> ## Documentation Index
> Fetch the complete documentation index at: https://kensou.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# Ontology

# Ontology — Spatial AI 領域學術 taxonomy

> **本文是 Spatial AI 領域的「概念骨架」** — 不是手冊章節指南（→ [`functional_map.md`](./functional_map.md)）；不是論文目錄（→ 各 zone overview）；不是失敗圖鑑（→ [`cross_zone_failure_atlas.md`](./cross_zone_failure_atlas.md)）。本文回答：**這個領域的概念是怎麼被分類的？它們之間什麼關係？**
>
> 適合：想搞清楚 SLAM / VIO / VO / SfM / NeRF / 3DGS / VGGT 這些詞**到底是什麼分類軸下的什麼**、它們互相是子集還是並列、為什麼一篇 paper 同時被叫好幾個名字。

***

## 60 秒總綱

Spatial AI 不是一個方法，是 **5 個正交軸的張量積**：

```
                Problem (做什麼)
                       ×
              Representation (用什麼存)
                       ×
                  Sensor (從哪來)
                       ×
                  Paradigm (怎麼算)
                       ×
                    Time (即時 / 離線 / 增量)
                       ↓
                一條具體的 "spatial AI" stack
```

當你看到一個方法名（ORB-SLAM3 / VGGT / FoundationPose / 3DGS），它在這 5 個軸上**都有一個座標**。學會用座標讀法，每篇 paper 都會分類自如。

***

## §1 · 5 個分類軸

| 軸                  | 問什麼                | 取值範例                                                                          |
| ------------------ | ------------------ | ----------------------------------------------------------------------------- |
| **Problem**        | 你想算出什麼？            | pose / map / depth / object 6D / 場景圖 / affordance                             |
| **Representation** | 結果用什麼數據結構存？        | sparse points / mesh / NeRF MLP / 3DGS / voxel / BEV / scene graph            |
| **Sensor**         | 從什麼物理訊號來？          | mono / stereo / RGB-D / IMU / LiDAR / event / sonar / radar / GNSS            |
| **Paradigm**       | 用什麼計算範式？           | geometric / filter / optimization / end-to-end learned / hybrid / generative  |
| **Time**           | 線上還是離線？增量還是 batch？ | online incremental / online streaming / offline batch / feed-forward one-shot |

5 個軸是**正交**的（沒有一個包含另一個），所以同一個方法可以在每個軸上單獨指認。

***

## §2 · Problem 軸

**最常見的混淆來自這軸** — VO / VIO / SLAM / VSLAM / SfM 都長得很像，但其實是父子集 + 並列的混合。

```
spatial AI problems
├── Localization (我在哪)
│   ├── VO    (Visual Odometry) — 單純從連續 image 推 pose，無 map
│   ├── VIO   (Visual-Inertial Odometry) — VO + IMU 融合，metric scale 回來了
│   ├── LIO   (LiDAR-Inertial Odometry) — LiDAR 替代相機
│   ├── Relocalization — 給定 map，重新定位
│   └── Place recognition — 「這場景我見過嗎？」（比 reloc 弱，沒 6-DoF）
│
├── Mapping (世界長怎樣)
│   ├── Sparse map — 3D landmarks (keypoints)
│   ├── Dense map — voxel / mesh / TSDF
│   ├── Semantic map — sparse/dense + per-element 標籤
│   └── Topological map — graph (節點=地點，邊=可達)
│
├── SLAM (= Localization + Mapping 同時)
│   ├── Visual SLAM (VSLAM) — 視覺主，可加 IMU (= VINS)
│   ├── LiDAR SLAM — LiDAR 主
│   ├── Multi-session SLAM — 多次跑同地，map 接力
│   └── Multi-agent SLAM — 多機共享 map（→ SG-Reg 之類）
│
├── Reconstruction (世界長得多漂亮)
│   ├── SfM (Structure from Motion) — 離線、batch、無 IMU
│   ├── MVS (Multi-View Stereo) — SfM 之後的 densify 步驟
│   ├── Feed-forward 3D — one-shot 從多 view 出 pose+depth+points (VGGT / DUSt3R)
│   ├── Novel-view synthesis — NeRF / 3DGS 為主任務
│   └── 4D reconstruction — 加時間軸 (4DGS / NeRF-T)
│
├── Tracking (東西去哪)
│   ├── Object 6-DoF pose tracking — 已知物體模型 (FoundationPose / MegaPose)
│   ├── Object 2D tracking — bounding box (SORT / ByteTrack)
│   ├── Pixel-level / point tracking — RAFT / CoTracker / TAP
│   ├── Optical flow — dense 2D motion field
│   └── Visual tracking (classical) — KCF / CSRT, no learning
│
├── Spatial reasoning (這場景什麼意思)
│   ├── VLM 空間 QA — 「杯子在桌子左邊嗎」(3DSRBench / BLINK)
│   ├── Scene graph — 物體 + 空間關係
│   ├── Affordance — 「這物體可以怎麼操作」
│   └── Open-vocabulary 3D — LangSplat / OpenScene
│
├── Pose estimation (孤立任務)
│   ├── Camera pose (PnP / DLT) — 給 2D-3D 對應算 6-DoF
│   ├── Human pose — body / hand / face landmarks
│   └── Object pose — instance / category-level
│
└── Action interface (→ VLA)
    ├── 3D feature cloud → policy
    ├── Goal/waypoint → planner
    └── Affordance → grasp planner
```

