ICP (point-to-point)
迭代最近點（Iterative Closest Point, ICP）將資料形狀分解為點集後，每次迭代先為每一點找模型形狀上的最近點，再以 Horn 的單位四元數封閉解計算最小平方剛體轉換並更新位姿，直到均方誤差的變化小於門檻。作者證明此演算法對均方距離單調收斂至局部極小值，並提出在更新方向一致時以直線或拋物線外插的加速版本，通常可把 50 次以上的迭代縮減為 15 至 20 次。模型可為點集、折線、參數或隱式曲線與曲面及三角網格；全域配準需從多組初始旋轉出發，局部配準另需多組初始平移。作者也指出，資料中若有大量點不對應模型，此方法並不適用，且易受粗大離群值影響。實驗包含合成點集、雜訊曲線與 Bezier 曲面、NRCC 面具雷射三角量測資料及 Tucson 附近的地形資料。
本頁內容
ICP alternates closest-point correspondence and mean-square distance minimization for 6-DoF rigid alignment; it converges monotonically but only to a local minimum, so initialization matters.
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 | 未記錄 |
|---|---|
| 原文測試平台 | 未記錄 |
| 狀態估計 | iterative: closest points, then Horn's closed-form unit-quaternion least-squares registration (preferred over SVD in 2-D and 3-D because reflections are not desired), applied to the original data set, until the mean-square error change falls below a threshold; accelerated variant extrapolates the registration vector by a line or parabola when the last update directions agree within about 10 deg, with v_max = 25 ||dq|| (Sec. III-C, IV-A, IV-C) |
| 資料關聯 | closest point on the model shape for each data point; point sets, polylines, triangle sets, parametric and implicit curves and surfaces (parametric entities via a simplex approximation followed by Newton iterations; implicit entities via a simplex approximation plus a constrained Lagrange-multiplier solve, although the implemented system handled implicit surfaces through special cases or parametric forms); O(Np Nx) worst case, O(Np log Nx) average; k-d trees suggested as future speed-up (Sec. III, IV-A, VIII) |
| 時間表示 | 不適用 (pairwise rigid registration) |
| 去畸變 | 不適用 |
| 迴圈閉合 | none |
| 全域最佳化 | none; global matching by running ICP from a set of initial rotation states (e.g., four states from principal moments when eigenvalues are distinct, or 12, 24, 60 polyhedral group states, 40 or 312 quaternion combinations) and, for local matching, initial translation states (Sec. V-A, V-C) |
| 地圖表示 | point sets, curves or surfaces (representation-independent per abstract) |
| 先驗資訊 | no prior pose for global matching when a sufficient set of initial rotations is used, provided the data covers a significant portion of the model (condition with alpha1 = 1/sqrt(2)); otherwise an initial pose inside the correct basin is needed (Sec. V-A, V-B) |
| 可輸出幾何 | 6-DoF rigid transformation |
| 計算需求 | C programs on a single-processor computer rated at 1.6 Mflops (Linpack 100 x 100); 8 vs 11 points under 1 s; 250 points vs 450 triangles about 3 min (24 rotations); 2546 mask points vs 8442 triangles about 10 min; 13 655 terrain points about 1 hr (Sec. VI) |
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 |
|---|---|---|---|---|---|
| 運算硬體 | single-processor computer rated at 1.6 Mflops on the 100 x 100 double-precision Linpack benchmark | 執行運算平台 | 未標示 | all programs written in C | (Besl & McKay, 1992, Sec. VI) |
