L1 ⚛ L1-079 ⊙ Testnet

High Dynamic Range (HDR) Imaging via Multi-Exposure Fusion

Computational Photography · Dynamic-range extension

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⬇ L1-079.md

# ⚛ L1 Principle — High Dynamic Range (HDR) Imaging via Multi-Exposure Fusion **ID:** `L1-079` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Photography — *Dynamic-range extension* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D hdr irradiance > **📡 Carrier:** photon · **🌫 Noise:** poisson gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554171 --- ## 🧠 1. Introduction **High Dynamic Range (HDR) Imaging via Multi-Exposure Fusion** is a **nonlinear inverse problem** whose unknown lives in **2D hdr irradiance** space, within the **Dynamic-range extension** sub-domain of **Computational Photography**. Measurements consist of photons collected by an optical detector via a **multi exposure** sensing mechanism. The forward operator applies, in order: S · scan · exposure operator; L · apply · crf operator; D · saturate operator; detector accumulates flux over the exposure window. Observations are corrupted by Poisson shot noise plus Gaussian read-out noise. Well-conditioned when saturation is avoided at some exposure for every pixel (dynamic-range cover). Degrades when (a) motion causes ghosting, (b) all exposures saturate in hotspots, (c) CRF calibration drifts. Under-covered bins (no exposure contains them unsaturated) are unrecoverable. ## ⚙ 2. Forward Model Physical chain: **x** → S · scan · exposure → L · apply · crf → D · saturate → Temporal integration → **y** (detector). ``` y = ∫_t dt `D.saturate` `L.apply.crf` `S.scan.exposure` x + n, Poisson + 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.scan.exposure` | S · scan · exposure operator | | `L.apply.crf` | L · apply · crf operator | | `D.saturate` | D · saturate operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Photography | | Sub domain | Dynamic-range extension | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 2D_hdr_irradiance | | Noise model | poisson_gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3.1 | ## 📡 4. Measurement Model Well-conditioned when saturation is avoided at some exposure for every pixel (dynamic-range cover). Degrades when (a) motion causes ghosting, (b) all exposures saturate in hotspots, (c) CRF calibration drifts. Under-covered bins (no exposure contains them unsaturated) are unrecoverable. | Metric | Value | |---|---| | Metric | HDR_PSNR_mu_dB | | Secondary | HDR_VDP_2 | ## 📏 5. Operating Range (Ω) **Center problem class:** `hdr_multi_exposure_fusion` · **Forward operator:** `multi_exposure_crf` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 1080 | | W | px | 1920 | | Bit depth | — | 12 | | K exposures | — | 3 | | Exposure stops | — | 2 | | Under coverage | — | 0 | | Motion ghosting | — | 0 | | Crf calibration error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 256 – 4096 | | W | px | 256 – 4096 | | Bit depth | — | 8 – 14 | | K exposures | — | 2 – 9 | | Exposure stops | — | 1.0 – 4.0 | | Under coverage | — | 0.0 – 0.3 | | Motion ghosting | — | 0.0 – 0.5 | | Vignetting residual | — | 0.0 – 0.1 | | White balance drift | — | 0.0 – 0.1 | | Crf calibration error | — | 0.0 – 0.05 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 42.0 dB HDR-PSNR-mu | Metric | Range | |---|---| | Hdr psnr mu db | 25.0 – 55.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **HDR_PSNR_mu_dB**, with κ = `600` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x85f66a618ed8b3068d7a4cd5f2c452123fb749cc33e416b1b060679f3305483b` - **Chain tx hash:** `0x975e6e11208ebbb9666cc5bb5e7218359b6fa81a1c4a8c1cf67b6c3de08834af` - **Chain block:** `41554171` --- ## File Mapping This bundle consists of: `L1-079.md`, `L1-079.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-079.md` | Source of truth — edit this | Human or LLM | | `L1-079.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 `L1-079`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-079.md).
Regenerate L1-079.json so every field matches the Markdown.
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L2-079-001 HDR Multi-Exposure Fusion Mismatch-Only Spec

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📋 JSON metadata

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  "chain_tx_hash": "0x975e6e11208ebbb9666cc5bb5e7218359b6fa81a1c4a8c1cf67b6c3de08834af",
  "domain": "Computational Photography",
  "hardness_fn": {
    "delta": 3,
    "kappa": 600,
    "metric": "HDR_PSNR_mu_dB",
    "type": "epsilon_fn"
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    "regime": "Well-conditioned when saturation is avoided at some exposure for every pixel (dynamic-range cover). Degrades when (a) motion causes ghosting, (b) all exposures saturate in hotspots, (c) CRF calibration drifts. Under-covered bins (no exposure contains them unsaturated) are unrecoverable.",
    "secondary": "HDR_VDP_2"
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  "physics_fingerprint": {
    "L_DAG": 3.1,
    "carrier": "photon",
    "difficulty_delta": 3,
    "domain": "Computational Photography",
    "integration_axis": "temporal",
    "noise_model": "poisson_gaussian",
    "primitives": [
      "S.scan.exposure",
      "L.apply.crf",
      "D.saturate",
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    "sensing_mechanism": "multi_exposure",
    "solution_space": "2D_hdr_irradiance",
    "sub_domain": "Dynamic-range extension",
    "title": "High Dynamic Range (HDR) Imaging via Multi-Exposure Fusion"
  },
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      "under_coverage",
      "vignetting_residual",
      "white_balance_drift"
    ],
    "allowed_problem_classes": [
      "hdr_multi_exposure_fusion",
      "single_image_hdr",
      "hdr_video"
    ],
    "center_spec": {
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      "forward_operator": "multi_exposure_crf",
      "input_format": "K_ldr_frames_plus_exposure_times",
      "omega": {
        "H": 1080,
        "K_exposures": 3,
        "W": 1920,
        "bit_depth": 12,
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        "exposure_stops": 2.0,
        "motion_ghosting": 0.0,
        "under_coverage": 0.0
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      "problem_class": "hdr_multi_exposure_fusion"
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      ]
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      "K_exposures": [
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      "W": [
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      "exposure_stops": [
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      "motion_ghosting": [
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      "under_coverage": [
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      ],
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      ],
      "white_balance_drift": [
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        0.1
      ]
    }
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Dynamic-range extension",
  "title": "High Dynamic Range (HDR) Imaging via Multi-Exposure Fusion"
}

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