ShinyNeRF: Anisotropic Neural Volumetric Rendering

• ShinyNeRF is a neural volumetric rendering framework that models isotropic and anisotropic specular reflections using a physically motivated ASG reflectance model.
• It jointly estimates surface normals, tangent orientations, specular concentration, and anisotropy to enable edit-friendly and high-fidelity view synthesis.
• The system achieves state-of-the-art performance with superior metrics and robust handling of complex materials such as brushed metals and fabrics.

ShinyNeRF is a neural volumetric rendering framework that extends standard Neural Radiance Fields (NeRF) to accurately digitize and synthesize isotropic and anisotropic specular reflections, particularly for complex materials such as brushed metals and fabrics. ShinyNeRF enables joint estimation and rendering of surface normals, tangent directions, specular concentration, and anisotropy, leveraging a physically motivated Anisotropic Spherical Gaussian (ASG) reflectance model, which is tractably approximated for neural integration by a mixture of von Mises–Fisher (vMF) distributions. It is the first system in the NeRF family that unifies physically interpretable anisotropic appearance modeling and high-fidelity view synthesis, validated across controlled and real cultural heritage objects (Barreiro et al., 25 Dec 2025).

1. Physical Motivation for Anisotropic Appearance Modeling

Traditional NeRF and its first reflectance extensions are limited to view-independent (i.e., Lambertian) or simple isotropic specular effects, where the specular lobe is uniform in all directions around the surface normal. Materials with directionally dependent reflection—such as brushed metals—exhibit highlights that maintain elongation along specific tangent axes and compression along bitangent directions. ShinyNeRF addresses these limitations by learning for every 3D point: the surface normal $\hat{\mathbf{n}'}$, tangent orientation $\phi$, specular concentration $\kappa$, and anisotropy magnitude $e$. This enables physically plausible and edit-friendly renderings for both isotropic and strongly anisotropic regimes (Barreiro et al., 25 Dec 2025).

2. Outgoing Radiance: The Anisotropic Spherical Gaussian (ASG) Model

ShinyNeRF parameterizes specular lobes via the ASG distribution,

$$\mathrm{ASG}(\mathbf{v};[\mathbf{x},\mathbf{y},\mathbf{z}],\lambda,\mu,c) = c\;\max(\mathbf{v}\!\cdot\!\mathbf{z},0)\; \exp\bigl(-\lambda(\mathbf{v}\!\cdot\!\mathbf{x})^2 -\mu(\mathbf{v}\!\cdot\!\mathbf{y})^2\bigr)$$

where $\lambda$ and $\mu$ are directional bandwidths (controlling elongation and compression), $\mathbf{x}$ is the tangent, $\mathbf{y}$ the bitangent, and $\mathbf{z}$ the surface normal. The network predicts overall concentration $\kappa$ (specular sharpness) and anisotropy $e$ (elongation), mapped as: $$\lambda = \tfrac{1}{2}\kappa(1+e), \quad \mu = \tfrac{1}{2}\kappa(1-e)$$ This formulation ensures a smooth transition from isotropic ($e=0$) to maximally anisotropic ($e\to 1$) reflectance.

3. ASG Approximation with von Mises–Fisher Mixtures

Direct integration of the ASG into the NeRF volume rendering equation is intractable. ShinyNeRF solves this by approximating the ASG lobe as a symmetric mixture of $N=2L+1$ von Mises–Fisher (vMF) distributions (isotropic spherical Gaussians): $$\hat p_{\mathrm{ASG}}(\mathbf{v}) = \sum_{i=-L}^{L} \alpha_i\;\mathrm{vMF}(\mathbf{v};\,\mathbf{z}_i,\kappa_i)$$ where each vMF is centered along a rotated direction in the tangent-normal plane and weighted by $\alpha_i$. This mixture maintains the physical shape of specular highlights while being compatible with neural volume integration. The mapping from ASG parameters to vMF mixture parameters is handled by a small, pretrained, and frozen "ASG2vMF" network.