| 其他 | Hyscan laser triangulation sensor | 資料集感測器 | NRCC (National Research Council of Canada) African mask range data | commercially available laser triangulation sensor; a low-resolution 64 x 68 gridded image computed from the original data | (Besl & McKay, 1992, Sec. VI-C2) |
作者報告的優勢與限制
優勢
- ["handles the full six degrees of freedom and is independent of shape representation (Sec. VII)", "no feature extraction, derivative estimation or preprocessing needed when statistical outliers are near zero (Sec. VII)", "monotonic convergence theorem
- accelerated ICP typically reduces more than 50 basic iterations to 15 or 20 (Sec. IV-B, IV-C)", "handles normally distributed vector noise with standard deviation up to 10% of object size in the reported tests (Sec. VII)", "relatively insensitive to minor segmentation errors, shown on the African mask parametric model (Sec. VI-C2, VII)", "mask registration with 0.59 mm RMS error for all trial positionings (Sec. VI-C2)"]
限制
- ["converges only to the nearest local minimum
- global matching relies on a set of initial states (abstract, Sec. V)", "not useful when a significant part of the data does not correspond to the model (Sec. V-C)", "susceptible to gross statistical outliers unless a robust method is substituted (Sec. VII)", "fast quaternion and SVD solves are not easily extended to weighted least squares, so unequal point uncertainties (e.g., navigation laser radars) are not handled (Sec. VII)", "local matching becomes costly for small allowable occlusion (about 10% or less) (Sec. VII)", "'sea urchin' or 'planet' shapes can defeat any fixed set of initial rotations (Sec. V-B, VII)", "does not solve segmentation
- intermixed data from two shapes gives wrong registrations (Sec. VII)"]
營建工程相關證據
原文未報告（實驗為合成點集、曲線與曲面、NRCC 面具雷射三角量測資料及 Tucson 附近地形資料；主要應用為剛體零件檢測前的模型配準，未涉及營建工地）
原文驗證環境：模擬、受控實驗
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 41 個比較組，合計 262 筆紀錄。以下列出本方法紀錄最多的 4 組，其餘 37 組列在最後，並連到性能比較頁。
Pomerleau et al., 2013 · Table 6 本方法 72 筆
表格設定（擷取紀錄原文）：35 scan pairs per data set (overlap 0.30 to 0.99) with 64 Gaussian perturbations per level (EP easy, MP medium, HP hard); errors after registration against theodolite ground truth: translation = Euclidean norm (m), rotation = geodesic angle (rad); A50/A75/A95 quantiles (Pomerleau et al., 2013, Table 6)
translation error A50，Challenging Laser Registration (Pomerleau et al. 2012) · Apartment, EP (easy)
只並列這張表在相同設定下報告的方法；以「本方法：」開頭者為本頁方法。失敗、未執行與未報告以標記呈現，不是 0。
按 Tab 進入圖表後，用上下方向鍵逐一瀏覽各類別，Esc 關閉提示框；也可開啟表格檢視閱讀全部數值。
這些是 Pomerleau et al., 2013 在此表設定下報告的數值（author-reported results），只能在同一個比較組內對照，不代表方法在其他資料或設定下的表現。
資料來源作者報告值(Pomerleau et al., 2013, Table 6)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| point-to-plane ICP (libpointmatcher baseline, 70% trimmed) | 0.06 m | (Pomerleau et al., 2013, Table 6 (top)) |
| point-to-point ICP (libpointmatcher baseline, 75% trimmed)本方法 | 0.13 m | (Pomerleau et al., 2013, Table 6 (top)) |
Vizzo et al., 2021 · Table II 本方法 26 筆