**關鍵子集關係**：

* VIO ⊂ VO（加 IMU）
* VSLAM ⊂ Localization + Mapping（VO 後加 mapping + loop closure）
* VINS = VIO + map = VSLAM with IMU
* SfM ⊂ Reconstruction（offline VSLAM 的離線批處理變體）
* VGGT 同時是 Reconstruction + 隱含的 Localization（它輸出 pose + depth + points）

***

## §3 · Representation 軸

```
              dense ←──────────────────────────────→ sparse
                │                                       │
   continuous   │ 3DGS  TSDF  voxel  mesh  occupancy   │ landmarks
   implicit     │ NeRF                                 │ keypoints
                │                                       │
   structured   │ BEV   scene graph                    │ feature cloud
```

| 表徵                   | 是什麼                                           | 經典代表                                  | 何時選                         |
| -------------------- | --------------------------------------------- | ------------------------------------- | --------------------------- |
| **Sparse landmarks** | 幾百到幾萬個 3D 點 + descriptor                      | ORB-SLAM3 / VINS                      | localization 主，map 小，CPU OK |
| **Feature cloud**    | per-point semantic feature vector             | DINOv2 lifted / OpenScene / LangSplat | 開放詞匯查詢 / VLA 接口             |
| **Voxel grid**       | 規則 3D 網格 + occupancy 或 SDF                    | KinectFusion / Vox-Fusion             | dense reconstruction，內存可控   |
| **TSDF**             | Truncated SDF — voxel 存有符號距離                  | KinectFusion / Voxblox                | 高品質 mesh extract 用          |
| **Mesh**             | 三角形面片                                         | open3d / Trimesh                      | 渲染 / 物理仿真 / VR              |
| **Occupancy grid**   | binary or probability per voxel               | Octomap / 駕駛 occupancy net            | 規劃 / collision check        |
| **NeRF (implicit)**  | MLP(x,y,z,d) → (RGB,σ)                        | NeRF / Instant-NGP / Mip-NeRF         | 高品質 novel view，per-scene    |
| **3DGS (explicit)**  | N×(pos, scale, rot, color, opacity) Gaussians | 3DGS / Mip-Splatting                  | NeRF 級畫質 + 100× 渲染速度        |
| **BEV (driving)**    | 鳥瞰圖 + heightmap channels                      | BEVFormer / Tesla occupancy           | AD 路徑規劃，遠距                  |
| **Scene graph**      | 物體節點 + 空間關係邊                                  | ConceptGraphs / SG-Reg                | LLM/VLM 友好 query            |
| **Depth map**        | per-pixel depth (相機坐標)                        | Depth Anything / MoGE / VGGT          | feed-forward 中間結果           |

**正交於 problem 軸**：同一個 problem 可以用不同 representation（e.g., SLAM map 可以是 sparse landmarks **或** voxel **或** 3DGS）。

***

## §4 · Sensor 軸

**主光 / 主聲 / 主場 / 慣性**四個 modality 分類：

```
Sensor modality
├── Optical (主光)
│   ├── Passive
│   │   ├── Monocular RGB camera
│   │   ├── Stereo (passive baseline)
│   │   ├── Multi-camera array (Insta360 / GoPro 多視角)
│   │   └── Polarization camera
│   ├── Active
│   │   ├── Structured light (Kinect v1 / Realsense D435)
│   │   ├── ToF (Kinect v2 / iPhone LiDAR / Azure Kinect)
│   │   └── Active NIR (850 nm 主動投影紋理)
│   └── Specialty
│       ├── Event camera (DVS / DAVIS / Prophesee)
│       ├── Thermal IR (8-14 μm LWIR)
│       └── Hyperspectral
│
├── Inertial (慣性)
│   └── IMU = 3-axis accelerometer + 3-axis gyroscope (+ magnetometer = MARG)
│
├── Range / depth (距離直接)
│   ├── LiDAR (mechanical / solid-state / spinning)
│   ├── ToF (single-point / scanning)
│   ├── Ultrasonic (cm 級，cheap)
│   ├── mmWave radar (77/79 GHz, automotive)
│   └── FMCW radar (24 GHz / 60 GHz / 77 GHz)
│
├── Acoustic (聲學)
│   ├── Microphone array (beamforming)
│   ├── Multibeam sonar (marine 主圖)
│   ├── Side-scan sonar (海底紋理)
│   └── DVL (Doppler Velocity Log, marine 對地速度)
│
├── RF / EM (電磁 / 無線)
│   ├── GNSS / RTK (GPS / Galileo / BeiDou / GLONASS)
│   ├── UWB (室內 cm 級定位 anchor)
│   ├── WiFi-RTT (FTM-2nd-gen)
│   ├── Bluetooth AoA
│   └── Magnetometer (地磁場 yaw 校正)
│
└── Contact / proprioceptive (接觸 / 本體)
    ├── Force-torque sensor (wrist mounted)
    ├── Tactile (DIGIT / GelSight)
    ├── Joint encoder (機械臂 / 腿)
    └── Pressure (深度計 marine / 高度 aerial)
```

