L1 ⚛ L1-097 ⊙ Testnet

Structured-Light 3D Imaging (projector-camera triangulation)

Depth Imaging · Active triangulation with coded patterns

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⬇ L1-097.md

# ⚛ L1 Principle — Structured-Light 3D Imaging (projector-camera triangulation) **ID:** `L1-097` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Depth Imaging — *Active triangulation with coded patterns* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D depth map > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41547811 --- ## 🧠 1. Introduction **Structured-Light 3D Imaging (projector-camera triangulation)** is a **linear inverse problem** whose unknown lives in **2D depth map** space, within the **Active triangulation with coded patterns** sub-domain of **Depth Imaging**. Measurements consist of photons collected by an optical detector via a **projector camera triangulation** sensing mechanism. The forward operator applies, in order: S · project · pattern operator; L · reflect lambertian operator; L · triangulate operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Well-posed when K projector-pattern bits exceed log2(W_p) + phase-unwrap margin and surface is Lambertian. Degrades on specular, translucent, dark, and high-frequency surfaces (e.g. hair), in strong ambient light, and at occlusions (camera sees but projector cannot). ## ⚙ 2. Forward Model Physical chain: **x** → S · project · pattern → L · reflect lambertian → L · triangulate → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.triangulate` `L.reflect_lambertian` `S.project.pattern` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.project.pattern` | S · project · pattern operator | | `L.reflect_lambertian` | L · reflect lambertian operator | | `L.triangulate` | L · triangulate operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Depth Imaging | | Sub domain | Active triangulation with coded patterns | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_depth_map | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3.2 | ## 📡 4. Measurement Model Well-posed when K projector-pattern bits exceed log2(W_p) + phase-unwrap margin and surface is Lambertian. Degrades on specular, translucent, dark, and high-frequency surfaces (e.g. hair), in strong ambient light, and at occlusions (camera sees but projector cannot). | Metric | Value | |---|---| | Metric | depth_RMSE_mm | | Secondary | depth_MAE_mm | ## 📏 5. Operating Range (Ω) **Center problem class:** `structured_light_depth` · **Forward operator:** `phase_shift_gray_code` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1080 | | W | px | 1920 | | W p | — | 1024 | | K patterns | — | 24 | | Baseline mm | mm | 120 | | Photon count | — | 500 | | Ambient light | — | 0 | | Specular fraction | — | 0 | | Projector camera pose drift | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 480 – 4000 | | W | px | 640 – 4000 | | W p | — | 256 – 4096 | | K patterns | — | 4 – 64 | | Baseline mm | mm | 30 – 500 | | Photon count | — | 50 – 10000 | | Ambient light | — | 0.0 – 100000 | | Specular fraction | — | 0.0 – 0.5 | | Occlusion fraction | — | 0.0 – 0.3 | | Subsurface scattering | — | 0.0 – 0.3 | | Projector camera pose drift | — | 0.0 – 0.002 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.5 mm depth RMSE | Metric | Range | |---|---| | Depth rmse mm | 0.1 – 20.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **depth_RMSE_mm**, with κ = `600` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb0f648b5592f9e7acd3f02ed5540ca01b3a470930c9815fe5bcad170aebe27ad` - **Chain tx hash:** `0xaf6d7c9dd89cedbd85561c6fe7bca07d2b5f8137e6714bbc680ff5f91f89f5f7` - **Chain block:** `41547811` --- ## File Mapping This bundle consists of: `L1-097.md`, `L1-097.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-097.md` | Source of truth — edit this | Human or LLM | | `L1-097.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 `L1-097`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-097.md).
Regenerate L1-097.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

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L2-097-001 Structured-Light Depth Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41547811,
  "chain_hash": "0xb0f648b5592f9e7acd3f02ed5540ca01b3a470930c9815fe5bcad170aebe27ad",
  "chain_tx_hash": "0xaf6d7c9dd89cedbd85561c6fe7bca07d2b5f8137e6714bbc680ff5f91f89f5f7",
  "domain": "Depth Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 600,
    "metric": "depth_RMSE_mm",
    "type": "epsilon_fn"
  },
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      "license_hash": null,
      "name": "primary",
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    "regime": "Well-posed when K projector-pattern bits exceed log2(W_p) + phase-unwrap margin and surface is Lambertian. Degrades on specular, translucent, dark, and high-frequency surfaces (e.g. hair), in strong ambient light, and at occlusions (camera sees but projector cannot).",
    "secondary": "depth_MAE_mm"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Depth Imaging",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "S.project.pattern",
      "L.reflect_lambertian",
      "L.triangulate",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "projector_camera_triangulation",
    "solution_space": "2D_depth_map",
    "sub_domain": "Active triangulation with coded patterns",
    "title": "Structured-Light 3D Imaging (projector-camera triangulation)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
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      "random_speckle_ir",
      "single_shot_de_bruijn"
    ],
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      "W",
      "W_p",
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      "baseline_mm",
      "photon_count",
      "specular_fraction",
      "ambient_light",
      "projector_camera_pose_drift",
      "occlusion_fraction",
      "subsurface_scattering"
    ],
    "allowed_problem_classes": [
      "structured_light_depth",
      "active_stereo",
      "scan_to_mesh"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.5 mm depth RMSE",
      "forward_operator": "phase_shift_gray_code",
      "input_format": "K_pattern_images_plus_calibration",
      "omega": {
        "H": 1080,
        "K_patterns": 24,
        "W": 1920,
        "W_p": 1024,
        "ambient_light": 0.0,
        "baseline_mm": 120,
        "photon_count": 500,
        "projector_camera_pose_drift": 0.0,
        "specular_fraction": 0.0
      },
      "problem_class": "structured_light_depth"
    },
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        20.0
      ]
    },
    "omega_bounds": {
      "H": [
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        4000
      ],
      "K_patterns": [
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        64
      ],
      "W": [
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        4000
      ],
      "W_p": [
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        4096
      ],
      "ambient_light": [
        0.0,
        100000
      ],
      "baseline_mm": [
        30,
        500
      ],
      "occlusion_fraction": [
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      ],
      "photon_count": [
        50,
        10000
      ],
      "projector_camera_pose_drift": [
        0.0,
        0.002
      ],
      "specular_fraction": [
        0.0,
        0.5
      ],
      "subsurface_scattering": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Active triangulation with coded patterns",
  "title": "Structured-Light 3D Imaging (projector-camera triangulation)"
}

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