGS, our approach is plug-and-play compatible with most existing 3DGS frameworks and may improve their rendering quality. Another promising direction is to further subdivide specialized Gaussian kernels to represent finer-grained rendering components.
REPRODUCIBILITY STATEMENT
The source code and dataset for this paper will be made publicly available. Implementation de- tails can be found in Section 4.1 while Appendix Appendix[A|preeente, more comprehensive hyperparameter settings. Appendix provides pseudocode for inverse Gaussian splatting.
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ACKNOWLEDGEMENTS
This work was supported in parts by the National Key R&D Program of China (2024YFB3908500, 2024YFB3908502). NSFC (U21B2023) Guangdong Basic and Applied Basic Research Foundation (2023B1515120026), and Scientific Development Funds from Shenzhen University.
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A FULL IMPLEMENTATION DETAILS
We optimize the 2D Gaussian primitives in image space using the Adam Kingma (2014) optimizer, where the learning rate for image-space coordinates X2n is set 0.001 multiplied by the mean of the image dimensions (width and height), with learning rates of 0.01 for color C2D. 0.02 for opacity Q2D. 0.001 for scale S2D. and 0.02 for rotation angle T2D. Every 200 iterations, 20% of Gaussian primitives are added, while those with opacity below 0.005 or covering fewer than 25 pixels are pruned. For supplementary Gaussians, the initial value of T is set 70: ppi, constrained within the range of 0.01 to 1.0.
Prior to projecting 2D Gaussian kernels into world space, the sampling pixels are clustered re- move foreground or background pixels. Upon obtaining world space coordinates corresponding to pixels covered by Gaussians, these coordinates are classified using the single linkage merging al- gorithm (iison 1973). which operates by iteratively merging the closest cluster pairs based on the minimum distance between any two points from distinct clusters. The process continues until ei- ther a single cluster remains or termination threshold is satisfied. The initial termination threshold determined by the depth value of the Gaussian kernel's central pixel, specifically by computing the world-space distance 5d between two adjacent pixels this depth, with the threshold set to 5 -d. In cases of clustering failure, the threshold is multiplied by 1.5 and the procedure is repeated. Pseudocode is provided in Appendix C
During the final joint optimization stage, learning rates are configured as follows: 0.000016 for position, 0.001 for diffuse color, 0.001/20 for higher-order spherical harmonic coefficients, 0.02 for opacity, 0.002 for scaling, 0.0005 for rotation, 0.001 for opacity lobe orientation d, 0,0002 for opacity lobe width T, and 0.002 for sharpness B8. Concurrently, SparseAdam is employed to optimize the opacity of original Gaussian primitives visible in the current viewpoint. All experiments were conducted on workstation equipped with an Intel 19-13900K CPU and an NVIDIA RTX 4090 GPU.On the Mip-NeRF 360 dataset, the training and projection of 2D Gaussians averages approximately minutes per scene, as detailed in T
Table 6: The time consumption for the post-enhancement stage on the Mip-NeRF 360 and NeRF Synthetic datasets is reported as follows. It should be noted that using multiple GPUs can signifi- cantly accelerate this process, as the 2D-stage training operates independently on each image.
Dataset
Mip-NeRF 360 NeRF Synthetic
2D Training and Projection
7
178
Joint Optimization
168 s
s
B ANALYSIS ON OPACITY LOBE
While DBS Liu et al. 2025) replaces spherical harmonics with spherical beta functions in their formulation, approach fundamentally differs by applying generalized Phong shading to opacity modulation rather than radiance modeling. The implementation of view-dependent opacity intro- duces greater stability and flexibility in radiance reconstruction, because the opacity lobe can de- couple each individual Gaussian kernel's contribution to the final exitant radiance. This distinction empirically validated through a controlled experiment simulating three overlapping Gaussian ker- nels in Fig. []] where we compare two configurations: 1) optimization with spherical beta functions governing color distributions while maintaining fixed opacity values, versus 2) our methodology em- ploying view-dependent opacity modulation with fixed color magnitudes. Under identical opacity settings (a = 0.5 for all kernels). The spherical beta approach requires exponentially increas- ing color magnitudes for subsurface Gaussians to compensate for occlusion effects from overlying kernels (Fig. 5 top-left), creating instability because kernel depth ordering varies dynamically during optimization and view changes. Conversely, our method (second row) achieves target radi- ance distributions through adaptive opacity variations while maintaining constant color magnitudes, demonstrating remarkable resilience to permutation of depth sorting. This comparative analysis clusively demonstrates that our Gaussian kernel formulation exhibits substantially greater stability and flexibility than DBS's design.