**Sensor 屬於物理層，跟 problem 軸獨立**：同一個 problem（如 VO）可以靠 mono 或 stereo 或 RGB-D；同一個 sensor（如 IMU）可以給 VIO 也可以給 LIO 也可以給 humanoid 全身平衡。

***

## §5 · Paradigm 軸

**算法範式** — 是用幾何 + 優化還是學習？

```
┌──────────────────────────────────────────────────────────┐
│  Geometric / classical (基於幾何 + 標定 + 優化)            │
│  ├── Filter-based                                         │
│  │   ├── KF (Kalman Filter)                              │
│  │   ├── EKF (Extended) — 非線性，第一階 Taylor          │
│  │   ├── UKF (Unscented) — sigma point，避 Jacobian     │
│  │   ├── MSCKF (Multi-State Constraint) — OpenVINS      │
│  │   └── Particle filter — non-Gaussian                  │
│  ├── Optimization-based                                   │
│  │   ├── Bundle Adjustment (BA) — 全局 reprojection      │
│  │   ├── Factor graph (GTSAM / iSAM2)                    │
│  │   ├── Pose graph optimization                          │
│  │   └── Sparse non-linear solvers (Ceres / g2o)         │
│  └── Closed-form                                          │
│      ├── PnP (P3P / EPnP) — 2D-3D → pose                 │
│      ├── DLT (Direct Linear Transform)                    │
│      ├── 8-point algorithm (essential matrix)             │
│      └── ICP (Iterative Closest Point)                    │
│                                                            │
│  Learned / data-driven (端到端神經網絡)                    │
│  ├── End-to-end                                           │
│  │   ├── DROID-SLAM — 學 BA layer                        │
│  │   ├── VGGT / DUSt3R — feed-forward 多 view → pose+depth│
│  │   └── NeuralRecon — voxel + neural surface             │
│  ├── Feature learning                                     │
│  │   ├── SuperPoint / DISK — learned keypoint+descriptor │
│  │   ├── LoFTR / LightGlue — detector-free matching      │
│  │   └── R2D2 / SiLK                                      │
│  ├── Depth foundation                                     │
│  │   ├── Depth Anything (v1/v2) — relative depth         │
│  │   ├── Metric3D — metric scale                          │
│  │   ├── MoGE — 多任務 geometry foundation               │
│  │   └── FoundationStereo                                │
│  └── Pose foundation                                      │
│      ├── FoundationPose / MegaPose — 6-DoF object        │
│      └── PoseDiffusion                                   │
│                                                            │
│  Hybrid (學習 + 幾何混合)                                  │
│  ├── Learned front-end + classical back-end              │
│  │   ├── SuperGlue+VINS                                  │
│  │   └── LightGlue+COLMAP                                │
│  ├── Differentiable rendering                             │
│  │   ├── NeRF (MLP + volume rendering + GD)              │
│  │   └── 3DGS (Gaussian + rasterization + GD)            │
│  └── Differentiable simulation                            │
│      ├── MuJoCo MJX (XLA-JIT)                            │
│      └── NVIDIA Warp                                      │
│                                                            │
│  Generative (生成式)                                       │
│  ├── Video diffusion as 3D prior — Sora / Genie          │
│  ├── World models — Wayve GAIA / Cosmos                  │
│  └── 3D diffusion — Zero123 / Wonder3D                   │
└──────────────────────────────────────────────────────────┘
```

**Paradigm 跟 Problem / Representation 全正交**：同一個 problem（如 VSLAM）可以用 geometric（ORB-SLAM3）、learned（DROID-SLAM）、hybrid（GS-SLAM）三種範式做。

***

## §6 · Time 軸

| 模式                         | 特徵                             | 代表                                   |
| -------------------------- | ------------------------------ | ------------------------------------ |
| **Incremental online**     | 每幀來就更新 state；增加 / 刪除 keyframe  | ORB-SLAM3 / VINS-Fusion / OpenVINS   |
| **Streaming online**       | 每幀來就出結果，狀態固定大小                 | EKF-VIO / MSCKF / LIO                |
| **Sliding-window**         | 維護最近 N 幀的 state，舊的 marginalize | VINS-Fusion / OpenVINS（也算 streaming） |
| **Offline batch**          | 所有 image 一起進去，跑到最優             | COLMAP / OpenMVG / SfM 經典            |
| **Feed-forward one-shot**  | 多 view 一次性 → output（無增量 / 無優化） | VGGT / DUSt3R / MoGE                 |
| **Per-scene optimization** | 一個場景訓一次 model                  | NeRF / 3DGS / LERF / LangSplat       |

