# ⚛  L1 Principle — Photogrammetry Structure-from-Motion

**ID:** `L1-470` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geodesy — *Photogrammetry*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D point cloud camera poses
> **📡 Carrier:** photon · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555299

---

## 🧠 1. Introduction

**Photogrammetry Structure-from-Motion** is a **nonlinear inverse problem** whose unknown lives in **3D point cloud camera poses** space, within the **Photogrammetry** sub-domain of **Geodesy**.

Measurements consist of photons collected by an optical detector via a **bundle adjustment sfm** sensing mechanism.

The forward operator applies, in order: S · sfm · feature matching operator; a fixed-point or gradient iteration on the unknown; O · reprojection · error operator.

Observations are corrupted by additive Gaussian noise. Existence of the recovered 3D_point_cloud_camera_poses is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 200); GPS_geotag_accuracy_m dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → S · sfm · feature matching → O · reprojection · error → **y** (detector).

```
y = `O.reprojection.error` `S.sfm.feature_matching` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `S.sfm.feature_matching` | S · sfm · feature matching operator |
| `O.reprojection.error` | O · reprojection · error operator |

**🛠 Solver components** _(used inside the solver, not in the forward equation)_:

| Primitive | What it does |
|---|---|
| `O.iter` | A fixed-point or gradient iteration on the unknown |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geodesy |
| Sub domain | Photogrammetry |
| Carrier | photon |
| Problem class | nonlinear_inverse |
| Solution space | 3D_point_cloud_camera_poses |
| Noise model | gaussian |
| Integration axis | image_network |
| Difficulty delta | 3 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Existence of the recovered 3D_point_cloud_camera_poses is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 200); GPS_geotag_accuracy_m dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | GCP_RMSE_cm |
| Secondary | reprojection_error_px |

## 📏 5. Operating Range (Ω)

**Center problem class:** `nonlinear_inverse` · **Forward operator:** `bundle_adjustment_sfm`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N gcps | — | 5 |
| N images | — | 200 |
| Overlap percent | — | 80 |
| Flight altitude m | m | 120 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N gcps | — | 0 – 50 |
| N images | — | 10 – 10000 |
| Overlap percent | — | 50 – 95 |
| Flight altitude m | m | 30 – 2000 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 3.0 GCP_RMSE_cm

| Metric | Range |
|---|---|
| Gcp rmse cm | 0.5 – 20.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **GCP_RMSE_cm**, with κ = `10000.0` and δ = `3`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xf3c8207115e276cca032e9e270613281d8590d3b9040e6e05205b1375254785d`
- **Chain tx hash:** `0xd7d86be7c33fe9a9df4bc677e263b501a9378e6e342b95ae376b042bd2739e61`
- **Chain block:** `41555299`

---

## File Mapping

This bundle consists of: `L1-470.md`, `L1-470.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-470.md` | Source of truth — edit this | Human or LLM |
| `L1-470.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-470`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._