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Reconstruction spherical beta Target exitant radiance
Recorstruction wi opacity lohe Target exitant radiance
Figure 5: Comparison between Spherical Beta functions in DBS Liu et al. (2025) and opacity lobe. The three Gaussians in the first model color using three differently oriented spherical beta functions, with maximum function values of 1, 2, and 4, all having an opacity of 0.5. The kernels in the second identical color intensity. Our method is more stable and flexible in reconstructing outgoing radiance, it less affected by the ordering of Gaussian kernels and has greater numerical stability.
three differently oriented opacity lobes, with the same maximum amplitude and
GT
DBS (sb=2)
Ours (MCMC) (sh=3)
glossy
glossy
specular buddha
specular material
buddha
material
Figure 6: Qualitative comparison our synthetic shiny dataset rendered using environment maps with complex lighting conditions.
To validate that, we built a synthetic shiny dataset under extreme illumination conditions, as shown in Fig. We demonstrated improved reconstruction fidelity that scales with the complexity of surface exitant radiance distributions, which supports the superiority of our enhanced Gaussians in stacking opacity lobes across different kernels.
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def inverse spw.rttinnla (gaussian 2d, depth_mag camera)
pixels_ world pixels coveree (gaussian_22) 2d, dapth_map, camera)
I Step 1. Foroground-backggounn separation
threshoid sample_tex (depth caussian_2d.conees do:
threshold threshold
groups cluster_points (threshold, pixels_world
The PCA algorithm requi res at least three input data points. while croups.min_size <
# Step2. WPCA
11
filtered points, points,, INCLUDE CENTER prime group (groups) rotation, scaling WPCA (fitteeeeeeeeps
trrine_groupp
12
13
I Gaussian center included in the filtered points
if INCLUDE_CENTER;
15
depth sample_test (depth_map, seteaainndd.ceteer
16
else:
17
depth = weighteddmean
filtered_points.
weight)
position
gaussian_2d.eenterr center, camera)
19
Step3. Scaling calibration
on
Q project (rotation, scaling, position, camera)
21
k (1Q * gaussian_2d.com com froben sesnermmssnmmmmm (Q) ** 2)
scaling - scaling
return rotation, scaling, position
Listing Pseudocode for our inverse splatting algorithm.
C INVERSE GAUSSIAN SPLATTING
By leveraging the rendered depth map and camera parameters, project the 2D Gaussians from image space into world space. Fig. Fig-7com compares the rendered Gaussians from a single training image before and after projecting them into world space. This process is implemented through three steps to ensure reasonable and accurate projection results, with pseudocode provided in List
D ADDITIONAL COMPARISONS AND RESULTS
Fig. 8 presents more qualitative analysis of our full model. Table g and 10 present the rendering metrics of each scene in Table of the main paper, enhanced with supplementary kernels. For outdoor scenes in Mip-NeRF 360, our method achieves approximately 0,1 dB PSNR improvement, while indoor scenes with complex lighting and material variations exhibit 1-2 dB gains. Tables
12 and [3 quantify performance variations before and after radiance field augmentation, while Table 14 and 15 presents comparison of the memory footprint for the scenes in the Mip-NeRF 360 dataset. The proposed opacity lobe introduces minimal overhead, requiring only parameters per instance, with 10% of primitives storing these additional parameters. This design ensures negligible memory impact compared to baseline implementations.
Fig. shows more results of our diffuse-specular decomposition. investigate the performance, we further conducted a qualitative comparison with DBS's ss Liu al. (2025) decomposition in Fig. I0 Because the dataset lacks ground-truth specular data, quantitative metrics cannot be reported. Visu- ally, our method produces specular component comparable that of DBS.
