L1 ⚛ L1-082 ⊙ Testnet

Neural Radiance Fields (NeRF) — implicit volumetric scene representation

Computational Optics · Implicit 3D scene reconstruction

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⬇ L1-082.md

# ⚛ L1 Principle — Neural Radiance Fields (NeRF) — implicit volumetric scene representation **ID:** `L1-082` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Optics — *Implicit 3D scene reconstruction* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D implicit field > **📡 Carrier:** photon · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554183 --- ## 🧠 1. Introduction **Neural Radiance Fields (NeRF) — implicit volumetric scene representation** is a **nonlinear inverse problem** whose unknown lives in **3D implicit field** space, within the **Implicit 3D scene reconstruction** sub-domain of **Computational Optics**. Measurements consist of photons collected by an optical detector via a **multi view photogrammetry** sensing mechanism. The forward operator applies, in order: S · scan · view operator; L · ray march operator; L · volume render operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Strongly non-convex MLP fitting. Unique 3D scene only when K views cover the scene with sufficient baseline and pose accuracy; view-dependent effects (specularity, transparency) can be absorbed into radiance ambiguously. Pose error, lighting drift, and under-covered regions cause floaters, baked-in artifacts, and depth collapse. ## ⚙ 2. Forward Model Physical chain: **x** → S · scan · view → L · ray march → L · volume render → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.volume_render` `L.ray_march` `S.scan.view` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.scan.view` | S · scan · view operator | | `L.ray_march` | L · ray march operator | | `L.volume_render` | L · volume render operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Optics | | Sub domain | Implicit 3D scene reconstruction | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 3D_implicit_field | | Noise model | gaussian | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Strongly non-convex MLP fitting. Unique 3D scene only when K views cover the scene with sufficient baseline and pose accuracy; view-dependent effects (specularity, transparency) can be absorbed into radiance ambiguously. Pose error, lighting drift, and under-covered regions cause floaters, baked-in artifacts, and depth collapse. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `nerf_novel_view_synthesis` · **Forward operator:** `volume_rendering_integral` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 800 | | W | px | 800 | | K views | — | 100 | | Photon count | — | 1000 | | Scene bbox m | m | 2 | | N samp per ray | — | 192 | | Lighting drift | — | 0 | | Non lambertian | — | 0 | | Pose error rad | rad | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 200 – 2000 | | W | px | 200 – 2000 | | K views | — | 10 – 500 | | Photon count | — | 100 – 10000 | | Scene bbox m | m | 0.5 – 50.0 | | N samp per ray | — | 32 – 512 | | Lighting drift | — | 0.0 – 0.3 | | Non lambertian | — | 0.0 – 0.5 | | Pose error rad | rad | 0.0 – 0.1 | | Under view coverage | — | 0.0 – 0.5 | | Motion blur per frame | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30.0 dB PSNR | Metric | Range | |---|---| | Psnr db | 18.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `12000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xfc26484e23acfbeba8106c0d2ca83d0dac52d242b98b1f3b88ba13ff81119e0b` - **Chain tx hash:** `0x41d42c5cfe79db3ee35ee05e64e799f2e6ec7ac0a03b8b03a394d7af892d8a06` - **Chain block:** `41554183` --- ## File Mapping This bundle consists of: `L1-082.md`, `L1-082.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-082.md` | Source of truth — edit this | Human or LLM | | `L1-082.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 `L1-082`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-082.md).
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L2-082-001 NeRF Novel-View Synthesis Mismatch-Only Spec

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📋 JSON metadata

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    "title": "Neural Radiance Fields (NeRF) \u2014 implicit volumetric scene representation"
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  "status": "testnet",
  "sub_domain": "Implicit 3D scene reconstruction",
  "title": "Neural Radiance Fields (NeRF) \u2014 implicit volumetric scene representation"
}

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