# TextureSplat: Per-Primitive Texture Mapping for Reflective Gaussian Splatting

Mae Younes, Adnane Boukhayma

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Mae Younes, Adnane Boukhayma. TextureSplat: Per-Primitive Texture Mapping for Reflective Gaussian Splatting. 3DV 2026 - International Conference on 3D Vision, Simon Fraser University, Mar 2026, Vancouver (BC), Canada. hal-05484246

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# TextureSplat: Per-Primitive Texture Mapping for Reflective Gaussian Splatting

Mae Younes

Adnane Boukhayma

Inria France

<figure><img src="image_2.png" /><figcaption>Figure 1. *Method Overview:* We introduce planar primitive material textures — as opposed to single attributes — within physically based Gaussian Splatting rendering optimization. The increased representation power from spatially varying normal and material in object space enables fidelity reconstruction of high frequency specular in highly reflective scenes. Our hardware-accelerated implementation using texture atlases improves rendering efficiency at test time.</figcaption></figure>

## Abstract

Gaussian Splatting have demonstrated remarkable novel view synthesis performance at high rendering frame rates. Optimization-based inverse rendering within complex capture scenarios remains however a challenging problem. A particular case is modelling complex surface light interactions for highly reflective scenes, which results in intricate high frequency specular radiance components. We hypothesize that such challenging settings can benefit from increased representation power. We hence propose a method that tackles this issue through a geometrically and physically grounded Gaussian Splatting borne radiance field, where normals and material properties are spatially variable in the primitive's local space. Using per-primitive texture maps for this purpose, we also propose to harness the GPU hardware to accelerate rendering at test time via unified material texture atlas. Code will be available at TextureSplat.

## 1. Introduction

3D reconstruction and inverse rendering from multi-view images are pivotal problems receiving constant interest and investigation from computer vision, graphics and machine learning research communities, with a myriad of direct applications in key industrial domains requiring high-quality 3D modeling and visualization.

Neural Radiance Fields (NeRF) [42] revolutionized the field by representing scenes as continuous neural implicit functions optimized through differentiable volume rendering. Building on this foundation, 3D Gaussian Splatting (3DGS) [27] reintroduced point-based graphics by replacing neural networks with explicit 3D Gaussian primitives,

achieving both real-time rendering and state-of-the-art quality. These primitives are rendered through volume resampling [87], with their parameters optimized via gradient descent-based differentiable rendering. More recently, 2D Gaussian Splatting (2DGS) [18] improved multi-view consistency by using planar Gaussian primitives that better align with surfaces.

Despite these advances, accurately representing highly reflective surfaces remains challenging. Reflective objects exhibit complex view-dependent effects that depend on surface normals, material properties, and environmental lighting. Recent methods such as RefGaussian [73] and 3DGS-DR [76] attempt to model these effects using per-Gaussian material properties and physically-based rendering approaches. However, they often struggle with high-frequency specular highlights and sharp reflections. We hypothesize that this is due in part to the inherent resolution limitations of using a single attribute value per primitive.

In this paper, we ask the question: *How can we enhance the representation power of Gaussian splatting for reflective scenes while maintaining computational efficiency and leveraging hardware acceleration?* Our key insight is that the planar nature of 2D Gaussian primitives naturally defines a parameterization that can be exploited for texture mapping, enabling us to store spatially varying material properties per primitive.

Inspired by the distinction between Gouraud shading [15] (constant per-vertex attributes) and Phong shading [53] (interpolated attributes) in traditional computer graphics, we introduce per-primitive texture maps for material properties in 2D Gaussian splatting. This approach effectively decouples the geometric representation (Gaussian primitives) from the appearance representation (material textures), allowing us to model high-frequency material
variations without increasing the number of primitives.

Our method leverages the closed-form ray-splat intersection of 2DGS to accurately map screen-space pixels to local texture coordinates, enabling proper texture filtering. Crucially, we transform tangential normal maps to world space using the primitive's rotation matrix, analogous to normal mapping in traditional rendering. This enables detailed normal variations across each primitive's surface, significantly enhancing the rendering of specular highlights and reflections.

For efficient rendering after optimization, we pack the primitive textures into atlases that leverage GPU hardware-accelerated texture filtering operations. Our approach is fully compatible with deferred shading pipelines, allowing us to incorporate physically-based rendering models for accurate light interactions.

Through experiments on standard benchmarks for reflective scene reconstruction, we demonstrate that our method outperforms state-of-the-art approaches in terms of both quantitative metrics and visual quality. Our method achieves more accurate reflections and sharper specular highlights while maintaining real-time rendering performance. The benefits extend beyond reflective scenes, as our approach improves rendering quality for standard scenes as well.

Our contributions include:

* A per-primitive texture mapping approach for 2D Gaussian splatting that enhances representation power while maintaining computational efficiency.

* Leveraging a normal mapping technique in the context of Gaussian Splatting that significantly improves the quality of specular reflections.

* A hardware-accelerated implementation using texture atlases that enhances real-time rendering at test time.

* State-of-the-art results on benchmarks for reflective scene reconstruction, demonstrating significant improvements in rendering quality and accuracy.

# 2. Related Work

## 2.1. Radiance Fields for 3D Scene Representations

Neural Radiance Fields [42] (NeRFs) have been dominating the 3D shape and appearance modelling recently, based on the astounding success of implicit representations combined with differentiable volume rendering [31, 41]. They represent scenes using view-dependent radiance and density fields parameterized by MLPs. When density is modeled as a function of a signed distance field, NeRF variants enable more accurate geometry reconstruction [21, 34, 64, 70, 74, 78]. However, multi-scale volume rendering demands frequent MLP evaluations, limiting real-time performance. Grid-based methods [7, 10, 11, 43, 58, 59] alleviate this but often struggle with large, unbounded scenes even with

level-of-detail grids [38]. Implicit reconstruction has been made more robust to noise and sparse observations, whether from images or point clouds, through the use of generalizable data priors (e.g. [6, 19, 26, 32, 46, 47, 49, 52, 79]) and a variety of regularization strategies (e.g. [2, 8, 16, 20, 33, 45, 48–51, 72]). Gaussian splatting (3DGS) [27] emerged lately as a strong alternative to NeRFs, offering state-of-the-art novel view synthesis and real time rendering frame rates. It extends the elliptical weighted average (EWA) volume resampling framework [86, 87] to inverse rendering, modelling scenes with explicit Gaussian kernel primitives, that can be sorted and rasterized efficiently. Recent extensions of Gaussian splatting include building generalizable models [5, 23, 39, 61], bundle-adjustment-based formulations [12, 22, 75, 84], using higher-dimensional primitives [9], spatiotemporal models [69], in addition to several methods to improve density control [28, 65, 82], anti-alising [37, 77, 80], model compactness [30, 66] and training speed [17, 29, 83]. The 2DGS representation [18] leverages planar 2D primitives instead of volumetric ones (3DGS), and performs precise 2D kernel evaluation in object space as opposed to approximative ones in screen space (3DGS), thus leading to superior geometric modelling and multi-view consistency.