We compare the training time, memory usage, and FPS with Spec-Gaussiae Yang et al. (0244) in Table 7 Since Spec-Gre Gaue-Ga employs neural network for real-time rendering, significantly impacts the FPS. This also affects the seene reconstruction speed. Our method requires less memory and achieves much higher FPS.
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Table 7: Analysis of training time, memory usage, and FPS. "Total time" represents the combined duration of the original scene reconstruction and post-processing enhancement.
Mip-NeRF 360
NeRF Synthetic
Method
Total(Post-roo.), time
Memory
FPS
Totap(Post-proc)) time
Memory
FPS
Spee-Gaussian
44.8 min
882 MB
43
12.0 min
75 MB
136
Ours (3DGS,
27.9(15.0) min $1.9(14.9)) min 25.3(11.22)in
691 MB
110
6.0(3.4) min
68 MB
446
Ours (MCMC,sh=2)
467 MB
96
7.0(3.2)min
44 MB
434
Ours (MCMC,sh=3)
722 MB
90
7.9(3.5) min
68 MB
414
Table 8: Quantitative results of rendering quality per scene on Mip-NeRF 360 dataset.
metrics
bicycle
flowers
garden
stump
treehill
room
counter
kitchen
bonsai
mean
NeRF
PSNRT
25.80
22.40
28.20
27.55
23.89
32.65
29.38
32.50
34.46
28.54
Zip-
SSIM
0.769
0.642
0.860
0.800
0.681
0.925
0.902
0.928
0.949
0.828
LPIPS
0.208
0.273
0.118
0.193
0.242
0.196
0.185
0.116
0.173
0.189
DBS 3DGS-
MCMC
PSNR1
26.15
22.12
28.16
27.80
23.31
32.48
29.51
32.27
32.88
28.29
SSIM
0.81
0.64
0.89
0.82
0.66
0.94
0.92
0.94
0.95
0.84
LPIPS
0.18
0.31
0.10
0.19
0.29
0.25
0.22
0.14
0.22
0.21
PSNRT
26.04
22.44
28.15
27.56
23.49
32.83
30.36
32.61
33.90
28.60
(30k)
SSIM
0.804
0.650
0.882
0.815
0.676
0.941
0.930
0.939
0.957
0.844
LPIPS
0.169
0.308
0.096
0.184
0.293
0.168
0.154
0.110
0.156
0.182
Ours
3DGS
sh=3
PSNR
25.85
21.81
28.21
27.30
23.00
32.39
30.48
32.24
34.26
28.39
SSIM
0.793
0.633
0.881
0.796
0.660
0.931
0.924
0.936
0.954
0.834
LPIPS
0.174
0.294
0.093
0.186
0.289
0.183
0.166
0.110
0.165
0.184
MCMCMCMC
PSNRT
26.31
22.34
28.35
27.97
23.49
33.32
30.64
33.01
34.60
28.89
Ours Ours
sh=3 sh=2
SSIM
0.815
0.658
0.887
0.827
0.680
0.942
0.928
0.940
0.957
0.848
LPIPS
0.158
0.273
0.088
0.159
0.262
0.169
0.160
0.108
0.161
0.171
PSNR1
26.32
22.44
28.36
27.90
23.46
33.45
30.82
33.15
34.78
28.96
SSIM
0.814
0.663
0.887
0.825
0.680
0.942
0,930
0.941
0.958
0.849
LPIPS
0.158
0.270
0.086
0.161
0.259
0.170
0.158
0.106
0.159
0.170
E
LIMITATIONS
The nack-proeection of 2D Gaussians into world space relies on depth maps training cameras, where high-quality depth estimation could improve projection accuracy. However, this work does not incorporate geometric constraints or deep neural networks to generate refined depth maps, re- sulting in projected Gaussian kemells that do not accurately conform to object surfaces. Addition- ally, the designed two-stage optimization strategy prolongs scene reconstruction time, which could be alleviated by integrating the initialization of newly added Gaussians with the training process of the original scene. Furthermore, although fixed ration between added and original Gaussians maintained accommodate most scenarios, this approach may introduce redundancy in scenes dominated by diffuse materials. Adaptively determining the number of additional Gaussians per scene remains a promising direction for future improvements.
