Fourier Feature Regression Eval

---
name: fourier-feature-regression-eval
description: Evaluates how well coordinate-based MLPs with different input feature mappings (none, basic, positional encoding, Gaussian random Fourier features) can learn high-frequency functions across various low-dimensional regression tasks in computer vision and graphics. Use when the user wants to benchmark on Natural images, Text images, 3D shape, Shepp-Logan phantoms, ATLAS dataset, NeRF ATLAS scene, or asks about evaluating this task. Reports PSNR, IoU.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2006.10739
  bibtex_key: tancik2020fourier
  confidence: high
---

# fourier-feature-regression-eval

> Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains — Tancik et al. (2020) (arXiv:2006.10739, 2020)

## What this evaluates

Evaluates how well coordinate-based MLPs with different input feature mappings (none, basic, positional encoding, Gaussian random Fourier features) can learn high-frequency functions across various low-dimensional regression tasks in computer vision and graphics.

## Datasets

- **Natural images** — total ?; splits: train (-1), test (-1)
- **Text images** — total ?; splits: train (-1), test (-1)
- **3D shape** — total ?; splits: train (-1), test (-1)
- **Shepp-Logan phantoms** — total ?; splits: train (-1), test (-1)
- **ATLAS dataset** — total ?; splits: train (-1), test (-1)
- **NeRF ATLAS scene** — total ?; splits: train (-1), test (-1)

## Metrics

- `PSNR` **(primary)** — range: dB
  - Peak Signal-to-Noise Ratio computed from the mean squared error between predicted and ground truth values. Higher is better.
- `IoU` **(primary)** — range: [0, 1]
  - Intersection over Union between predicted binary occupancy and ground truth occupancy on points sampled near the mesh surface. Higher is better.

## Input / output format

**Input**: 2D or 3D spatial coordinates (pixel or voxel locations) passed to a coordinate-based MLP.

**Output**: Continuous values (RGB color, volume density, or atomic response) or binary occupancy (0/1), depending on the task.

## Scoring recipe

```python
if task == '3D_shape':
    pred_occ = sigmoid(mlp_output) > 0.5
    iou = intersection(pred_occ, gold_occ) / union(pred_occ, gold_occ)
    return iou
else:
    mse = mean_squared_error(pred_vals, gold_vals)
    max_val = max(gold_vals) # or 255 for images
    psnr = 10 * log10(max_val**2 / mse)
    return psnr
```

## Common pitfalls

- Direct vs indirect supervision: Direct tasks use ground truth labels per coordinate, while indirect tasks pass network outputs through a forward model (e.g., integral projection, Fourier transform, volume rendering) before computing loss.
- The scale parameter (σ) for Fourier feature mappings is highly task-dependent and requires hyperparameter sweeping; the paper notes scale is more critical than the distribution shape.
- PSNR is the standard metric for all tasks except 3D shape regression, which exclusively uses IoU.

## Evidence (verbatim from paper)

> All results are reported in PSNR except 3D shape, which uses IoU (higher is better for all).

## Citation

```bibtex
@misc{tancik2020fourier,
  title={Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains},
  author={Tancik et al. (2020)},
  year={2020},
  note={arXiv:2006.10739}
}
```

- arXiv: 2006.10739