Geometric Accuracy Eval

---
name: geometric-accuracy-eval
description: Evaluates the geometric fidelity and surface reconstruction accuracy of neural 3D scene representations (NeRF and Gaussian Splatting variants) against metric-scale laser scan ground truth. Use when the user wants to benchmark on Robotic Manipulation Scenes, or asks about evaluating this task. Reports CD_{P\rightarrow G}.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2604.18205
  bibtex_key: zielinski2026comparative
  confidence: high
---

# geometric-accuracy-eval

> A Comparative Evaluation of Geometric Accuracy in NeRF and Gaussian Splatting — Zielinski et al. (2026) (arXiv:2604.18205, 2026)

## What this evaluates

Evaluates the geometric fidelity and surface reconstruction accuracy of neural 3D scene representations (NeRF and Gaussian Splatting variants) against metric-scale laser scan ground truth.

## Datasets

- **Robotic Manipulation Scenes** — total 19; splits: test (19)

## Metrics

- `CD_{P\rightarrow G}` **(primary)** — range: other
  - Chamfer Distance from predicted to ground truth point cloud. Lower values indicate better surface alignment. Computed as the average minimum distance from each point in the prediction to the ground truth set.
- `F1@5mm` — range: [0, 1]
  - Harmonic mean of precision and recall computed by counting points within a 5 mm distance threshold as true positives. Balances correctness and completeness at manipulation-relevant tolerances.

## Input / output format

**Input**: RGB images (1280×720) per scene for reconstruction; laser scan point clouds serve as ground truth.

**Output**: Reconstructed 3D point clouds or meshes per scene.

## Scoring recipe

```python
def chamfer_distance(pred_pts, gt_pts):
    dists_p2g = min_dist(pred_pts, gt_pts)
    dists_g2p = min_dist(gt_pts, pred_pts)
    return np.mean(dists_p2g) + np.mean(dists_g2p)

def threshold_f1(pred_pts, gt_pts, tol_mm):
    tp = count_points_within(pred_pts, gt_pts, tol_mm)
    fp = len(pred_pts) - tp
    fn = len(gt_pts) - count_points_within(gt_pts, pred_pts, tol_mm)
    prec = tp / (tp + fp) if (tp + fp) > 0 else 0
    rec = tp / (tp + fn) if (tp + fn) > 0 else 0
    return 2 * prec * rec / (prec + rec) if (prec + rec) > 0 else 0
```

## Common pitfalls

- Sparse reconstructions (e.g., COLMAP) yield artificially low CD but poor coverage.
- Unfiltered dense point clouds (e.g., Tri-Splats) inflate CD due to noise outliers.
- Threshold selection (2mm vs 5mm) drastically changes F1 scores; 5mm is more relevant for robotic manipulation tolerances.

## Evidence (verbatim from paper)

> Table 1 summarizes surface accuracy and completeness metrics, while Table 2 reports threshold-based precision, recall, and F1 scores at tolerances of 2 mm and 5 mm.

## Citation

```bibtex
@misc{zielinski2026comparative,
  title={A Comparative Evaluation of Geometric Accuracy in NeRF and Gaussian Splatting},
  author={Zielinski et al. (2026)},
  year={2026},
  note={arXiv:2604.18205}
}
```

- arXiv: 2604.18205