18

---

Published as a conference paper at ICLR 2026
Ground Truth
GS
Projection
LI distance
Projection results of 2D Gaussians. We present the optimization results the 2D primi- tives in image space along with the rendered outputs after back-projection into world space. The 4th column images display the L.1 distance between the renderings before and after enhancement. The additional Guassians can also help restore the background reconstruction for outdoor scenes.
Figure 7:
Ground Truth
3DGS-MCMC
DBS
Ours (MCMC, sb-3)
Figure Qualitative analysis across real-captured scenes.
19

---

Published as a conference paper at ICLR 2026
Ground Truth
Augmented
Diffuse
Spocular
Figure 9: Diffuse specular decomposition. We convert both the diffuse color rendering of the original Gaussians and the enhanced rendering into linear color space to decouple the diffuse and specular components.
Ground Truth
DBS
Ours (sh-3)
Figure 10: Qualitative comparison with DBS on diffuse-specnn specular decomposition. The top-right and bottom-right sub-figun dib-figures display the diffuse and specular components, respectively.
20

---

Published as a conference paper at ICLR 2026
Table 9: Quantitative results of rendering quality per scene on Tanks and Temples and Deep Blend- ing dataset.
Tanks and Temples
Deep Blending playroom
metrics
truck
train
mean
drjohnson
mean
(30k) MCMC NeRF
PSNR
DES 3DGS. Zip
SSIM
LPIPS.
PSNR
26.11
22.47
24.29
29.00
30.33
29.67
SSIM
0.89
0.83
0.86
0.89
0.90
0.89
LPIPS_
0.14
0.24
0.19
0.33
0.31
0.32
PSNR
26.44
23.13
24.79
29.39
30.82
30.10
SSIM
0.897
0.839
0.868
0.908
0.912
0.910
LPIPS
0.110
0.185
0.147
0.240
0.240
0.240
Ours
3DGS
sh
PSNR1
25.71
22.09
23.90
29.31
30.50
29.90
SSIM
0.886
0.826
0.856
0.902
0.905
0.903
LPIPS
0.131
0.185
0.158
0.236
0.237
0.237
PSNR
26.78
23.30
25.04
29.90
30.77
30.33
Ours
sh=2
Ours MCMCMCMM
SSIM
0.899
0.842
0.871
0.904
0.914
0.909
LPIPS
0.110
0.182
0.146
0.234
0.236
0.235
PSNR
26,86
23.27
25.06
29.85
30.58
30.22
sh=3
SSIM
0.900
0.844
0.872
0.904
0.913
0.909
LPIPS
0.106
0.181
0.144
0.235
0.237
0.236
Table 10: Quantitative results of rendering quality per scene NeRF synthetic dataset.
