L1 ⚛ L1-076 ⊙ Testnet

Multi-Focus / Panorama Fusion (all-in-focus composite imaging)

Computational Photography · Image fusion and stitching

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⬇ L1-076.md

# ⚛ L1 Principle — Multi-Focus / Panorama Fusion (all-in-focus composite imaging) **ID:** `L1-076` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Photography — *Image fusion and stitching* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D spatial > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554170 --- ## 🧠 1. Introduction **Multi-Focus / Panorama Fusion (all-in-focus composite imaging)** is a **linear inverse problem** whose unknown lives in **2D spatial** space, within the **Image fusion and stitching** sub-domain of **Computational Photography**. Measurements consist of photons collected by an optical detector via a **multi frame capture** sensing mechanism. The forward operator applies, in order: S · scan · pose operator; K · psf · defocus operator; L · warp · affine operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Well-conditioned when scenes are Lambertian, inter-frame parallax is small (pure rotation or small translation), and focus distances span the scene depth range. Degrades catastrophically for moving subjects (ghosting) and unconstrained parallax (depth ambiguity). ## ⚙ 2. Forward Model Physical chain: **x** → S · scan · pose → K · psf · defocus → L · warp · affine → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.warp.affine` `K.psf.defocus` `S.scan.pose` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.scan.pose` | S · scan · pose operator | | `K.psf.defocus` | K · psf · defocus operator | | `L.warp.affine` | L · warp · affine operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Photography | | Sub domain | Image fusion and stitching | | Carrier | photon | | Problem class | linear_inverse | | Solution space | 2D_spatial | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Well-conditioned when scenes are Lambertian, inter-frame parallax is small (pure rotation or small translation), and focus distances span the scene depth range. Degrades catastrophically for moving subjects (ghosting) and unconstrained parallax (depth ambiguity). | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `image_fusion` · **Forward operator:** `multi_focus_stitch` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1024 | | W | px | 1024 | | K frames | — | 5 | | Parallax px | — | 0 | | Motion ghosting | — | 0 | | Exposure variation | — | 0 | | Registration error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 8192 | | W | px | 256 – 8192 | | K frames | — | 2 – 32 | | Parallax px | — | 0.0 – 30.0 | | Motion ghosting | — | 0.0 – 0.5 | | Chromatic fringing | — | 0.0 – 2.0 | | Exposure variation | — | 0.0 – 2.0 | | Registration error | — | 0.0 – 5.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 18.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `800` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x7400042a609bbd8255fe706b4468eb0638342ab1a6a4a3c62e50a87bdc0ae8ea` - **Chain tx hash:** `0x1e37c96911d8b9cab6153b6f94e24a64e1c68c42da4df71822eab05e82020828` - **Chain block:** `41554170` --- ## File Mapping This bundle consists of: `L1-076.md`, `L1-076.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-076.md` | Source of truth — edit this | Human or LLM | | `L1-076.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 `L1-076`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-076.md).
Regenerate L1-076.json so every field matches the Markdown.
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L2-076-001 Multi-Focus Fusion Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-076",
  "chain_block": 41554170,
  "chain_hash": "0x7400042a609bbd8255fe706b4468eb0638342ab1a6a4a3c62e50a87bdc0ae8ea",
  "chain_tx_hash": "0x1e37c96911d8b9cab6153b6f94e24a64e1c68c42da4df71822eab05e82020828",
  "domain": "Computational Photography",
  "hardness_fn": {
    "delta": 3,
    "kappa": 800,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Well-conditioned when scenes are Lambertian, inter-frame parallax is small (pure rotation or small translation), and focus distances span the scene depth range. Degrades catastrophically for moving subjects (ghosting) and unconstrained parallax (depth ambiguity).",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Computational Photography",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "S.scan.pose",
      "K.psf.defocus",
      "L.warp.affine",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "multi_frame_capture",
    "solution_space": "2D_spatial",
    "sub_domain": "Image fusion and stitching",
    "title": "Multi-Focus / Panorama Fusion (all-in-focus composite imaging)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "multi_focus_stitch",
      "panorama_homography",
      "focus_stack_depth"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "K_frames",
      "parallax_px",
      "motion_ghosting",
      "exposure_variation",
      "registration_error",
      "chromatic_fringing"
    ],
    "allowed_problem_classes": [
      "image_fusion",
      "panorama_stitching",
      "all_in_focus"
    ],
    "center_spec": {
      "epsilon_fn_center": "30.0 dB PSNR",
      "forward_operator": "multi_focus_stitch",
      "input_format": "K_aligned_frames",
      "omega": {
        "H": 1024,
        "K_frames": 5,
        "W": 1024,
        "exposure_variation": 0.0,
        "motion_ghosting": 0.0,
        "parallax_px": 0.0,
        "registration_error": 0.0
      },
      "problem_class": "image_fusion"
    },
    "epsilon_bounds": {
      "psnr_db": [
        18.0,
        40.0
      ]
    },
    "omega_bounds": {
      "H": [
        256,
        8192
      ],
      "K_frames": [
        2,
        32
      ],
      "W": [
        256,
        8192
      ],
      "chromatic_fringing": [
        0.0,
        2.0
      ],
      "exposure_variation": [
        0.0,
        2.0
      ],
      "motion_ghosting": [
        0.0,
        0.5
      ],
      "parallax_px": [
        0.0,
        30.0
      ],
      "registration_error": [
        0.0,
        5.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Image fusion and stitching",
  "title": "Multi-Focus / Panorama Fusion (all-in-focus composite imaging)"
}

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