NDT (2D)
常態分布轉換（Normal Distributions Transform, NDT）將二維平面切成 100 cm 見方的網格，每個至少含三點的網格以點的平均與共變異數建立常態分布，並使用四組錯開半格的重疊網格降低離散化影響，使一次掃描成為分段連續且可微的機率密度。另一次掃描的點經轉換後在此密度上計分，再以牛頓法最佳化位姿，不需建立明確的點對應。作者以此進行相對於關鍵影格的位置追蹤，並以關鍵影格及其全域位姿構成地圖，利用成對匹配的 Hessian 建立二次誤差模型，只在新關鍵影格三條邊以內的子圖上最佳化。實驗以 SICK 雷射掃描儀在未改造的室內走廊、不使用里程計完成建圖，在 1.4 GHz 電腦上離線每秒約可處理 97 次掃描。
本頁內容
Represents a 2D scan as per-cell normal distributions forming a differentiable density; another scan is matched by Newton's method without explicit correspondences.
技術屬性
欄位內容為文獻擷取紀錄的原文用語（英文），以原文為據；「未查證」表示本研究尚未讀到該資訊，不代表該方法不具備此能力。
| 感測輸入 | ["SICK 2D laser scanner, 180 deg field of view, 1 deg angular resolution (Sec. VIII)"] |
|---|---|
| 原文測試平台 | ["indoor mobile robot (model not named), driven from the lab along a corridor and back (Sec. VIII)"] |
| 狀態估計 | Newton's method on the negative NDT score (sum of Gaussian evaluations of transformed points), with analytic gradient and Hessian; Hessian replaced by H + lambda I when not positive definite (Sec. IV, V) |
| 資料關聯 | no explicit correspondences; points scored against per-cell normal distributions (abstract) |
| 時間表示 | 不適用 (pairwise scan matching) |
| 去畸變 | 原文未報告 |
| 迴圈閉合 | none demonstrated; the authors note that closing a cycle would require optimizing over all keyframes (Sec. VII-B) |
| 全域最佳化 | local graph optimization: pairwise matching results give quadratic score models (Taylor expansion with the converged Hessian) summed over edges; optimized only over the subgraph within three edges of the new keyframe to stay real time (Sec. VII-B) |
| 地圖表示 | per-scan 2D grid of 100 cm cells, each with a normal distribution (mean and covariance, at least three points), using four overlapping grids shifted by half a cell; the map is a collection of keyframes with global poses (Sec. III, VII) |
| 先驗資訊 | none required; the estimate is initialized by zero, odometry, or linear extrapolation of the previous step; the reported experiments used no odometry (Sec. IV, VI, VIII) |
| 可輸出幾何 | 2D pose (tx, ty, phi) per scan; map of 33 keyframes with poses and the estimated trajectory (Fig. 2, Sec. VIII) |
| 計算需求 | building an NDT takes around 10 ms and one Newton iteration around 2 ms on a 1.4 GHz machine, typically 1 to 5 iterations; offline processing of the test run took 58 s, 97 scans per second; Java implementation (Sec. VI, VIII) |
使用設備
原文使用的感測器、運算硬體與載具（equipment）。型號保留原文寫法，連結到設備頁中同一型號的歸併名稱；角色依原文用途分為方法輸入、資料集感測器、執行運算平台、參考或真值量測（reference or ground truth）與比較對象設備。
| 類別 | 型號（原文寫法） | 角色 | 資料集 | 原文規格 | 出處 |
|---|---|---|---|---|---|
| LiDAR | SICK laser scanner | 方法輸入 | 未標示 | covering 180 degree with an angular resolution of one degree (model number not stated) | (Biber & Strasser, 2003, Sec. VIII) |
| 運算硬體 | 1.4 GHz machine | 執行運算平台 | 未標示 | Java implementation | (Biber & Strasser, 2003, Sec. VI, VIII) |
作者報告的優勢與限制
優勢
- ["no explicit correspondences between points or features are needed (abstract, Sec. IX)", "all derivatives are analytic, which is fast and correct (Sec. IX)", "real-time indoor mapping without odometry in the reported run (Sec. VIII)", "tolerant to small environment changes such as opened or closed doors (Sec. VIII)"]
限制
- ["tested only indoors
- whether local normal distributions model less structured or outdoor scenes well is left open (Sec. IX)", "mapping without odometry works only while 2D structure is present (Sec. VIII)", "full keyframe optimization is not real time as keyframes grow, so only a three-edge subgraph is optimized (Sec. VII-B)", "no ground-truth accuracy evaluation
- comparison of convergence radius with Lu and Milios left for future work (Sec. VIII, IX)", "NDT accuracy is sensitive to voxel resolution (Koide et al., 2021b Sec. I, secondary, for 3D NDT)"]
營建工程相關證據
原文未報告（實驗僅在機器人所在的實驗室與走廊等室內環境進行，未涉及建物施工或工地）
原文驗證環境：已完工建築
報告的性能數據
以下是原文作者報告的性能數值（author-reported results），不是本研究重新量測的結果。每張圖只並列同一個比較組（comparison group，同一張表、同一組實驗設定）內的方法；不同比較組之間的數值不可直接比較，也不構成排名。
本方法共出現在 2 個比較組，合計 4 筆紀錄。
Biber & Strasser, 2003 · Text Sec.VI 本方法 2 筆
資料集與序列authors' indoor SICK scans
表格設定（擷取紀錄原文）：Position tracking against a keyframe; per-scan cost of building the NDT (Biber & Strasser, 2003, Text Sec.VI)
time to build the NDT of a scan (around)，authors' indoor SICK scans
這張表在此指標與資料序列只列出本方法一筆，沒有可並列的其他方法，因此不畫圖，數值與出處見下表。這是 Biber & Strasser, 2003 在此表設定下報告的數值（author-reported results），不代表方法在其他資料或設定下的表現。
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| NDT (proposed)本方法原文提出硬體：1.4 GHz machine; Java implementation | 10 ms | (Biber & Strasser, 2003, Sec. VI) |
Biber & Strasser, 2003 · Text Sec.VIII 本方法 2 筆
資料集與序列authors' indoor SICK scans · lab to corridor and back, about 83 m, 20 min
表格設定（擷取紀錄原文）：Offline processing of the lab-corridor run (every fifth of 28 430 scans used, about 23 scans/s at a simulated 35 cm/s; tracking every scan, SLAM step every tenth scan, no odometry) (Biber & Strasser, 2003, Text Sec.VIII)
time to process all frames offline，authors' indoor SICK scans · lab to corridor and back, about 83 m, 20 min
這張表在此指標與資料序列只列出本方法一筆，沒有可並列的其他方法，因此不畫圖，數值與出處見下表。這是 Biber & Strasser, 2003 在此表設定下報告的數值（author-reported results），不代表方法在其他資料或設定下的表現。
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| NDT scan matcher with keyframe SLAM (proposed)本方法原文提出硬體：1.4 GHz machine; Java implementation | 58 s | (Biber & Strasser, 2003, Sec. VIII) |
來源
Biber & Strasser, 2003
（2003）The normal distributions transform: a new approach to laser scan matchingProceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), vol. 3, pp. 2743-2748
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