metrics
chair
drums
ficus
hotdog
lego
materials
mic
ship
mean
NeRF
PSNR
34.84
25.84
33.90
37.14
34.84
31.66
35.15
31.38
33.10
Zip-
SSIM
0.983
0.944
0.985
0.984
0.980
0.969
0.991
0.929
0.971
LPIPS
0.017
0.050
0.015
0.020
0.019
0.032
0.007
0.091
0.031
DBS 3DGS-
MCMC
PSNR1
36.51
26.29
35.07
37.82
36.01
30.59
37.29
30.82
33.80
SSIM
0.99
0.95
0.99
0.99
0.98
0.96
0.99
0.91
0.97
LPIPS
0.02
0.04
0.01
0.02
0.02
0.04
0.01
0.12
0.04
PSNRT
36.74
26.78
36.75
38.85
37.12
31.12
37.66
32.13
34.64
(30k)
SSIM
0.990
0.958
0.990
0.988
0.985
0.966
0.994
0.910
0.973
LPIPSI
0.010
0.033
0.010
0.015
0.014
0.032
0.005
0.103
0.028
Ours
3DGS
sh=3
PSNR1
35.73
26.59
35.71
38.21
36.39
30.74
37.13
31.63
34.02
SSIM
0.988
0.955
0.987
0.985
0.982
0.961
0.993
0.896
0.969
LPIPS
0.011
0.036
0.012
0.020
0.016
0.036
0.006
0.113
0.031
Ours MCMCMCMC
PSNR
36.05
26.39
35.47
38.34
36.44
30.69
37.27
31.59
34.03
Ours
sh=2
SSIMt
0.989
0.955
0.987
0.987
0.985
0.963
0.993
0.904
0.970
LPIPS
0.011
0.038
0.012
0.016
0.016
0.035
0.006
0.106
0.030
PSNR1
36.35
26.57
35.87
38.72
36.67
31.11
37.79
31.68
34.35
sh=3
SSIM
0.989
0.956
0.988
0.988
0.985
0.965
0.994
0.902
0.971
LPIPSL
0.011
0.036
0.011
0.016
0.015
0.033
0.006
0.106
0.029
Table 11: Quantitative analysis of rendering quality improvements after enhancement per scene on Mip-NeRF 360 dataset.
Method
Metries APSNRI
bicycle flowers garden stump trechill room counter kitchen bonsai
Mean
0.110
-0.067
0.307
0.089
0.168
0.720
1.230
0.806
1.765
0.570
Ours (3DGS, sh=3)
ASSIMT (10
3.26
5.17
2.84
4.77
3.19
2.77
5.49
2.11
5.25
3.87
ALPIPS (10-)
-5.09
-28.6
-3.00
-9.09
-14.9
-5.04
-8.08
-3.16
-7.23
-9.35
APSNR1
0.227
0.007
0.397
0.212
0.085
0.967
1.622
0.976
2.225
0.746
Ours (MCMC, sh=2)
ASSIM1 (10
4.44
3.39
4.83
3.25
2.96
4.52
8.66
3.14
6.39
4.62
ALPIPSL (10-5)
-5.58
-12.5
-5.24
-4.62
-7.04
-6.97
-11.7
-4.94
-7.93
-7.38
APSNRT
0.174
0.003
0.239
0.093
0.079
0.978
1.376
0.798
1.975
0.635
Ours (MCMC, sh=3)
ASSIM (10
3.24
2.75
3.48
2.24
1.60
3.88
6.60
2.59
5.11
3.50
ALPIPSL (10"
-6.26
-12.3
-4.57
-4.11
-6.91
-6.35
-9.66
-4.33
-6.83
-6.81
21

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Published as a conference paper at ICLR 2026
Table 12:
Quantitative analysis of rendering quality improvements after enhancement per
NeRF synthetic dataset.
Method
Metrics
chair
drums
ficus
hotdog
lego
materials
mic
ship
Mean
APSNRT
0.130 0.239 0.132 0,080
0.160
0.137
0.146 0.113
0.142
Ours (3DGS, sh=3)
ASSIM (10
1.82
4.45
1.97
2.37
3.57
4.38
1.50
6.20
3.28
ALPIPS (10
-0.724
-5.99
-1.73
-5.69
-3.56
-3.32
-1.25
-6.17
-3.55
APSNRT
0.265
0.288
0.419
0.231
0.364
0.400
0.464
0.235
0.333
Ours (MCMC, sh=2)
ASSIMT (10
4.74
6.54
5.85
6.45
12.5
4.36
3.86
5.97
ALPIPS (10
-4.92
-13.0
-5.97
-7.44
-6.47
-11.5
-3.69
-13.9
-8.36
APSNRT
0.174
0.251
0.252
0.150
0.271
0.185
0.278
0.114
0.209
Ours (MCMC, sh=3)
ASSIMT (10
2.38
4.72
3.70
2.57
4.88
5,31
2.51
3.04
3.64
ALPIPS (10
-4.55
-9.39
-4.50
-5.79
-5.41
-6.68
-2.32
-9.15
-5.22
Table 13: Quantitative analysis of rendering quality improvements after enhancement per scene.