## 2.2. Specular Reflection Modeling for Reflective Scenes

Both vanilla NeRFs and 3DGS assume low-frequency view dependency. Hence, they can struggle with highly reflective scenes. One strategy to improve in this department is using shading functions that are reflection direction aware [14, 25, 40, 57, 63]. For instance, Ref-NeRF [63] extends NeRFs with a new parameterization for view-dependent radiance and incorporates normal vector regularization. The shading function can be more physically grounded, and this enables additional application such as relighting and material editing. In this regard, other NeRF and GS based methods proposed to model light interaction using the explicit rendering equation with BRDF functions. ENVIDR [35] Uses environment maps to capture spatially-varying reflections in neural rendering. The next wave of work tackled shading for Gaussian Splatting (e.g. [13, 24, 36, 62, 73, 76, 85]). G [24] applies a simplified shading function on each fragment. 3DGS-DR [76] introduces deferred shading at pixel level, and stabilizes the optimization by smoothing out normal gradients.

Building on the 2DGS representation, our baseline Ref-Gaussian [73] decomposes the scene into geometry, material and lighting through the split-sum approximation of the rendering equation while incorporating an indirect light attribute, enabling inter-reflections while being fast to render. It achieves the state-of-the-art performance on the standard reflective scene novel view synthesis benchmarks. We pro-
pose to enhance its physical material and normal representations through the use of per-primitive textures.

## 2.3. Texture Attributes in Gaussian Splatting

Several works [4, 55, 56, 60, 68, 71] recently introduced the texture attribute representation for Gaussian Splatting as well. They use it to model a view independent component of the color. Differently, we explore this representation for rendering material properties and normals within 2DGS enabled physically based rendering to reconstruct challenging highly reflective scenes. We also propose leveraging texture atlases to enable hardware acceleration at test-time rendering. Closest to our context, concurrent work [1] manages to encode spatially varying primitive material attributes in a single compact texture map thanks to their pre-fitted template mesh.

## 3. Method

In this section, we present our approach to enhance 2D Gaussian Splatting (2DGS) [18] for representing highly reflective 3D scenes. We first provide background on 2DGS, then introduce our per-primitive texture mapping method that enables high-frequency detail on flat Gaussian primitives. Finally, we describe our hardware-accelerated implementation using texture atlases and the physically-based rendering model we use for reflective scenes.

### 3.1. Background: 2D Gaussian Splatting

We build upon 2D Gaussian Splatting (2DGS) [18], which represents a scene using oriented planar disks offering improved multi-view consistency compared to 3D Gaussian Splatting [27]. Each primitive k is characterized by its position $p_k$, tangential vectors $t_{u_k}$ and $t_{v_k}$, and scaling factors ($s_{u_k}$, $s_{v_k}$). The primitive's normal is defined by the cross product $n_k = t_{u_k} \times t_{v_k}$.

The 2D Gaussian is defined in a local tangent plane in world space with coordinates $(u, v)$, parameterized as:

$$P_k(u, v) = p_k + s_{u_k} t_{u_k} + s_{v_k} t_{v_k} v. \quad (1)$$

For a point $(u, v)$ in the local coordinate space corresponding to a given pixel $(x, y)$ (i.e. ray-splat intersection), the 2D Gaussian value is evaluated as:

$$\mathcal{G}_k(u, v) = \exp\left(-\frac{u^2 + v^2}{2}\right). \quad (2)$$

Each splat has also a learnable opacity $o_k$. The final pixel color is computed by alpha-blending all primitives that contribute to the pixel in front-to-back order:

$$\mathbf{A}(x, y) = \sum_{i=1}^{N} \mathbf{a}_i \alpha_i(x, y) \prod_{j=1}^{i-1} (1 - \alpha_j(x, y)) \quad (3)$$

where $\alpha_i(x, y) = o_i \mathcal{G}_i(u_i(x, y), v_i(x, y))$ is the effective opacity of the i-th primitive at pixel $(x, y)$ and $\mathbf{a}_i$ is its attribute (e.g., color), typically represented using spherical harmonics for view-dependent effects.

### 3.2. Per-Primitive Texture Mapping

While existing Gaussian splatting methods assign a single attribute value per primitive, we observe that the flat nature of 2D Gaussians naturally defines a local parameterization that can be leveraged for texture mapping. This enables encoding higher-frequency spatial detail without increasing the number of primitives, analogous to the distinction between Gouraud shading (constant per-primitive attributes) and Phong shading (interpolated attributes) in traditional rendering.

Rather than representing material properties with a single value per primitive, we define them as texture maps in the splat's local coordinate system:

$$\mathbf{a}_k(x, y) = \mathcal{T}_k(u_k(x, y), v_k(x, y)) \quad (4)$$

where $\mathcal{T}_k$ is the texture map associated with the k-th primitive, and $\mathbf{a}_k$ represents any reconstructed attribute.

This approach provides several advantages:

**Decoupling of geometry and appearance:** By separating the geometric representation (Gaussian primitives) from the appearance details ( textures), we can represent complex visual features without increasing the number of primitives.

**Higher fidelity appearance:** Textures can capture high-frequency detail that would otherwise require many more primitives to represent.

**Normal mapping:** Instead of using a single normal per primitive, we can store detailed normal maps, significantly improving the rendering of specular effects.

The 2DGS representation is particularly well-suited for texture mapping because the ray-splat intersection already provides exact $(u, v)$ coordinates in the primitive's local space and thus, enables accurate texture filtering.