***

## §7 · 跨軸座標表 — 代表方法在 5 軸上的座標

| 方法                     | Problem                       | Representation                         | Sensor                               | Paradigm                           | Time                   |
| ---------------------- | ----------------------------- | -------------------------------------- | ------------------------------------ | ---------------------------------- | ---------------------- |
| **ORB-SLAM3**          | VSLAM + reloc + multi-session | sparse landmarks + keyframe graph      | mono / stereo / RGB-D + IMU optional | geometric + ORB feature + BA       | incremental online     |
| **VINS-Fusion**        | VIO + GPS fusion              | sparse + IMU bias state                | mono + IMU + GNSS optional           | geometric + factor graph           | sliding-window online  |
| **OpenVINS**           | VIO                           | sparse + 21-state aug                  | mono / stereo + IMU                  | MSCKF (filter)                     | streaming online       |
| **DROID-SLAM**         | VO / VSLAM                    | dense flow + pose graph                | mono + IMU optional                  | learned end-to-end + diff BA       | online (GPU 需)         |
| **VGGT**               | Feed-forward 3D               | pose + depth + point cloud (all dense) | multi-view RGB                       | learned end-to-end                 | feed-forward one-shot  |
| **DUSt3R / MASt3R**    | Two-view → 3D                 | dense point cloud                      | 2 RGB images                         | learned end-to-end                 | feed-forward one-shot  |
| **Depth Anything v2**  | Depth estimation              | per-pixel depth map                    | single RGB                           | learned end-to-end (relative)      | feed-forward           |
| **MoGE**               | Multi-task geometry           | depth + normal + segmentation          | RGB                                  | learned (foundation)               | feed-forward           |
| **COLMAP**             | SfM                           | sparse → MVS dense                     | image collection                     | geometric BA + MVS                 | offline batch          |
| **NeRF**               | Novel-view synthesis          | implicit MLP field                     | RGB + poses (from COLMAP)            | hybrid (MLP + diff render)         | per-scene optimization |
| **3DGS**               | Novel-view synthesis          | explicit Gaussian set                  | RGB + poses (from COLMAP)            | hybrid (Gaussian + diff rasterize) | per-scene optimization |
| **LangSplat**          | Open-vocab 3D                 | 3DGS + CLIP feature field              | RGB + CLIP teacher                   | hybrid + distillation              | per-scene              |
| **OpenScene**          | Open-vocab 3D                 | voxel + CLIP feature                   | RGB-D                                | zero-shot CLIP fusion              | streaming or batch     |
| **FoundationPose**     | Object 6-DoF pose             | mesh template + RGB-D                  | RGB-D + object mesh                  | learned + diff render refine       | online                 |
| **MegaPose**           | Object 6-DoF pose (unseen)    | rendered template hypothesis           | RGB + mesh                           | learned coarse + refine            | online                 |
| **RAFT**               | Optical flow                  | dense per-pixel 2D flow                | 2 RGB frames                         | learned iterative refine           | feed-forward           |
| **CoTracker**          | Point tracking                | per-point trajectory                   | video                                | learned transformer                | online                 |
| **ByteTrack**          | Multi-object 2D tracking      | bbox + ID                              | detection input                      | data association + Kalman          | streaming online       |
| **EKF (from scratch)** | VIO 基線                        | 15-state vector + covariance           | IMU + camera measurements            | filter (EKF)                       | streaming online       |
| **Min-snap**           | Trajectory generation         | polynomial pieces + waypoints          | (no sensor, planner)                 | optimization (QP)                  | offline                |

***

## §8 · 概念依賴圖

```mermaid theme={null}
graph TD
    %% 數學底層
    LIE["Lie group<br/>SE(3) / SO(3)"]
    BA["Bundle Adjustment"]
    EKF["Kalman / EKF"]
    PNP["PnP / DLT"]

    LIE --> BA
    LIE --> EKF
    LIE --> PNP

    %% 物理感知層
    IMU["IMU model<br/>(Allan / preintegration)"]
    CAM["Camera model<br/>(pinhole / fisheye)"]
    STEREO["Stereo geometry<br/>(epipolar / disparity)"]

    %% Problem 層
    VO["VO (Visual Odometry)"]
    VIO["VIO"]
    VSLAM["VSLAM"]
    SFM["SfM (offline)"]
    SLAM["SLAM"]
    RECON["3D Reconstruction"]

    CAM --> VO
    STEREO --> VO
    PNP --> VO
    IMU --> VIO
    VO --> VIO
    VO --> VSLAM
    VSLAM --> SLAM
    VO --> SFM
    SFM --> RECON

    %% 表徵層
    SPARSE["Sparse landmarks"]
    NERF_R["NeRF"]
    GS["3DGS"]
    MESH["Mesh"]
    VOXEL["Voxel / TSDF"]
    BEV["BEV (driving)"]
    SG["Scene Graph"]

    BA --> SPARSE
    SPARSE --> VSLAM
    RECON --> NERF_R
    RECON --> GS
    RECON --> MESH
    RECON --> VOXEL

    %% 現代 paradigm
    FF["Feed-forward 3D<br/>(VGGT / DUSt3R)"]
    DF["Depth foundation<br/>(Depth Anything / MoGE)"]
    LEARN["Learned end-to-end"]

    LEARN --> FF
    LEARN --> DF
    FF --> RECON
    DF --> FF

    %% Action 接口
    SEM["Semantic 3D<br/>(LangSplat / OpenScene)"]
    GS --> SEM
    NERF_R --> SEM
    VLA["VLA action policy<br/>(姊妹仓)"]
    SEM --> VLA
    SG --> VLA

    style LIE fill:#1a1a2e,stroke:#4361ee,color:#fff
    style FF fill:#0f3460,stroke:#f77f00,color:#fff
    style VLA fill:#1a1a2e,stroke:#2a9d8f,color:#fff
    style SLAM fill:#1a1a2e,stroke:#e94560,color:#fff
```