Tanks and Temples
Deep Blending
Method
Metrics
truck
train
Mean
drjohnson
playroom
Mean
APSNR
0.348
0.356
0.352
0.169
0.059
0.114
Ours (3DGS, sh=3)
ASSIMT (10-9
2.90
3.04
2.97
1.29
0.537
0.915
ALPIPS (10-3)
-7.44
-3.34
-5.39
-5.96
-6.31
-6.14
APSNRT
0.460
0.522
0.491
0.256
0.126
0.191
Ours (MCMC, sh=2)
ASSIM (10-9) 3)
4.07
6.18
5.12
2.17
1.28
1.72
ALPIPS (10 (10-5)
-7.40
-7.87
-7.63
-6.14
-7.87
-7.01
APSNRT
0.442
0.618
0.530
0.231
0.238
0.235
Ours (MCMC, sh=3)
ASSIM (10-3)
3.62
6.58
5.10
1.83
1.35
1.59
ALPIPS (10-5
-7.45
-7.00
-7.22
-5.0
-8.08
-6.94
Table 14: Quantitative results of memory footprint per scene on Mip-NeRF 360 dataset.
Method
Metries
bicycle flowers garden stump trechill room counter kitchen bonsai
Mean
Primitives (10*)
4.8
3,0
4.1
4.5
3.3
1.4
1.2
1.5
1.2
2.8
3DGS
Memory (MB)
1081
675
928
1017
732
316
263
328
275
624
Primitives (10")
6.0
3.0
5.0
4.5
3.5
1.5
1.5
1.5
1.5
3.1
DBS
Memory (MB)
618
309
515
464
361
155
155
155
155
320
Primitives (10*)
5.3
4.5
5.0
3.6
1.5
1.3
1.6
1.3
Ours (3DGS, sh=3)
Memory (MB)
1198
748
1029
1128
811
350
291
363
305
691
Table 15: Quantitative results of memory footprint per scene on Mip-NeRF 360 dataset.
bicycle flowers garden stump treehill room counter kitchen bonsai
Mean
Method 3DGS-MCMC Ours (MCMC, sh=2)
Primitives (10")
5.9
3.3
5.2
4.8
3.7
1.5
1.2
1.8
1.3
3.2
1328
743
1170
1069
833
338
270
405
293
716
Memory (MB)
865
484
763
697
543
220
176
264
191
467
Ours (MCMC, sh=3)
1338
748
1179
1077
839
340
272
408
295
722
22


Reviews:
[{"review_id": "DfFk948kji", "reviewer": "Reviewer_zmRh", "summary": "This paper proposes a strategy to enhance the under-reconstructed regions of 3DGS. The method begins by learning a 3DGS model to fit the given multi-view images. However, due to limitations in the original densification and optimization processes of 3DGS, certain regions may not be reconstructed effectively.\n\nTo address this, the method identifies under-reconstructed regions by comparing the rendered images with the GT images. An error-weighted adaptive strategy is then employed to sample 2DGS on each view screen, targeting these problematic regions. Using the original rendered images as backgrounds, the 2DGS in each view is optimized to correct the image and align it with the GT.\n\nAlthough 2DGS is defined in screen space, the order of the splats is determined by the depth of the nearest rendered pixel. After optimization, clustering is performed for each 2D Gaussian to identify inlier pixels. These inliers are back-projected into 3D space, and a weighted PCA is applied to analyze their Gaussian distribution. The resulting 3D points are then directly used to initialize the supplemented 3DGS.\n\nFinally, these supplemented 3DGS points, along with the opacity of the original 3DGS, are jointly optimized to fit the input images, resulting in a more accurate 3D reconstruction.", "questions": "- I hold a positive attitude toward the proposed method; however, my main concern is the limited comparison with the closely related baselines mentioned, which weakens the overall persuasiveness of the paper. I would be willing to raise the score to accept if these comparisons are included. :)\n\n- The proposed method does not appear to be restricted to a specific representation, such as 3DGS. Beyond 3DGS, other flexible primitives, such as Deformable Beta Splatting (DBS), 3D Convex Splatting, and Deformable Radial Kernel (DRK), can also efficiently capture sharp regions and varying boundaries. These primitives could be incorporated into the 2D fixing step as well. Among them, DRK stands out as a strict projection-based representation, making it much easier to back-project and achieve accurate depth rendering. I suggest including a discussion on the potential application of the method to these more flexible primitives, as it could provide valuable insights and inspiration for future research.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "1. The paper addresses the under-reconstruction problem of 3D Gaussian Splatting (3DGS) directly and effectively by employing a smart solution: correcting problematic regions through 2D fitting and back-projection. The entire process carefully accounts for various factors in the pipeline that could lead to artifacts, making the approach both robust and practical. By \"reintegrating missing details into 3D space,\" the method achieves improved reconstruction. The idea is plausible, insightful, and highly meaningful.