表格設定（擷取紀錄原文）：KITTI odometry training sequences 00-10; relative errors averaged over 100-800 m segments; all methods share the range-image normals and Huber loss; Map None = frame-to-frame, Map Point cloud = frame-to-model on the last N scans; DA = data association (NN nearest neighbour, Proj. projective, RC ray casting). Per-sequence rotational errors omitted to respect the row cap; only the rotational average is kept (Vizzo et al., 2021, Table II)
relative translational error (%)，KITTI Odometry · average of 00-10
只並列這張表在相同設定下報告的方法；以「本方法：」開頭者為本頁方法。失敗、未執行與未報告以標記呈現，不是 0。
按 Tab 進入圖表後，用上下方向鍵逐一瀏覽各類別，Esc 關閉提示框；也可開啟表格檢視閱讀全部數值。
這些是 Vizzo et al., 2021 在此表設定下報告的數值（author-reported results），只能在同一個比較組內對照，不代表方法在其他資料或設定下的表現。
資料來源作者報告值(Vizzo et al., 2021, Table II)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| point-to-point ICP [3] (map: None, DA: NN)本方法 | 4.86% | (Vizzo et al., 2021, Table II) |
| point-to-plane ICP [32] (map: None, DA: NN) | 7.6% | (Vizzo et al., 2021, Table II) |
| GICP [33] (map: None, DA: NN) | 14.35% | (Vizzo et al., 2021, Table II) |
| SuMa [1] (map: None, DA: Proj.) | 2.93% | (Vizzo et al., 2021, Table II) |
| point-to-point ICP [3] (map: Point cloud, DA: NN)本方法 | 29.98% | (Vizzo et al., 2021, Table II) |
| point-to-plane ICP [32] (map: Point cloud, DA: NN) | 18.92% | (Vizzo et al., 2021, Table II) |
| GICP [33] (map: Point cloud, DA: NN) | 20.43% | (Vizzo et al., 2021, Table II) |
| Ours (Δtree = 10) (map: Mesh, DA: NN) | 2.15% | (Vizzo et al., 2021, Table II) |
| Ours (Δtree = 10) (map: Mesh, DA: RC)原文提出 | 1.55% | (Vizzo et al., 2021, Table II) |
Li et al., 2019 · Table 1 本方法 16 筆
表格設定（擷取紀錄原文）：KITTI odometry metric: t_rel = average translational RMSE (%) and r_rel = average rotational RMSE (deg/100 m) over 100-800 m lengths. LO-Net trained on KITTI 00-06 and tested on 07-10 and on Ford without fine-tuning; loop closure disabled for all methods. LOAM values outside brackets come from the authors' modified re-run; bracketed values are quoted from the LOAM paper [45]. Velas et al. values quoted from [35] (r_rel and Ford NA). ICP variants run with PCL. Truncated: per-sequence rows 00-06 (training sequences) omitted; the mean over them (mean-dagger) is kept. (Li et al., 2019, Table 1)
t_rel: average translational RMSE (%) on length of 100 m-800 m，KITTI odometry · 07 (not used for training)
只並列這張表在相同設定下報告的方法；以「本方法：」開頭者為本頁方法。失敗、未執行與未報告以標記呈現，不是 0。
按 Tab 進入圖表後，用上下方向鍵逐一瀏覽各類別，Esc 關閉提示框；也可開啟表格檢視閱讀全部數值。
這些是 Li et al., 2019 在此表設定下報告的數值（author-reported results），只能在同一個比較組內對照，不代表方法在其他資料或設定下的表現。
資料來源作者報告值(Li et al., 2019, Table 1)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| ICP-po2po (PCL)本方法 | 5.17% | (Li et al., 2019, Table 1) |
| ICP-po2pl (PCL) | 1.55% | (Li et al., 2019, Table 1) |
| GICP [30] | 0.64% | (Li et al., 2019, Table 1) |
| CLS [34] | 1.04% | (Li et al., 2019, Table 1) |
| LOAM [45] (authors' modified re-run) | 0.69% | (Li et al., 2019, Table 1) |
| Velas et al. [35] (values from [35]) | 1.77% | (Li et al., 2019, Table 1) |