***

## §9 · 60+ term glossary

> 一行定義 + 在 handbook 何處深拆。

### 9.1 · Math / Geometry

| Term                                   | 一句話                                                       | 深拆                                                                                                                  |
| -------------------------------------- | --------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------- |
| **SE(3)**                              | 6-DoF rigid transformation group (rotation + translation) | [`foundations/spatial-math/se3_so3_lie_groups_primer.md`](../foundations/spatial-math/se3_so3_lie_groups_primer.md) |
| **SO(3)**                              | 3D rotation group (沒平移)                                   | 同上                                                                                                                  |
| **so(3)**                              | SO(3) 的 Lie algebra（skew-symmetric matrices）              | 同上                                                                                                                  |
| **Lie group**                          | smooth manifold + group operation；機器人 pose 的代數結構          | 同上                                                                                                                  |
| **Exponential map**                    | algebra → group (e^ξ̂ → SE(3))；preintegration 核心          | [`imu_preintegration_math.md`](../foundations/spatial-math/imu_preintegration_math.md)                              |
| **Quaternion**                         | 4D unit-norm rotation representation；無 gimbal lock        | [`rotation_intuition_primer.md`](../foundations/spatial-math/rotation_intuition_primer.md)                          |
| **6D rotation rep**                    | Zhou 2019：DL regression 用 6D 比 quat / euler 收斂好           | [`rotation_reps_in_deep_learning_primer.md`](../foundations/spatial-math/rotation_reps_in_deep_learning_primer.md)  |
| **Manifold**                           | 局部歐氏，全局彎曲；SO(3) / SE(3) 都是                                | 同 SE(3)                                                                                                             |
| **Tangent space**                      | manifold 上某點的線性化（用來算梯度）                                   | 同上                                                                                                                  |
| **Jacobian (on manifold)**             | manifold 上的 right/left Jacobian for retraction            | 同上                                                                                                                  |
| **Rodrigues formula**                  | axis-angle → rotation matrix 公式                           | 同 quaternion                                                                                                        |
| **Bundle Adjustment**                  | joint optimize poses + landmarks，min reprojection         | [`bundle_adjustment.md`](../foundations/spatial-math/bundle_adjustment.md)                                          |
| **Factor graph**                       | bipartite graph of variables + factors；GTSAM 主數據結構        | [`pose_graph_optimization.md`](../foundations/spatial-math/pose_graph_optimization.md)                              |
| **Schur complement**                   | 解 BA Hessian 時邊化掉 landmark 用的線性代數                         | [`bundle_adjustment.md`](../foundations/spatial-math/bundle_adjustment.md)                                          |
| **Marginalization**                    | 從 state 裡去掉舊變量保留信息（sliding window 必需）                     | [`bayesian_filtering_ekf_msckf.md`](../foundations/spatial-math/bayesian_filtering_ekf_msckf.md)                    |
| **iSAM / iSAM2**                       | incremental factor graph solver                           | 同 factor graph                                                                                                      |
| **Gauss-Newton / Levenberg-Marquardt** | non-linear LSQ 的兩個經典 solver                               | 同 BA                                                                                                                |