\n\n2. The rendered images produced by this method significantly outperform the baselines. Highlighted and specular regions are reconstructed with remarkable accuracy. This improvement is largely attributed to the proposed directional decaying opacity, which enables the method to better capture and fit high-frequency details in these challenging areas.", "weaknesses": "The primary weakness of the paper lies in the limited comparison with baselines. The main baseline used in the study is deformable beta splatting, which explores alternative primitive representation functions to replace Gaussians. However, two additional relevant baselines are worth considering for comparison:\n\n1. **Spec-Gaussian**: Spec-Gaussian introduces a more advanced lighting function to replace SHs, enabling better handling of commonly observed anisotropic appearances. It achieves superior results in specular and highlight regions, making it closely related to the view-dependent opacity proposed in the paper.\n\n2. **AbsGS**: AbsGS leverages the absolute gradient norm accumulation as a metric to densify 3DGS. By using the absolute gradients from the 2D screen, it can effectively identify under-reconstructed regions, thereby improving the densification of Gaussians in problematic areas. This is closely related to the enhancement-on-the-bad idea proposed in the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "FSeMuWO0lD", "reviewer": "Reviewer_mqPT", "summary": "The paper augments 3D Gaussian Splatting (3DGS) with a view-dependent opacity lobe to better reproduce specular effects. It introduces a post-enhancement pipeline that (i) detects high-residual regions in image space and optimizes sparse 2D Gaussians there, (ii) back-projects these into 3D via an “inverse splatting” procedure, and (iii) jointly optimizes the enhanced set with the original scene. The module is positioned as plug-and-play for existing 3DGS pipelines and aims to improve quality with modest runtime overhead.", "questions": "1. How to compute the gradients when performing the optimization in image space? As described in 209-210, the depth is updated via the nearest-neighbor sampling during optimization. However, since the emulated 3DGS differentiable rendering (described on line 201) requires depth sorting (in both forward and backward pass), this depth updating strategy will influence the gradients computation. Specifically, how many rasterization passes are performed during an optimization step? when to perform the depth updating, like before or after updating other parameters?\n2. What are the end-to-end training time and rendering FPS, compared with baselines (including baselines designed for specular scenes, such as SpecGaussian)?", "limitations": "", "rating": 2, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The two-stage 2D residual fixing, inverse splatting, and joint optimization could improve the final rendering quality.\n2. The proposed method could be served as a post-hoc module on top of the 3DGS-based methods.", "weaknesses": "1. The primary concern is the design choice to separate diffuse and specular components across different primitives. In real scenes, most surfaces exhibit a mixture of both (with mirrors as a special extreme), and prior work that models these components within unified primitives enables shared optimization, coherent regularization, and cleaner support for inverse rendering and relighting. By contrast, the proposed error-driven initialization of dedicated “specular” primitives breaks this unification, ties specular capacity to residual patterns rather than material properties, and risks uneven coverage and missed interactions. As a result, the approach sacrifices some of the interpretability and downstream utility.\n2. Lobe-based models for specular appearance (notably spherical Gaussians) are well established in rendering and have been adopted within 3DGS frameworks (e.g., SpecGaussian [A]). Beyond these, there are various prior works tailored to specular scenes, including methods with broader applications such as inverse rendering and relighting. The manuscript would benefit from direct comparisons with these baselines to demonstrate the performance of the proposed design.\n3. Some statements about \"SH inherently fails to decouple diffuse and specular components\" on line 070 conflict with the definitions of the specular and diffuse components on line 138. SH0 could capture view-dependent colors, with higher orders capturing view-dependent colors. Some explanations about why SH inherently fails to decouple diffuse and specular components are needed.