### 3.3. Texture Mapping Implementation

To implement our texture mapping approach, we map the local splat coordinates $(u, v)$ to texture coordinates $(s, t)$ that account for the Gaussian kernel's support. Since the Gaussian kernel effectively drops to zero at approximately $S_\sigma = 3$ standard deviations, we scale the local coordinates to ensure that the effective support of the Gaussian ($[-S_\sigma, S_\sigma] \times [-S_\sigma, S_\sigma]$) maps to the texture space $[0, 1] \times [0, 1]$:

$$s = \frac{u + S_{\sigma}}{2S_{\sigma}}, \quad t = \frac{v + S_{\sigma}}{2S_{\sigma}}. \quad (5)$$
The attribute value $a_k(x, y)$ for primitive $k$ at pixel $(x, y)$ is then obtained by bilinear filtering from its texture map $\mathcal{T}_k$:

$$a_k(x, y) = \text{BilinearFilter}(\mathcal{T}_k, s(u_k(x, y)), t(v_k(x, y))). \qquad (6)$$

## 3.4. Hardware Acceleration via Texture Atlases

To efficiently render optimized scenes at test time with per-primitive textures, we leverage hardware-accelerated texture filtering by packing individual primitive textures into texture atlases. This approach is inspired by methods like Ptex [3] and seamless texture atlases [54], adapted to the specific needs of Gaussian splatting. We provide details about Texture Atlas construction and texture sampling in the Supplementary Material (Section 1).

## 3.5. Physically-Based Deferred Rendering

Following the deferred rendering approach used in 3DGS-DR [76] and Ref-Gaussian [73], we first splat material attributes to screen-space buffers, then apply physically-based shading in a separate pass.

### 3.5.1 Material Properties

Each 2D Gaussian is associated with texture maps for the following material properties: Albedo $\lambda \in [0, 1]^3$, Metallic $m \in [0, 1]$, Roughness $r \in [0, 1]$, Tangent normal $n^t \in [0, 1]^3$ representing normal perturbations in the tangent space. For memory efficiency, we encode tangent normals using only two components ($n_x^t, n_y^t$) and reconstruct the third component at runtime using $n_z^t = \sqrt{\max(0, 1 - (n_x^t)^2 - (n_y^t)^2)}$.

### 3.5.2 Normal Mapping

A key factor in our approach is the use of normal mapping instead of a single normal per primitive. The tangent normal map encodes normal perturbations in the primitive's local coordinate system. These are transformed to world space using:

$$n_k(x, y) = R_k \cdot n_k^t(x, y) \qquad (7)$$

where $R_k$ is the primitive's rotation matrix. This enables detailed normal variations across the surface of each primitive, critical for capturing high-frequency specular effects.

### 3.5.3 Attribute Splatting

We splat the material attributes to screen-space buffers using alpha-blending:

$$X(x, y) = \sum_{i=1}^{N} x_i(x, y) \alpha_i(x, y) \prod_{j=1}^{i-1} (1 - \alpha_j(x, y)), \quad (8)$$

where $X$ represents the combined screen-space buffers:

$$X = \begin{bmatrix} \Lambda \\ M \\ R \\ \mathbf{N} \\ \mathbf{L}_{\text{ind}} \end{bmatrix}, \quad x_i = \begin{bmatrix} \lambda_i(x, y) \\ m_i(x, y) \\ r_i(x, y) \\ \mathbf{n}_i(x, y) \\ \mathbf{l}_i^{\text{ind}}(x, y) \end{bmatrix} \qquad (9)$$

This deferred approach treats alpha-blending as a smoothing filter, stabilizing the optimization of features sampled from textures and producing more cohesive rendering results compared to shading directly on the Gaussians [73, 76].

### 3.5.4 Physically-Based Shading

With the aggregated material maps, we apply the rendering equation to compute the outgoing radiance $L_o(x, y, \omega_o)$ in the direction $\omega_o$:

$$L_o(x, y, \omega_o) = L_d(x, y, \omega_o) + L_s(x, y, \omega_o). \qquad (10)$$

The diffuse term writes:

$$L_d(x, y, \omega_o) = \frac{\Lambda(x, y)}{\pi} (1 - M(x, y)) L_{\text{env}}^{\text{diffuse}}(N(x, y)), \qquad (11)$$

where $L_{\text{env}}^{\text{diffuse}}$ is the pre-integrated diffuse environment irradiance. Following the split-sum approximation, we compute the specular component efficiently:

$$L_s(x, y, \omega_o) \approx \text{BRDF}_{\text{LUT}}(N(x, y) \cdot \omega_o, R(x, y)) \cdot (V(x, y)L_{\text{dir}}(x, y, \omega_r, R(x, y)) + (1 - V(x, y))L_{\text{ind}}(x, y)). \qquad (12)$$

The first term, BRDF$_{LUT}$, depends solely on the view angle and roughness, which is precomputed and stored in a 2D lookup texture. $L_{\text{dir}}(x, y, \omega_r, R(x, y))$ is the direct environment lighting queried from a learnable environment map in the reflection direction $\omega_r$, using roughness $R(x, y)$ for mipmap selection. $L_{\text{ind}}(x, y)$ is the blended indirect lighting component. We follow the baseline method [73] in modeling inter-reflections by approximating visibility with ray tracing an extracted mesh and encoding indirect lighting with spherical harmonics. We follow prior work [73] and use [44] for the PBR shading.

## 3.6. Training

Splat parameters $p_k, t_{u_k}, t_{v_k}, s_{u_k}, s_{v_k}, o_k$, their material texture maps $\mathcal{T}_k^\lambda, \mathcal{T}_k^m, \mathcal{T}_k^r, \mathcal{T}_k^{n^t}$, per-splat indirect lighting SH coefficients for $l_k^{\text{ind}}$, and the environment maps $(\mathcal{L}_{\text{env}}^{\text{diffuse}}, \mathcal{L}_{\text{env}}^{\text{spec}})$, are optimized end-to-end using a composite loss:

$$\mathcal{L} = \mathcal{L}_{\text{img}} + \lambda_n \mathcal{L}_n, \qquad (13)$$
where $L_{\text{img}} = (1 - \lambda)L_1 + \lambda L_{\text{D-SSIM}}$ is the RGB reconstruction loss with balancing weight $\lambda = 0.2$. The normal consistency loss $L_n = 1 - \tilde{N}(x, y)^T N(x, y)$ encourages alignment of the Gaussians with the surface by minimizing the cosine difference between the rendered normal $N(x, y)$ and the surface normal $\tilde{N}(x, y)$ derived from rendered depth. We use a single NVIDIA RTX A6000 GPU in our experiments.