### 9.2 · Sensor physics

| Term                               | 一句話                                              | 深拆                                                                                                                 |
| ---------------------------------- | ------------------------------------------------ | ------------------------------------------------------------------------------------------------------------------ |
| **IMU**                            | accel + gyro (+ mag = MARG)；6-axis 或 9-axis      | [`imu_physics_and_noise_model.md`](../foundations/sensor-physics/imu_physics_and_noise_model.md)                   |
| **Allan variance**                 | IMU noise 的標準化測量（bias instability / random walk） | [`sensor_noise_modeling_allan_variance.md`](../foundations/sensor-physics/sensor_noise_modeling_allan_variance.md) |
| **IMU preintegration**             | 把 IMU 數據壓成 keyframe 間的 delta，避免每 step 重算         | [`imu_preintegration_math.md`](../foundations/spatial-math/imu_preintegration_math.md)                             |
| **Bias (IMU)**                     | 慣性測量的 DC offset；隨溫度 / 時間漂移                       | 同上                                                                                                                 |
| **Rolling shutter**                | CMOS 逐行曝光 → 動態時幾何畸變                              | [`rolling_vs_global_shutter.md`](../foundations/sensor-physics/rolling_vs_global_shutter.md)                       |
| **Global shutter**                 | 全幀同時曝光；無 RS 偽影；機器人首選                             | 同上                                                                                                                 |
| **Pinhole camera**                 | 最簡相機模型（focal + principal point）                  | [`stereo_camera_geometry_physics.md`](../foundations/sensor-physics/stereo_camera_geometry_physics.md)             |
| **Fisheye / equidistant**          | 廣角畸變模型；FOV > 120° 用                              | 同上                                                                                                                 |
| **Distortion model**               | Brown-Conrady (徑向 + 切向) / Mei / KB               | 同上                                                                                                                 |
| **Disparity**                      | 立體匹配的水平偏移；換 depth 用 baseline / disparity         | [`classical_stereo_primer.md`](../foundations/depth-foundation/classical_stereo_primer.md)                         |
| **Baseline**                       | stereo 兩相機距離；越長 depth 越準但 occlusion 越多           | 同上                                                                                                                 |
| **ToF (Time-of-Flight)**           | 主動發光 + 量飛行時間 → depth                             | [`tof_physics_for_embodied_ai.md`](../foundations/sensor-physics/tof_physics_for_embodied_ai.md)                   |
| **Event camera (DVS)**             | 像素級異步亮度變化事件流；高速 / HDR 利器                         | [`event_camera_dvs_physics.md`](../foundations/sensor-physics/event_camera_dvs_physics.md)                         |
| **LiDAR**                          | 激光距離 + 反射強度；mechanical / solid-state             | （見 sensor-physics zone）                                                                                            |
| **mmWave radar**                   | 60-77 GHz；穿霧 / 雨 / 灰塵；分辨率比 LiDAR 低               | [`mmwave_radar_physics_for_ad.md`](../foundations/sensor-physics/mmwave_radar_physics_for_ad.md)                   |
| **GNSS / RTK**                     | 衛星定位；RTK 載波相位 cm 級                               | [`gnss_multi_constellation_rtk.md`](../foundations/sensor-physics/gnss_multi_constellation_rtk.md)                 |
| **UWB**                            | 室內 anchor 系統 cm 級 ToF                            | [`uwb_ultra_wideband_positioning.md`](../foundations/sensor-physics/uwb_ultra_wideband_positioning.md)             |
| **DVL (Doppler Velocity Log)**     | 水下 marine 用聲波測對地速度                               | [`underwater_sonar_physics.md`](../foundations/sensor-physics/underwater_sonar_physics.md)                         |
| **Calibration (intrinsic)**        | 相機自己的參數（focal / dist）                            | [`sensor_calibration_drift_in_production.md`](../deployment/calibration/sensor_calibration_drift_in_production.md) |
| **Calibration (extrinsic)**        | sensor 間的相對 pose（cam ↔ IMU ↔ LiDAR）              | 同上                                                                                                                 |
| **Time sync (PTP / trigger / sw)** | 多 sensor 對時；hardware trigger 是金本位                | [`hardware_trigger_vs_ptp_vs_software.md`](../deployment/multi-modal-sync/hardware_trigger_vs_ptp_vs_software.md)  |

### 9.3 · SLAM / Estimation

| Term                               | 一句話                                            | 深拆                                                                                               |
| ---------------------------------- | ---------------------------------------------- | ------------------------------------------------------------------------------------------------ |
| **VO (Visual Odometry)**           | 連續 image → 相對 pose；無 map，無 loop closure        | （見 classical-slam zone）                                                                          |
| **VIO (Visual-Inertial Odometry)** | VO + IMU；找回 metric scale + 提升 robustness       | [`embodiments/aerial/vio/overview.md`](../embodiments/aerial/vio/overview.md)                    |
| **VINS**                           | Visual-Inertial Navigation System = VIO 完整工程實作 | [`vins_mono_fusion_dissection.md`](../embodiments/aerial/vio/vins_mono_fusion_dissection.md)     |
| **SLAM**                           | Simultaneous Localization And Mapping          | （見 classical-slam / pose-tracking）                                                               |
| **VSLAM**                          | Visual SLAM；camera 主，可加 IMU                    | [`orb_slam3_dissection.md`](../foundations/classical-slam/orb_slam3_dissection.md)               |
| **Loop closure**                   | 「我回到老地方了」→ 全局優化矯正 drift                        | 同上                                                                                               |
| **Relocalization**                 | 給 map + 一幀 → 在 map 裡定位                         | 同上                                                                                               |
| **Place recognition**              | 「這場景我見過嗎」（bag-of-words / NetVLAD）              | 同上                                                                                               |
| **Keyframe**                       | 選代表幀做 mapping anchor；省計算                       | 同上                                                                                               |
| **MSCKF**                          | Multi-State Constraint KF — OpenVINS 用，CPU 友好  | [`openvins_dissection.md`](../embodiments/aerial/vio/openvins_dissection.md)                     |
| **EKF-SLAM**                       | extended KF state 含 robot + landmarks；scale 差  | [`bayesian_filtering_ekf_msckf.md`](../foundations/spatial-math/bayesian_filtering_ekf_msckf.md) |
| **Graph SLAM**                     | pose 之間用 factor graph 表達，全局優化                  | [`pose_graph_optimization.md`](../foundations/spatial-math/pose_graph_optimization.md)           |
| **Atlas (multi-map)**              | ORB-SLAM3 的多 session map 合併機制                  | [`orb_slam3_dissection.md`](../foundations/classical-slam/orb_slam3_dissection.md)               |
| **Sliding window**                 | 只保留最近 N 幀；舊的 marginalize                       | [`vins_mono_fusion_dissection.md`](../embodiments/aerial/vio/vins_mono_fusion_dissection.md)     |
| **Tight vs loose coupling**        | sensor 融合在 state space 內（tight）還是後處理（loose）    | 同上                                                                                               |