| LO-Net原文提出 | 1.7% | (Li et al., 2019, Table 1) |
| LO-Net+Mapping原文提出 | 0.56% | (Li et al., 2019, Table 1) |
Wang et al., 2021c · Table 1 本方法 13 筆
表格設定（擷取紀錄原文）：KITTI odometry, trained on 00-06 (marked *) and tested on 07-10; trel = average translational RMSE (%) over 100-800 m subsequences; rows other than LOAM w/o mapping and Ours are copied from LO-Net [10]; LOAM is a full system with mapping, others are odometry only (Wang et al., 2021c, Table 1)
trel (average translational RMSE, %)，KITTI odometry · 07 (test)
只並列這張表在相同設定下報告的方法；以「本方法：」開頭者為本頁方法。失敗、未執行與未報告以標記呈現，不是 0。
按 Tab 進入圖表後，用上下方向鍵逐一瀏覽各類別，Esc 關閉提示框；也可開啟表格檢視閱讀全部數值。
這些是 Wang et al., 2021c 在此表設定下報告的數值（author-reported results），只能在同一個比較組內對照，不代表方法在其他資料或設定下的表現。
資料來源作者報告值(Wang et al., 2021c, Table 1)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| Full LOAM [31] | 0.69% | (Wang et al., 2021c, Table 1) |
| ICP-po2po本方法 | 5.17% | (Wang et al., 2021c, Table 1) |
| ICP-po2pl | 1.55% | (Wang et al., 2021c, Table 1) |
| GICP [19] | 0.64% | (Wang et al., 2021c, Table 1) |
| CLS [21] | 1.04% | (Wang et al., 2021c, Table 1) |
| Velas et al. [22] | 1.77% | (Wang et al., 2021c, Table 1) |
| LO-Net [10] | 1.7% | (Wang et al., 2021c, Table 1) |
| DMLO [11] | 0.73% | (Wang et al., 2021c, Table 1) |
| LOAM w/o mapping (published code run by authors) | 10.87% | (Wang et al., 2021c, Table 1) |
| Ours (PWCLO-Net)原文提出 | 0.6% | (Wang et al., 2021c, Table 1) |
其他比較組
列出其餘 37 個比較組
- Censi, 2008 · Fig. 3 table
- Pang et al., 2018 · Table II
- Rusinkiewicz, 2019 · Fig. 5
- Razlaw et al., 2015 · Table III
- Pang et al., 2018 · Table I
- Liu et al., 2023a · Table II
- Lim et al., 2024 · Table 6
- Zhang et al., 2024b · Table 2
- Zhou et al., 2016 · Table 3
- Deng et al., 2023 · Table 3
- Deng et al., 2023 · Table 5
- Besl & McKay, 1992 · Text Sec.VI-C2
- Koide et al., 2021b · Table II
- Magnusson et al., 2007 · Text Sec. 5.2.1
- Magnusson, 2009 · Text Sec. 6.4.2 (Figs. 6.20-6.21 captions)
- Pang et al., 2018 · Text Sec. IV-E
- Pomerleau et al., 2013 · Text Sec. 5.2.4
- Besl & McKay, 1992 · Text Sec.VI-A
- Besl & McKay, 1992 · Text Sec.VI-C1
- Censi, 2008 · Text Sec. V.B table
- Lee et al., 2025a · Table VI
- Koide et al., 2021b · Table I
- Magnusson et al., 2009 · Text Fig. 7 caption
- Magnusson, 2009 · Text Sec. 6.4.2 (Crossing)
- Magnusson, 2009 · Text Sec. 6.4.3 (Figs. 6.27-6.28 captions)
- Pang et al., 2018 · Table IV
- Pang et al., 2018 · Text Sec. IV-F
- Liu et al., 2023a · Table III
- Besl & McKay, 1992 · Text Sec.VI-A1
- Besl & McKay, 1992 · Text Sec.VI-C3
- Magnusson et al., 2007 · Text Sec. 5.2.2
- Magnusson et al., 2009 · Text Fig. 8 caption
- Magnusson et al., 2009 · Text Sec. IV-D-2
- Magnusson et al., 2009 · Text Sec. IV-D-3
- Pang et al., 2018 · Text Sec. IV-D-2
- Zhang et al., 2024a · Table 8
- Zhang et al., 2024a · Table 9
來源
Besl & McKay, 1992
（1992）A method for registration of 3-D shapesIEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2):239-256
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