# 4. Experiments

<figure><img src="image_3.png" /><figcaption>Figure 2. Qualitative comparisons of novel view synthesis on synthetic scenes. From top to bottom: helmet from Shiny Blender [63] and potion from Glossy Synthetic [40]. Notice how we reconstruct reflections with more fidelity and less distortion.</figcaption></figure>

Following the baseline method [73], we evaluate our work quantitatively and qualitatively under standard multi-view reconstruction benchmarks of challenging reflective scenes. We use the datasets: Shiny Blender [63] and Glossy Synthetic [40] for novel view synthesis of reflective objects, and dataset Ref-Real [63] to account for real world open reflective scenes. We also provide results on the Synthetic NeRF [42] dataset to showcase our method under non-reflective scenes and illustrate its practicality in the supplementary material (Section 2). We compare to state-of-the-art methods in the reflective scene setting, including the baseline Ref-Gaussian [73], other reflective Gaussian splatting based methods GShader [24] and 3DGS-DR [76], 3DGS [27] and 2DGS [18] for reference, and seminal NeRF based approaches such as Ref-NeRF [63] and

<figure><img src="image_4.png" /><figcaption>Figure 3. Qualitative comparisons of novel view synthesis on real scenes [63]. From left to right: garden spheres and sedan. Notice how we recover reflections with more fidelity.</figcaption></figure>

ENVIDR [35]. We provide additional results and ablation studies in the supplementary material.

## 4.1. Implementation Details

We follow a two-stage optimization for stability. We first train for half the total number of iterations using per-splat single attribute optimization. During the second stage, we start optimizing the material and normal textures initialized from the corresponding attributes from the first stage, and we freeze the positions of the primitives. In all our evaluations, we use texture resolution of 2 × 2. We use the same hyperparameters and training strategies defined by our baseline Ref-Gaussian [73]. We also follow the latter in replacing the integrated diffuse lighting by a spherical harmonics view dependent color for better fitting in the reflective setting. We implement efficient CUDA kernels on top of 2DGS and Ref-Gaussian for forward and backward operations involving material textures and normal mapping, as well as the texture atlases construction, packing and hardware bilinear filtering at test time.