### 9.4 · 3D Representation

| Term                         | 一句話                                          | 深拆                                                                                        |
| ---------------------------- | -------------------------------------------- | ----------------------------------------------------------------------------------------- |
| **NeRF**                     | MLP(x,y,z,d) → (RGB, σ)；volume rendering     | [`nerf_original_dissection.md`](../foundations/nerf-family/nerf_original_dissection.md)   |
| **3DGS**                     | N×Gaussian primitives 顯式表徵                   | [`3dgs_original_dissection.md`](../foundations/3dgs-family/3dgs_original_dissection.md)   |
| **Instant-NGP**              | NeRF + multi-resolution hash grid → 秒級訓練     | [`instant_ngp_dissection.md`](../foundations/nerf-family/instant_ngp_dissection.md)       |
| **Mip-NeRF / Mip-Splatting** | 多尺度抗鋸齒版本                                     | [`mip_nerf_360_dissection.md`](../foundations/nerf-family/mip_nerf_360_dissection.md)     |
| **TSDF**                     | Truncated Signed Distance Field；voxel 存有符號距離 | （見 sensor-physics + classical-slam）                                                       |
| **Voxel grid**               | 規則 3D 格子；KinectFusion / Octomap              | 同上                                                                                        |
| **Occupancy grid**           | binary or probability per voxel              | [`embodiments/driving/bev_and_occupancy.md`](../embodiments/driving/bev_and_occupancy.md) |
| **Mesh**                     | 三角形面片；可從 TSDF marching cube 得                | （見 generative-3d-sim）                                                                     |
| **BEV**                      | bird's-eye-view；driving stack 標配             | [`embodiments/driving/bev_and_occupancy.md`](../embodiments/driving/bev_and_occupancy.md) |
| **Scene graph**              | 物體節點 + 空間關係邊；planner 友好                      | [`semantic-3d/overview.md`](../foundations/semantic-3d/overview.md)                       |
| **Feature cloud**            | per-point CLIP/DINOv2 feature；語義可查詢          | 同上                                                                                        |

### 9.5 · Modern foundation (2023-2026)

| Term                 | 一句話                                                              | 深拆                                                                                                   |
| -------------------- | ---------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------- |
| **VGGT**             | CVPR 2025 best paper；feed-forward 多 view → pose + depth + tracks | [`vggt_cvpr2025_dissection.md`](../foundations/feed-forward-3d/vggt_cvpr2025_dissection.md)          |
| **DUSt3R / MASt3R**  | Naver Labs；two-view → dense point cloud                          | [`feed-forward-3d/overview.md`](../foundations/feed-forward-3d/overview.md)                          |
| **MapAnything**      | Meta；feed-forward 3D 通用                                          | [`mapanything_dissection.md`](../foundations/feed-forward-3d/mapanything_dissection.md)              |
| **Depth Anything**   | ByteDance；relative depth foundation                              | [`depth_anything_v2_dissection.md`](../foundations/depth-foundation/depth_anything_v2_dissection.md) |
| **Metric3D**         | metric scale depth foundation                                    | [`metric3d_dissection.md`](../foundations/depth-foundation/metric3d_dissection.md)                   |
| **MoGE**             | Microsoft；multi-task geometry foundation (depth + normal + seg)  | [`moge_dissection.md`](../foundations/depth-foundation/moge_dissection.md)                           |
| **FoundationStereo** | NVIDIA；stereo 的 foundation model                                 | [`foundationstereo_dissection.md`](../foundations/depth-foundation/foundationstereo_dissection.md)   |
| **FoundationPose**   | NVIDIA；6-DoF object pose foundation                              | [`foundation_pose_dissection.md`](../foundations/pose-tracking/foundation_pose_dissection.md)        |
| **LangSplat**        | CVPR 2024；3DGS + language feature distillation                   | [`langsplat_dissection.md`](../foundations/semantic-3d/langsplat_dissection.md)                      |
| **OpenScene**        | CVPR 2023；voxel + CLIP，無 per-scene 訓練                            | [`openscene_dissection.md`](../foundations/semantic-3d/openscene_dissection.md)                      |