\n\n[A] Spec-Gaussian: Anisotropic View-Dependent Appearance for 3D Gaussian Splatting", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "P6TkHS5KJu", "reviewer": "Reviewer_LiBR", "summary": "This paper addresses limitations of 3D Gaussian Splatting (3DGS) in handling complex reflections due to its reliance on spherical harmonics for color encoding. The authors propose an enhanced Gaussian kernel that models specular effects via view-dependent opacity, combined with an error-driven compensation strategy to improve rendering quality. Their method starts with 2D Gaussian initialization, followed by adaptive insertion and optimization of enhanced kernels to produce an augmented radiance field.", "questions": "See Weaknesses", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "This paper proposes a novel post-enhancement method for Gaussian splatting based on the Phong shading model, aiming to improve the modeling of view-dependent color.", "weaknesses": "- The paper leverages geometric information from depth maps of a pre-trained 3DGS and back-projects the screen-space 2D Gaussians into world space. However, due to the limitation of low-order spherical harmonics in 3DGS, the reconstructed scene geometry tends to be quite poor. As is well known, more accurate geometry modeling typically leads to more reliable view-dependent color estimation. Unfortunately, the paper does not provide any comparison between the optimized depth results and those from the pre-trained 3DGS. For instance, in the garden scene of the Mip-NeRF 360 dataset, the flat tabletop region could have been used as a clear example for such a comparison.\n- The proposed method does not fundamentally address the limitation of using spherical harmonics in 3DGS for separating diffuse and specular components. For example, Spec-Gaussian leverages anisotropic spherical Gaussians to better model view-dependent appearance. Instead of optimizing a pre-trained 3DGS, it might be more meaningful to design a more effective approach for modeling view-dependent effects directly, since the use of low-order SH inherently reflects a trade-off between rendering speed and quality.\n\nThe paper has some typos:\n1. Line 101, \"prossesses\"\n2. Line 155-156, \"view-dependently\"\n3. Line 188, \"...  reconstructs intricate radiance field\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RNgPkglT9I", "reviewer": "Reviewer_eJHV", "summary": "The paper presents Augmented Radiance Field (ARF), a plug-and-play framework that enhances 3D Gaussian Splatting (3DGS) for realistic view synthesis. While 3DGS achieves real-time rendering, its spherical harmonic color model struggles with specular reflections and material separation. ARF introduces a Gaussian kernel with view-dependent opacity to explicitly model specular effects. It further proposes an error-driven refinement that inserts and optimizes additional Gaussians in high-error regions. Experiments on multiple benchmarks show that ARF outperforms state-of-the-art NeRF and 3DGS variants.", "questions": "See weakness.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper introduces a new Gaussian kernel with view-dependent opacity that effectively models specular reflections and high-frequency lighting effects.\n\n2. The proposed 2D-to-3D error compensation mechanism adaptively adds and optimizes supplementary Gaussians in challenging regions.\n\n3. Extensive experiments across several benchmarks demonstrate consistent improvements over state-of-the-art NeRF and 3DGS methods, even with lower-order spherical harmonics.", "weaknesses": "1. Since the method refines pre-trained 3DGS scenes rather than learning end-to-end, it may accumulate suboptimal biases from the base model and depend on prior scene quality. The image-space optimization and 2D-to-3D projection introduce extra computation and memory costs compared to standard 3DGS.\n\n2. The paper does not analyze training stability or convergence behavior when optimizing new Gaussians, especially in highly reflective or complex lighting conditions.\n\n3. The rendering quality heavily depends on the tuning of the opacity lobe parameters beta; the paper does not provide an analysis of how these parameters influence optimization.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)