## 4.2. Novel View Synthesis

Table 1 shows numerical results in the standard reflective benchmark. We report Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM) [67], and Learned Perceptual Image Patch Similarity (LPIPS)
<table><caption>Table 1. Per-scene image quality comparison in the reflective novel view synthesis setting.</caption><thead><tr><th rowspan="2">Datasets</th><th rowspan="2"></th><th colspan="7">Shiny Blender [63]</th><th colspan="7">Glossy Synthetic [40]</th><th colspan="3">Real [63]</th></tr><tr><th>ball</th><th>car</th><th>coffee</th><th>helmet</th><th>teapot</th><th>toaster</th><th>angel</th><th>bell</th><th>cat</th><th>horse</th><th>luyu</th><th>potion</th><th>tbell</th><th>teapot</th><th>garden</th><th>sedan</th><th>toycar</th></tr></thead><tbody><tr><td rowspan="6">PSNR ↑</td><td>Ref-NeRF</td><td>33.16</td><td>30.44</td><td>33.99</td><td>29.94</td><td>45.12</td><td>26.12</td><td>20.89</td><td>30.02</td><td>29.76</td><td>19.30</td><td>25.42</td><td>30.11</td><td>26.91</td><td>22.77</td><td>22.01</td><td>25.21</td><td>23.65</td></tr><tr><td>ENVIDR</td><td>41.02</td><td>27.81</td><td>30.57</td><td>32.71</td><td>42.62</td><td>26.03</td><td>29.02</td><td>30.88</td><td>31.04</td><td>25.99</td><td>28.03</td><td>32.11</td><td>28.64</td><td>26.77</td><td>21.47</td><td>24.61</td><td>22.92</td></tr><tr><td>3DGS</td><td>27.65</td><td>27.26</td><td>32.30</td><td>28.22</td><td>45.71</td><td>20.99</td><td>24.49</td><td>25.11</td><td>31.36</td><td>24.63</td><td>26.97</td><td>30.16</td><td>23.88</td><td>21.51</td><td>21.75</td><td>26.03</td><td>23.78</td></tr><tr><td>2DGS</td><td>25.97</td><td>26.38</td><td>32.31</td><td>27.42</td><td>44.97</td><td>20.42</td><td>26.95</td><td>24.79</td><td>30.65</td><td>25.18</td><td>26.89</td><td>29.50</td><td>23.28</td><td>21.29</td><td>22.53</td><td>26.23</td><td>23.70</td></tr><tr><td>G ann</td><td>30.99</td><td>27.96</td><td>32.39</td><td>28.32</td><td>45.86</td><td>26.28</td><td>25.08</td><td>28.07</td><td>31.81</td><td>26.56</td><td>27.18</td><td>30.09</td><td>24.48</td><td>23.58</td><td>21.74</td><td>24.89</td><td>23.76</td></tr><tr><td>3DGS-DR</td><td>33.43</td><td>30.48</td><td>34.53</td><td>31.44</td><td>47.04</td><td>26.76</td><td>29.07</td><td>30.60</td><td>32.59</td><td>26.17</td><td>28.96</td><td>32.65</td><td>29.03</td><td>25.77</td><td>21.82</td><td>26.32</td><td>23.83</td></tr><tr><td rowspan="2">Ref-Gaussian Ours</td><td></td><td>36.07</td><td>31.32</td><td>34.2</td><td>32.3</td><td>47.15</td><td>28.28</td><td>30.55</td><td>28.57</td><td>33.04</td><td>26.76</td><td>30.1</td><td>33.39</td><td>30.1</td><td>25.97</td><td>23.09</td><td>26.23</td><td>24.74</td></tr><tr><td></td><td>39.27</td><td>31.72</td><td>34.82</td><td>32.97</td><td>48.27</td><td>28.4</td><td>30.85</td><td>29.16</td><td>33.51</td><td>27.08</td><td>30.48</td><td>34.03</td><td>30.77</td><td>26.42</td><td>23.34</td><td>26.45</td><td>24.95</td></tr><tr><td rowspan="6">SSIM ↑</td><td>Ref-NeRF</td><td>0.971</td><td>0.950</td><td>0.972</td><td>0.954</td><td>0.995</td><td>0.921</td><td>0.853</td><td>0.941</td><td>0.944</td><td>0.820</td><td>0.901</td><td>0.933</td><td>0.947</td><td>0.897</td><td>0.584</td><td>0.720</td><td>0.633</td></tr><tr><td>ENVIDR</td><td>0.997</td><td>0.943</td><td>0.962</td><td>0.987</td><td>0.995</td><td>0.922</td><td>0.934</td><td>0.954</td><td>0.965</td><td>0.925</td><td>0.931</td><td>0.960</td><td>0.947</td><td>0.957</td><td>0.561</td><td>0.707</td><td>0.549</td></tr><tr><td>3DGS</td><td>0.937</td><td>0.931</td><td>0.972</td><td>0.951</td><td>0.996</td><td>0.894</td><td>0.792</td><td>0.908</td><td>0.959</td><td>0.797</td><td>0.916</td><td>0.938</td><td>0.900</td><td>0.881</td><td>0.571</td><td>0.771</td><td>0.637</td></tr><tr><td>2DGS</td><td>0.934</td><td>0.930</td><td>0.972</td><td>0.953</td><td>0.997</td><td>0.892</td><td>0.918</td><td>0.911</td><td>0.958</td><td>0.909</td><td>0.918</td><td>0.939</td><td>0.902</td><td>0.886</td><td>0.609</td><td>0.778</td><td>0.597</td></tr><tr><td>G ann</td><td>0.966</td><td>0.932</td><td>0.971</td><td>0.951</td><td>0.996</td><td>0.929</td><td>0.914</td><td>0.919</td><td>0.961</td><td>0.933</td><td>0.914</td><td>0.936</td><td>0.898</td><td>0.901</td><td>0.576</td><td>0.728</td><td>0.637</td></tr><tr><td>3DGS-DR</td><td>0.979</td><td>0.963</td><td>0.976</td><td>0.971</td><td>0.997</td><td>0.942</td><td>0.942</td><td>0.959</td><td>0.973</td><td>0.933</td><td>0.943</td><td>0.959</td><td>0.958</td><td>0.942</td><td>0.581</td><td>0.773</td><td>0.639</td></tr><tr><td rowspan="2">Ref-Gaussian Ours</td><td></td><td>0.985</td><td>0.966</td><td>0.976</td><td>0.971</td><td>0.997</td><td>0.952</td><td>0.956</td><td>0.943</td><td>0.975</td><td>0.942</td><td>0.953</td><td>0.966</td><td>0.947</td><td>0.942</td><td>0.628</td><td>0.766</td><td>0.679</td></tr><tr><td></td><td>0.992</td><td>0.969</td><td>0.977</td><td>0.975</td><td>0.998</td><td>0.954</td><td>0.958</td><td>0.947</td><td>0.977</td><td>0.946</td><td>0.956</td><td>0.97</td><td>0.97</td><td>0.947</td><td>0.631</td><td>0.772</td><td>0.688</td></tr><tr><td rowspan="6">LPIPS ↓</td><td>Ref-NeRF</td><td>0.166</td><td>0.050</td><td>0.082</td><td>0.086</td><td>0.012</td><td>0.083</td><td>0.144</td><td>0.102</td><td>0.104</td><td>0.155</td><td>0.098</td><td>0.084</td><td>0.114</td><td>0.098</td><td>0.251</td><td>0.234</td><td>0.231</td></tr><tr><td>ENVIDR</td><td>0.020</td><td>0.046</td><td>0.083</td><td>0.036</td><td>0.009</td><td>0.081</td><td>0.067</td><td>0.054</td><td>0.049</td><td>0.065</td><td>0.059</td><td>0.072</td><td>0.069</td><td>0.041</td><td>0.263</td><td>0.387</td><td>0.345</td></tr><tr><td>3DGS</td><td>0.162</td><td>0.047</td><td>0.079</td><td>0.081</td><td>0.008</td><td>0.125</td><td>0.088</td><td>0.104</td><td>0.062</td><td>0.077</td><td>0.064</td><td>0.093</td><td>0.102</td><td>0.125</td><td>0.248</td><td>0.206</td><td>0.237</td></tr><tr><td>2DGS</td><td>0.156</td><td>0.052</td><td>0.079</td><td>0.079</td><td>0.008</td><td>0.127</td><td>0.072</td><td>0.109</td><td>0.060</td><td>0.071</td><td>0.066</td><td>0.097</td><td>0.125</td><td>0.101</td><td>0.254</td><td>0.225</td><td>0.396</td></tr><tr><td>G ann</td><td>0.121</td><td>0.044</td><td>0.078</td><td>0.074</td><td>0.007</td><td>0.079</td><td>0.082</td><td>0.098</td><td>0.056</td><td>0.562</td><td>0.064</td><td>0.088</td><td>0.091</td><td>0.122</td><td>0.274</td><td>0.259</td><td>0.239</td></tr><tr><td>3DGS-DR</td><td>0.105</td><td>0.033</td><td>0.076</td><td>0.050</td><td>0.006</td><td>0.082</td><td>0.052</td><td>0.050</td><td>0.042</td><td>0.057</td><td>0.048</td><td>0.068</td><td>0.059</td><td>0.060</td><td>0.247</td><td>0.208</td><td>0.231</td></tr><tr><td rowspan="2">Ref-Gaussian Ours</td><td></td><td>0.089</td><td>0.031</td><td>0.078</td><td>0.048</td><td>0.006</td><td>0.067</td><td>0.040</td><td>0.067</td><td>0.037</td><td>0.049</td><td>0.043</td><td>0.061</td><td>0.070</td><td>0.059</td><td>0.266</td><td>0.258</td><td>0.257</td></tr><tr><td></td><td>0.074</td><td>0.028</td><td>0.075</td><td>0.042</td><td>0.004</td><td>0.063</td><td>0.038</td><td>0.064</td><td>0.034</td><td>0.045</td><td>0.040</td><td>0.055</td><td>0.041</td><td>0.055</td><td>0.283</td><td>0.257</td><td>0.27</td></tr></tbody></table>

[81] as metrics. Our method performs favorably compared to other methods, including baseline Ref-Gaussian, which is also the state-of-the-art method currently under this benchmark to the best of our knowledge. We provide qualitative results to accompany this table, for real scenes in Figure 3 and synthetic ones in Figure 2. Our method displays superior ability in capturing reflections on the surface with more fidelity, while Ref-Gaussian and 3DGS-DR suffer from distorted or missing reflections. We also show in the supplementary material numerical (Tab. 1 in Supp. Mat.) and qualitative (Fig. 1 in Supp. Mat.) comparisons under non-reflective data on Nerf Synthetic Scenes [42]. In that generic setting, we perform competitively with the state-of-the-art. The improvement brought by our method over the baseline Ref-Gaussian particularly, under both reflective and non-reflective scenes, is a testimony of the efficacy and versatility of our representation.

