Surf Nerf Eval

---
name: surf-nerf-eval
description: Evaluates a NeRF model's ability to reconstruct reflective scenes with high visual fidelity and accurate geometry. It specifically probes the model's capacity to separate Lambertian and specular appearance components while enforcing surface regularisation to resolve shape-radiance ambiguity. Use when the user wants to benchmark on Shiny Objects, Shiny Real, Koala, or asks about evaluating this task. Reports PSNR.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2411.18652
  bibtex_key: naylor2024surfnerf
  confidence: high
---

# surf-nerf-eval

> Surf-NeRF: Surface Regularised Neural Radiance Fields — Naylor et al. (2024) (arXiv:2411.18652, 2024)

## What this evaluates

Evaluates a NeRF model's ability to reconstruct reflective scenes with high visual fidelity and accurate geometry. It specifically probes the model's capacity to separate Lambertian and specular appearance components while enforcing surface regularisation to resolve shape-radiance ambiguity.

## Datasets

- **Shiny Objects** — total ?; splits: train (-1), test (-1)
- **Shiny Real** — total ?; splits: train (-1), test (-1)
- **Koala** — total ?; splits: train (40), test (10)

## Metrics

- `PSNR` **(primary)** — range: dB
  - Peak Signal-to-Noise Ratio measured in decibels (dB). Computed as 10 * log10(1 / MSE) between rendered and ground-truth RGB images. Higher values indicate better pixel-wise reconstruction fidelity.
- `SSIM` — range: [0, 1]
  - Structural Similarity Index measuring perceptual similarity between rendered and ground-truth images. Ranges from 0 to 1, with 1 indicating identical structure.
- `MAE` — range: degrees
  - Mean Angular Error of surface normals, measured in degrees. Calculates the average angular difference between predicted and ground-truth normal vectors.
- `RMSE` — range: inverse units
  - Root Mean Squared Error of disparity maps, measured in inverse units. Computes the square root of the average squared difference between predicted and ground-truth disparity values.

## Input / output format

**Input**: Posed RGB images for training; posed RGB images with ground-truth surface normals and disparity maps for testing.

**Output**: Rendered RGB image, surface normal map, and disparity map per test view.

## Scoring recipe

```python
def compute_metrics(pred_rgb, gt_rgb, pred_normals, gt_normals, pred_disp, gt_disp):
    psnr = 10 * math.log10(1.0 / np.mean((pred_rgb - gt_rgb)**2))
    ssim = structural_similarity(pred_rgb, gt_rgb)
    mae = np.degrees(np.arccos(np.clip(np.sum(pred_normals * gt_normals, axis=-1), -1.0, 1.0)))
    rmse = np.sqrt(np.mean((pred_disp - gt_disp)**2))
    return psnr, ssim, mae, rmse
```

## Common pitfalls

- Enforcing geometric consistency via surface regularisation trades off photometric accuracy, leading to slightly lower PSNR scores compared to non-regularised baselines.
- Grid-based discretisation methods inherently produce higher disparity errors (RMSE) than positional encoding methods due to interpolation limitations.
- Surface regularisation degrades the representation of volumetric elements like hair or subsurface scattering, as the method assumes scene geometry can be modelled as surfaces.

## Evidence (verbatim from paper)

> We compare visual fidelity by peak-signal-to-noise ratio (PSNR) in decibels (dB) and structural similarity scores (SSIM), and geometric fidelity by mean angular error (MAE) of surface normals in degrees and root mean squared error (RMSE) of the disparity in inverse units.

## Citation

```bibtex
@misc{naylor2024surfnerf,
  title={Surf-NeRF: Surface Regularised Neural Radiance Fields},
  author={Naylor et al. (2024)},
  year={2024},
  note={arXiv:2411.18652}
}
```

- arXiv: 2411.18652