4. Network Architecture and Ray Rendering

The volumetric approach follows a discrete NeRF pipeline, with several specialized neural networks:

• Spatial MLP ($f_\tau$): 8-layer, width 256, predicts for every $\mathbf{x}$: volume density $\tau$, diffuse color $\mathbf{c}_d$, specular tint $\mathbf{s}$, bottleneck feature vector $\mathbf{b}\in\mathbb{R}^{32}$, surface normal, concentration, anisotropy, and tangent orientation.
• Tangent Construction: Instantiates an orthonormal basis by generating provisional tangent and bitangent vectors from $\hat{\mathbf{n}'}$, then rotating by the predicted $\phi$.
• ASG2vMF MLP: Converts log-bandwidths into mixture parameters with positional encoding, yielding $\{\theta_i,\kappa_i,\alpha_i\}$ for all $N$ lobes.
• Directional MLP ($f_c$): Aggregates bottleneck features, vMF mixture encodings, and the dot product of viewing direction and predicted normal to produce the final specular color.

The rendered ray color is computed via the weighted sum over all sampled spatial points: $$C(\mathbf{o},\hat{\mathbf{d}}) = \sum_i w_i\bigl[\mathbf{c}_{d,i} + \mathbf{s}_i\odot\mathbf{c}_{s,i}\bigr], \quad w_i=e^{-\sum_{j<i}\tau_j\Delta t_j}\bigl(1-e^{-\tau_i\Delta t_i}\bigr)$$ with $w_i$ as the standard NeRF transmittance-weighted coefficients.

5. Objective Functions and Training Protocols

The total training objective combines several loss components:

• Photometric Loss:

$$\mathcal{L}_{\mathrm{rgb}} = \sum_{\mathbf{o},\hat d} \|\,C(\mathbf{o},\hat d)-C_{\mathrm{gt}}(\mathbf{o},\hat d) \|_2^2$$

• Normal Consistency Losses (NeRF-Casting, Ref-NeRF): Encourage consistency between predicted and sampled normals both for asymmetric (source → prediction) and symmetric (prediction → source) directions.
• Normal Orientation Penalty: Encourages normals to orient away from the viewer when appropriate.
• Distortion Loss (mip-NeRF 360): Discourages floaters.
• Proposal Loss (Zip-NeRF): Regularizes coarse-to-fine ray sampling.

Typical hyperparameters are: $\beta_{\mathrm{pred}}=3\cdot10^{-3}$, $\beta_{\mathrm{grad}}=3\cdot10^{-4}$, $\beta_{\mathrm{orient}}=1\cdot10^{-2}$, $\beta_{\mathrm{dist}}=3\cdot10^{-3}$, $\beta_{\mathrm{prop}}=3\cdot10^{-4}$.

6. Quantitative and Qualitative Performance

ShinyNeRF demonstrates state-of-the-art metrics for anisotropic appearance modeling:

Model	PSNR	SSIM	LPIPS	Normal MAE (°)	Tangent MAE (°)
ShinyNeRF	31.46	0.919	0.162	12.13	29.86
Ref-NeRF	27.72	0.860	0.220	20.52	—
Spec-Gauss.	27.86	0.903	0.138	53.72	—
AniSDF	28.82	0.882	0.205	8.36	—

Diverse datasets—including point-lit anisotropic objects (ASD), spheres under environment maps (ASPH), and cultural heritage artifacts (CHAO)—demonstrate that ShinyNeRF reproduces elongated highlights consistent with physical material properties, maintains accurate geometry, and supports high-fidelity novel-view synthesis. Notably, tangent orientation estimation is unique to ShinyNeRF.

7. Physical Interpretability and Editing Capabilities

ShinyNeRF provides direct, physically meaningful outputs: per-point surface normal, tangent orientation, specular concentration, and eccentricity. These can be interactively manipulated:

• Increasing $e$ stretches the highlight (greater anisotropy).
• Decreasing $\kappa$ blurs specular lobes (lower sharpness).
• Rotating $\phi$ shifts highlight orientation.

Such edits produce physically plausible, consistent results in both training and novel views. This interpretability aligns ShinyNeRF with analytic BRDF frameworks, offering practical utility for cultural heritage digitization and appearance editing.

8. Implementation Details and Limitations

Implementation utilizes spatial, directional, proposal, and ASG2vMF MLPs, with integral positional encoding and Zip-NeRF sampling (6000 rays/batch). Typical training uses dual RTX 3090 GPUs (30 GB VRAM, 20 h/object), Adam optimizer with learning rate decay, and gradient clipping at $1.0\times10^{-3}$. The optimal number of vMF lobes for ASG approximation is $N=29$.

ShinyNeRF handles ONB singularities using an epsilon fallback during tangent initialization. A noted limitation is that, like all neural fields, its fidelity may degrade in areas with ambiguous or insufficient highlight structure (Barreiro et al., 25 Dec 2025). A plausible implication is that further improvements could exploit auxiliary priors or structured light inputs.