## 4.3. Scene Decomposition

Figure 4 shows a comparison of the decomposition with respect to our baseline. Notice that our material properties are sharper and display less noise. Our normals replicate the smooth sphere shape more faithfully. We provide further comparisons in supplementary material including environment map estimation and material decomposition (Figures

3 & 2 in Supp. Mat.) showcasing the superiority of our results.

We further evaluate our normal estimation through the benchmark of the Shiny Blender dataset [63]. Table 2 reports the mean angular error of normal maps, where we outperform our baseline. This result validates our tangential normal representation and the use of normal mapping. Figure 5 shows qualitative comparisons of normals, where we recover superior geometry compared to other methods.

<figure><img src="image_5.png" /><figcaption>Figure 4. Comparison of scene decomposition between our method and the baseline.</figcaption></figure>

## 4.4. Hardware Acceleration Performance

While our per-primitive texture mapping approach improves rendering quality for reflective scenes, a potential concern is the additional computational cost of text-
<table><caption>Table 2. Normal quality evaluated by MAE°: comparisons on the Shiny Blender Dataset [63].</caption><thead><tr><th></th><th>G ann</th><th>NVDiffRec</th><th>ENVIDR</th><th>3DGS-DR</th><th>Ref-Gaussian</th><th>Ours</th></tr></thead><tbody><tr><th>MAE° ↓</th><td>22.31</td><td>17.02</td><td>4.618</td><td>4.871</td><td>2.078</td><td>1.78</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>Figure 5. Qualitative comparisons of normal reconstruction by different methods.</figcaption></figure>

ture sampling. To address this, we implemented hardware-accelerated texture filtering using texture atlases as described in Section 3.4. In this section, we evaluate the performance benefits of this implementation compared to software-based bilinear filtering.

We trained our model on the Shiny Blender dataset using different texture resolutions: 2x2, 4x4, 8x8 and 16x16. For each model, we then rendered the scenes using both the software implementation of bilinear filtering and our hardware-accelerated implementation with texture atlases. We measured the rendering performance in frames per second (FPS) and compared these values to the baseline method without textures.

As shown in Table 3, software-based bilinear filtering in-

<table><caption>Table 3. Rendering performance comparison between software bilinear filtering and hardware-accelerated texture atlas filtering at different texture resolutions. Values represent the ratio of FPS compared to the baseline method without textures, averaged across the Shiny Blender dataset scenes [63].</caption><thead><tr><th></th><th>2x2 Textures</th><th>4x4 Textures</th><th>8x8 Textures</th><th>16x16 Textures</th></tr></thead><tbody><tr><th>Baseline, No Textures</th><td>× 1.00</td><td>× 1.00</td><td>× 1.00</td><td>× 1.00</td></tr><tr><th>Software Bilinear</th><td>× 0.90</td><td>× 0.86</td><td>× 0.85</td><td>× 0.79</td></tr><tr><th>Hardware Texture Atlas</th><td>× 0.92</td><td>× 0.93</td><td>× 0.94</td><td>× 0.91</td></tr></tbody></table>

troduces some performance overhead compared to the baseline. This overhead increases with higher texture resolutions. In contrast, our hardware-accelerated implementation with texture atlases maintains rendering performance very close to the baseline method in comparison.

These results demonstrate that the texture atlas approach effectively leverages GPU hardware capabilities to minimize the performance impact of texture filtering. Several factors contribute to this efficiency including the use of dedicated texture units that are designed specifically for texture filtering operations, and are substantially faster than general-purpose compute.

We note that there is still room for improvement as we do not follow any strategy for packing the texture into the atlases, which could benefit from better locality if considering only primitives that are used for each frame or packing textures belonging to nearby primitives next to each other.

By leveraging hardware acceleration through texture atlases, we can achieve the best of both worlds: the improved rendering quality of per-primitive textures for reflective scenes while maintaining rendering speed comparable to methods without textures.

## 4.5. Ablation Study

To evaluate the effectiveness of our per-primitive texture mapping approach and understand the contribution of individual components, we conducted a series of ablation studies isolating different aspects of our method.

Additional experiments can be found in Sec. 3 of the supplementary material, notably a comparative analysis of Texture Mapping as opposed to increasing primitive count, and a comparative analysis of performance under reduced primitive count (Tab. 2 & Fig. 4 in Supp. Mat.).

**Impact of Normal Mapping** Our previous experiments suggested that normal mapping plays a particularly important role in the performance improvements observed with our method. To isolate this effect, we implemented a variant of the baseline that uses texture mapping only for normals while keeping other attributes (albedo, roughness, metallic) as per-primitive constants.

The results in Table 4 confirm that normal mapping alone accounts for a substantial portion of the performance im-
<table><caption>Table 4. Ablation study: Effect of normal mapping on average image and normal quality. We evaluate on the Shiny Blender dataset [63].</caption><thead><tr><th>Metric</th><th>Ref-Gaussian</th><th>+ Normal Mapping</th><th>Full Model(Ours)</th></tr></thead><tbody><tr><td>PSNR ↑</td><td>34.89</td><td>35.33</td><td>35.90</td></tr><tr><td>SSIM ↑</td><td>0.974</td><td>0.975</td><td>0.978</td></tr><tr><td>LPIPS ↓</td><td>0.053</td><td>0.053</td><td>0.047</td></tr><tr><td>Normal MAE ↓</td><td>2.078</td><td>1.783</td><td>1.78</td></tr></tbody></table>

<table><caption>Table 5. Ablation study: Effect of texture resolution on storage, average image and normal quality. We evaluate on the Shiny Blender dataset [63].</caption><thead><tr><th>Variants</th><th>PSNR ↑</th><th>SSIM ↑</th><th>LPIPS ↓</th><th>Normal MAE ↓</th><th>Storage</th></tr></thead><tbody><tr><td>Ref-Gaussian</td><td>34.88</td><td>0.974</td><td>0.053</td><td>2.078</td><td>× 1.00</td></tr><tr><td>2×2 Textures, Same Storage</td><td>35.66</td><td>0.976</td><td>0.048</td><td>1.823</td><td>× 1.00</td></tr><tr><td>2×2 Textures</td><td>35.90</td><td>0.977</td><td>0.047</td><td>1.780</td><td>× 1.20</td></tr><tr><td>4×4 Textures, Same Storage</td><td>35.33</td><td>0.977</td><td>0.048</td><td>1.881</td><td>× 1.00</td></tr><tr><td>4×4 Textures</td><td>35.94</td><td>0.978</td><td>0.047</td><td>1.830</td><td>× 1.96</td></tr></tbody></table>

provement. This is particularly evident in the normal mean angular error (MAE) metric, where normal mapping significantly reduces the error compared to the baseline.

