L1 ⚛ L1-470 ⊙ Testnet

Photogrammetry Structure-from-Motion

Geodesy · Photogrammetry

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⬇ L1-470.md

# ⚛ 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._

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Read the attached Markdown (L1-470.md).
Regenerate L1-470.json so every field matches the Markdown.
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L2-470-001 Photogrammetry Structure-from-Motion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555299,
  "chain_hash": "0xf3c8207115e276cca032e9e270613281d8590d3b9040e6e05205b1375254785d",
  "chain_tx_hash": "0xd7d86be7c33fe9a9df4bc677e263b501a9378e6e342b95ae376b042bd2739e61",
  "domain": "Geodesy",
  "hardness_fn": {
    "delta": 3,
    "kappa": 10000.0,
    "metric": "GCP_RMSE_cm",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
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  "observable_profile": {
    "metric": "GCP_RMSE_cm",
    "regime": "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.",
    "secondary": "reprojection_error_px"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Geodesy",
    "integration_axis": "image_network",
    "noise_model": "gaussian",
    "primitives": [
      "S.sfm.feature_matching",
      "O.iter",
      "O.reprojection.error"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "bundle_adjustment_sfm",
    "solution_space": "3D_point_cloud_camera_poses",
    "sub_domain": "Photogrammetry",
    "title": "Photogrammetry Structure-from-Motion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "bundle_adjustment_sfm"
    ],
    "allowed_omega_dimensions": [
      "N_images",
      "N_GCPs",
      "overlap_percent",
      "flight_altitude_m"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "3.0 GCP_RMSE_cm",
      "forward_operator": "bundle_adjustment_sfm",
      "input_format": "measurement_only",
      "omega": {
        "N_GCPs": 5,
        "N_images": 200,
        "flight_altitude_m": 120,
        "overlap_percent": 80
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "GCP_RMSE_cm": [
        0.5,
        20.0
      ]
    },
    "omega_bounds": {
      "N_GCPs": [
        0,
        50
      ],
      "N_images": [
        10,
        10000
      ],
      "flight_altitude_m": [
        30,
        2000
      ],
      "overlap_percent": [
        50,
        95
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Photogrammetry",
  "title": "Photogrammetry Structure-from-Motion"
}

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