### 9.6 · Tracking

| Term                          | 一句話                                       | 深拆                                                                                                            |
| ----------------------------- | ----------------------------------------- | ------------------------------------------------------------------------------------------------------------- |
| **RAFT**                      | learned optical flow，iterative refinement | [`raft_optical_flow.md`](../foundations/pose-tracking/raft_optical_flow.md)                                   |
| **CoTracker / TAP**           | 任意點長時跟蹤                                   | [`cotracker_and_tap_dissection.md`](../foundations/pose-tracking/cotracker_and_tap_dissection.md)             |
| **KCF / CSRT**                | 經典 visual tracker；OpenCV-shipped          | [`classical_visual_tracking_kcf_csrt.md`](../foundations/pose-tracking/classical_visual_tracking_kcf_csrt.md) |
| **SORT / ByteTrack**          | 2D 多物體跟蹤（IoU + Kalman）                    | [`sort_bytetrack_mot_dissection.md`](../foundations/pose-tracking/sort_bytetrack_mot_dissection.md)           |
| **MegaPose / FoundationPose** | unseen object 6-DoF pose                  | [`megapose_dissection.md`](../foundations/pose-tracking/megapose_dissection.md)                               |

### 9.7 · Embodiment / Deployment

| Term                    | 一句話                                         | 深拆                                                                                                                 |
| ----------------------- | ------------------------------------------- | ------------------------------------------------------------------------------------------------------------------ |
| **SWaP-C**              | Size, Weight, Power, Cost — 機器人 sensor 選型四維 | [`sensor_selection_decision_matrix.md`](../foundations/sensor-physics/sensor_selection_decision_matrix.md)         |
| **Onboard compute**     | 機器人本機 SoC（Jetson / Snapdragon / Orin）       | [`edge_inference_budget_engineering.md`](../deployment/compute-budget/edge_inference_budget_engineering.md)        |
| **Calibration drift**   | 標定參數半年後因溫度 / 振動失效                           | [`sensor_calibration_drift_in_production.md`](../deployment/calibration/sensor_calibration_drift_in_production.md) |
| **Latency budget**      | 從 sensor → action 的端到端時延上限                  | [`embodiments/aerial/real_flight_production_gotchas.md`](../embodiments/aerial/real_flight_production_gotchas.md)  |
| **State rate**          | 估計輸出頻率；aerial 要 ≥ 100 Hz                    | 同上                                                                                                                 |
| **Min-snap**            | 4 階導數最小的多項式 trajectory（HKUST 經典）            | [`min_snap_dissection.md`](../embodiments/aerial/planning/min_snap_dissection.md)                                  |
| **Cascaded controller** | aerial：position → attitude → motor 多層 PID   | [`dynamics_and_control_primer.md`](../embodiments/aerial/dynamics_and_control_primer.md)                           |

***

## §10 · 邊界 — 什麼不在 spatial AI 範圍

| 不算 spatial AI                   | 為什麼                                               | 去哪找                                                           |
| ------------------------------- | ------------------------------------------------- | ------------------------------------------------------------- |
| 2D 物體檢測 (Faster R-CNN 等)        | 沒 3D 輸出                                           | classical CV 課程                                               |
| 純語言 reasoning (LLM)             | 沒空間理解                                             | LLM 文獻                                                        |
| Image classification            | 沒幾何                                               | classical DL                                                  |
| Speech / NLP                    | 不同 modality                                       | 各自領域                                                          |
| VLA action policy               | 是 spatial AI 的 **下游消費者**，不是它                      | 姊妹仓 [VLA-Handbook](https://github.com/sou350121/VLA-Handbook) |
| 純 reinforcement learning policy | 沒 spatial state                                   | RL 文獻                                                         |
| Pure object 6-DoF pose（離 SLAM）  | 灰色帶 — 我們收 FoundationPose 等，因為它跟 manipulation 直接相連 | [`pose-tracking/`](../foundations/pose-tracking/)             |

***

## §11 · 跨參考

| Want                               | 去                                                                |
| ---------------------------------- | ---------------------------------------------------------------- |
| 看每個 zone 寫什麼                       | [`functional_map.md`](./functional_map.md)                       |
| 看 42 個工具的生死                        | [`cross_zone_failure_atlas.md`](./cross_zone_failure_atlas.md)   |
| 看 NeRF / 3DGS / SfM / VGGT 範式轉變時間線 | [`timeline.md`](./timeline.md)                                   |
| 看不同 representation 對比              | [`representation_comparison.md`](./representation_comparison.md) |
| 看每個 zone 入口                        | [`foundations/overview.md`](../foundations/overview.md)          |
| 從場景找入口                             | [`../ONBOARDING.md`](../ONBOARDING.md)                           |

***

*Last updated: 2026-05-24 · 5 axes / 60+ terms / 全 handbook 概念骨架·配合 functional\_map 讀。*