The effectiveness of normal mapping for reflective scenes can be attributed to the fact that reflective surfaces often exhibit high-frequency normal variations that are difficult to capture with a single normal per primitive and that more accurate and detailed normals lead to more precise reflection directions and therefore better specular highlights which is achieved by our spatially varying normals.

While normal mapping provides significant improvement, our full model with texture mapping for all material properties achieves the best overall performance, demonstrating that each component contributes to the final quality.

### Impact of Texture Resolution and Storage
The results in Table 5 show different configurations of our method in terms of the texture resolution, and whether we add them on top of the baseline or reduce the primitive count so that the total storage size is equal to the baseline. We perform this evaluation on the Shiny Blender dataset [63]. We experiment with resolutions 2×2 and 4×4 as we find that for the type of scenes in this dataset (object at the center of the scene and orbital views), enhancing primitives with much higher texture resolutions does not result in a desirable storage to quality tradeoff. Using higher resolutions can still be beneficial though for other scene types where some views are close to the object for instance.

We find that at a fixed storage budget, our method still achieves better performance compared to the baseline method in all metrics. This demonstrates the efficiency of our texture-based representation and that the memory over-

head is not a fixed cost but a tunable parameter. Our framework allows for adapting texture resolutions or selectively texturing only the most critical attributes to fit different memory budgets.

Supplementary material includes additional comparisons to the baseline with increased primitive count as well as the impact on performance with reduced primitive count; These experiments show that for reflective scenes, investing the parameter budget in appearance/normal complexity (textures) is often more effective than investing it purely in geometric complexity (primitives).

## 5. Limitations and Discussion

While our per-primitive texture mapping approach significantly enhances the representation power of 2D Gaussian Splatting for the reflective setting, it comes with some limitations that present opportunities for future work.

### Uniform Texture Resolution
In the current implementation, we assign textures of uniform resolution to all primitives regardless of their size or importance in the scene. This approach can be inefficient for large unbounded scenes where distant primitives occupy few pixels but still receive the same texture resolution as foreground elements. A more sophisticated approach would involve adaptive texture allocation based on primitive size, viewing distance, or local detail complexity. Primitives in the background could potentially use single attribute values while reserving detailed textures for more predominant foreground elements.

### Filtering Limitations
Our implementation currently relies on bilinear filtering for texture sampling. While effective for our evaluated scenes, it does not fully resolve texture minification artifacts that might manifest in more challenging scenarios. while implementing proper mipmapping with trilinear filtering could be beneficial, it would be challenging to integrate with the non-antialiased nature of 2D Gaussian primitives. Potential solutions could involve combining our approach with screen-space antialiasing techniques or developing specialized filtering methods for Gaussian-based representations.

Despite these limitations, our experimental results demonstrate that per-primitive texture mapping significantly improves the visual quality of reflective scenes while maintaining real-time rendering performance.

## 6. Conclusion

We presented a method that enhances 2D Gaussian Splatting for reflective scenes by introducing per-primitive texture mapping. By leveraging the flat nature of 2D Gaussians to define textures of material properties, our approach enables high-frequency detail representation without increas-
ing primitive count. Our hardware-accelerated implemen-
tation using texture atlases demonstrates that classical com-
puter graphics techniques can be effectively integrated with
modern differentiable rendering approaches. The results
show that this representation significantly improves the
quality of specular reflections, particularly through detailed
normal mapping, while maintaining real-time performance.
Our work bridges the gap between explicit primitive-based
representations and high-quality material modeling, offer-
ing advantages of both approaches.

Acknowledgments

This work was granted access to the HPC resources of IDRIS under the allocation 20XX-AD010616156 made by GENCI.

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# Supplementary Material

## 7. Implementation Details of Hardware Accelerated Texture Atlases

**Texture Atlas Construction** Each splat is associated with a small, fixed-resolution texture (e.g., $T \times T$ texels, where $T$ is typically in powers of 2). For $P$ splats and $C$ total channels for all textured attributes, this $P \times C \times T \times T$ texel data is organized into one or more large 2D atlas textures. We pack the individual primitive textures into larger texture atlases that can be efficiently accessed by the GPU by determining the maximum atlas dimensions based on GPU capabilities, calculating how many $T \times T$ textures fit along each dimension, computing the total number of textures per atlas, then determining the number of atlases needed.

To efficiently access the textures within the atlas, we create an indirection buffer that maps primitive IDs to texture chart coordinates within the atlas. This buffer stores the top-left corner coordinates ($chart_idx_x, chart_idx_y$) of each primitive's texture in the atlas. Since CUDA texture objects typically support up to 4 channels, multiple atlases are used if the total number of attribute channels exceeds this (e.g., one atlas for albedo (RGB) and roughness (A), another for tangent normals (RGB) and metallic (A)).

**Hardware Accelerated Texture Sampling** During test-time rendering, we perform texture sampling using hardware-accelerated filtering:

1. For a given primitive $k$ and local coordinates $(u, v)$, we map to normalized texture coordinates $(s, t) \in [0, 1] \times [0, 1]$ as described in the main paper (Section 3.3).

2. We retrieve the chart coordinates ($chart_idx_x, chart_idx_y$) from the indirection buffer.

3. We compute the atlas coordinates:

$$ 
\begin{aligned}
s_{\text{atlas}} &= \frac{\text{chart\_idx}_x \cdot T + s \cdot T}{N_{\text{charts}_x} \cdot T}, \\
t_{\text{atlas}} &= \frac{\text{chart\_idx}_y \cdot T + t \cdot T}{N_{\text{charts}_y} \cdot T}
\end{aligned} 
\qquad (14) 
$$

where $N_{\text{charts}_x}$ and $N_{\text{charts}_y}$ are the total number of charts along the width and height of the atlas, respectively.

4. We sample the atlas using hardware-accelerated bilinear filtering with CUDA's 'tex2D' intrinsic:

$$ \mathbf{a}_k(x, y) = \text{BilinearFilter}(\text{atlas}, s_{\text{atlas}}, t_{\text{atlas}}). \quad (15) $$

This approach fully leverages the GPU's texture units for filtering, which are significantly faster than software-based sampling approaches. It leverages dedicated texture caching and filtering hardware, significantly speeding up attribute fetching compared to manual interpolation from global memory arrays. By using texture atlases, we avoid the need for multiple texture bindings during rendering, improving performance and reducing API overhead.

