# ⚛  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._