# ⚛  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._