<figure><img src="image_7.png" /><figcaption>Figure 6. Qualitative comparisons on the Synthetic NeRF dataset. From top to bottom: drums, ficus and hotdog.</figcaption></figure>

## 8. Additional Results

**Performance on non-specular scenes** In Table 6, we show the performance of our method against different methods in non-specular scenes from the NeRF Synthetic dataset. Our method is capable of enhancing the baseline method thanks to the expressivity of material and normal texture splatting. It can even reach the level of performance of the vanilla 3DGS [27] on these scenes. We also show in
<table><caption>Table 6. Per-scene image quality comparison for novel view synthesis on NeRF Synthetic dataset.</caption><thead><tr><th></th><th>chair</th><th>drums</th><th>ficus</th><th>hotdog</th><th>lego</th><th>materials</th><th>ship</th></tr></thead><tbody><tr><td colspan="8" style="text-align: center; font-weight: bold;">PSNR ↑</td></tr><tr><td>3DGS</td><td>35.03</td><td>26.04</td><td>35.29</td><td>37.57</td><td>33.71</td><td>30.04</td><td>31.43</td></tr><tr><td>3DGS-DR</td><td>32.10</td><td>25.31</td><td>28.03</td><td>35.58</td><td>32.94</td><td>28.35</td><td>29.07</td></tr><tr><td>Ref-Gaussian</td><td>33.73</td><td>26.25</td><td>35.50</td><td>37.19</td><td>32.58</td><td>30.72</td><td>30.44</td></tr><tr><td>Ours</td><td>34.40</td><td>26.4</td><td>35.9</td><td>37.43</td><td>33.34</td><td>31.25</td><td>30.55</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">SSIM ↑</td></tr><tr><td>3DGS</td><td>0.987</td><td>0.954</td><td>0.987</td><td>0.985</td><td>0.975</td><td>0.959</td><td>0.906</td></tr><tr><td>3DGS-DR</td><td>0.977</td><td>0.946</td><td>0.963</td><td>0.982</td><td>0.978</td><td>0.950</td><td>0.894</td></tr><tr><td>Ref-Gaussian</td><td>0.979</td><td>0.952</td><td>0.987</td><td>0.982</td><td>0.972</td><td>0.966</td><td>0.895</td></tr><tr><td>Ours</td><td>0.981</td><td>0.953</td><td>0.988</td><td>0.983</td><td>0.974</td><td>0.969</td><td>0.896</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">LPIPS ↓</td></tr><tr><td>3DGS</td><td>0.012</td><td>0.040</td><td>0.012</td><td>0.021</td><td>0.027</td><td>0.040</td><td>0.111</td></tr><tr><td>3DGS-DR</td><td>0.024</td><td>0.055</td><td>0.055</td><td>0.033</td><td>0.026</td><td>0.044</td><td>0.129</td></tr><tr><td>Ref-Gaussian</td><td>0.023</td><td>0.043</td><td>0.013</td><td>0.029</td><td>0.031</td><td>0.036</td><td>0.127</td></tr><tr><td>Ours</td><td>0.022</td><td>0.042</td><td>0.012</td><td>0.028</td><td>0.029</td><td>0.033</td><td>0.126</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Figure 7. Decomposition results of our method. From top to bottom: cat, horse and potion.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 8. Qualitative comparisons of environment maps estimated by different methods.</figcaption></figure>

### Scene Decomposition and Environment Maps
Despite the under-constrained nature of the task in many cases, our optimization yields stable and physically plausible scene property factorization. Figure 7 illustrates decomposition examples for reflective objects into geometry normals, roughness and metallic. We also show the diffuse and specular components, in addition to the final rendering which preserves the ground truth. The specular highlights are mostly successfully factored out from the view-independent component.

We also compare estimated environment maps for our method and the competition in Figure 8. Notice that our estimated scene lighting bares more similarity with the reference maps and displays fewer distortions and artifacts generally, compared to our baseline.

## 9. Additional Ablation Studies

### Texture Mapping vs. Increased Primitive Count
A natural question when evaluating our texture-based method is whether similar quality improvements could be achieved by simply increasing the number of primitives in the baseline method. To investigate this, we compared our approach against baseline models with increased primitive counts. We created versions of the baseline with 2x and 4x the original number of primitives by lowering the gradient threshold for densification and increasing the frequency of cloning and splitting operations during optimization. We compare against our method that maintain the original primitive count with the 2x2 textures per primitive. Notably, even with these textures, our method has lower storage requirements than the 2x primitive count baseline as it only incurs an increase of 20% in storage compared to the baseline method. As shown in Table 7, the performance of the baseline method actually degrades as the number of primitives increases beyond the optimal point. This seemingly counter-intuitive result can be explained by the fact that in practice, increasing the number of primitives creates a more complex optimization and that more primitives require more extensive sorting operations during rendering, which can lead to primitives being placed in suboptimal orders, especially with the use of global sorting [27]. Primitives can also become cluttered, particularly in areas with complex geometry, leading to degraded normal estimation quality which is critical for reflective scenes.

Our texture-based approach avoids these issues by increasing representational power without increasing the number of primitives, leading to better rendering quality particularly for reflective surfaces.

### Performance with Reduced Primitive Count
To further demonstrate the efficiency of our texture-based representation, we conducted experiments with reduced primitive
<table><caption>Table 7. Ablation study: Effect of increasing primitive count for the baseline method on average image quality. We evaluate on the Shiny Blender dataset [63].</caption><thead><tr><th>Metric</th><th>Ours</th><th>Ref-Gaussian</th><th>×2 Primitives</th><th>×4 Primitives</th></tr></thead><tbody><tr><td>PSNR ↑</td><td>35.90</td><td>34.89</td><td>33.63</td><td>34.12</td></tr><tr><td>SSIM ↑</td><td>0.977</td><td>0.974</td><td>0.967</td><td>0.970</td></tr><tr><td>LPIPS ↓</td><td>0.047</td><td>0.053</td><td>0.061</td><td>0.057</td></tr></tbody></table>

counts. We created models using only 50% of the primitives used in our standard optimization process, for both the baseline method and our texture-based approach.

As illustrated in Figure 9, the baseline method with reduced primitive count suffers from significant degradation in normal reconstruction quality, exhibiting holes and artifacts due to the limited capacity of the model. In contrast, our texture-based method maintains smoother normal reconstruction even with the reduced primitive count, demonstrating the expressiveness of per-primitive texture mapping.

<figure><img src="image_10.png" /><figcaption>Figure 9. Comparison of novel view synthesis and normal rendering with fewer primitives</figcaption></figure>