GICP
GICP 將點對點與點對平面 ICP 納入同一機率框架：兩片點雲的每個點都被視為來自高斯分布，最小化步驟以最大概似估計計算位姿。作者依局部平面假設，令每點沿表面法向量的共變異數很小、沿平面方向很大，形成「平面對平面」配準；點對點與點對平面皆可視為其特例。對應點仍以歐氏距離與 kd-tree 搜尋，因此保留 ICP 的速度與簡潔。實驗使用射線追蹤模擬的 SICK 旋轉掃描（室內走廊與建物周邊戶外，1 cm 雜訊）及車頂 Velodyne 的郊區環線記錄；Velodyne 測試掃描對彼此相距 15 至 20 m 以上，各方法的初始誤差在每軸 ±1.5 m 與 ±15° 內隨機產生。真實資料的參考位姿來自結合 GPS 與 IMU 的成對約束 SLAM，作者自承並非完美的真值。論文結果只以圖呈現，沒有數值表。
本頁內容
GICP casts ICP's minimization step as MLE over Gaussian point models with surface-aligned covariances from both scans (plane-to-plane), with point-to-point and point-to-plane as special cases.
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 | ["3D LiDAR (simulated SICK scanner on a rotating joint、roof-mounted Velodyne on an instrumented car)", "GPS and IMU (car logs、used only to build ground truth)"] |
|---|---|
| 原文測試平台 | simulation、vehicle |
| 狀態估計 | maximum-likelihood estimate over Gaussian point models; minimized with conjugate gradients in the experiments (Sec. III-IV) |
| 資料關聯 | Euclidean nearest neighbour via kd-tree with max match distance d_max; plane-to-plane covariance weighting (Sec. III) |
| 時間表示 | 不適用 (pairwise rigid registration) |
| 去畸變 | 原文未報告 |
| 迴圈閉合 | none |
| 全域最佳化 | none |
| 地圖表示 | point clouds with per-point covariance from PCA of 20 nearest neighbours (Sec. III-B) |
| 先驗資訊 | initial transformation T0 required (Alg. 1) |
| 可輸出幾何 | 6-DoF rigid transformation |
| 計算需求 | 原文未報告 (no runtime given); kd-tree closest-point lookup needing O(n log n) explicit point comparisons (Sec. II, p. 2); all three algorithms minimized with conjugate gradients for comparability, capped at 250 iterations for standard ICP and 50 for point-to-plane and GICP (Sec. IV); 15,000 points per scan in the tests (Figs. 5, 9) |
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 scanner | 方法輸入 | simulated indoor hallway and outdoor building scenes | simulated by ray tracing, mounted on a rotating joint; Gaussian noise added (plots titled 15,000 points, 1 cm noise) | (Segal et al., 2009, Sec. IV (p. 4), Figs. 2, 3, 5) |
| LiDAR | Velodyne range finder | 方法輸入 | instrumented-car logs, suburban loop | roof-mounted on an instrumented car; scans cover a range of 70 to 100 m from the sensor | (Segal et al., 2009, Sec. IV (pp. 4 and 8), Fig. 4) |
| 慣性量測單元（IMU） | IMU | 參考或真值量測 | instrumented-car logs, suburban loop | 原文未報告 | (Segal et al., 2009, Sec. IV (p. 4)) |
| GNSS 接收器 | GPS | 參考或真值量測 | instrumented-car logs, suburban loop | 原文未報告 | (Segal et al., 2009, Sec. IV (p. 4)) |
| 載具平台 | instrumented car | 方法輸入 | instrumented-car logs, suburban loop | 原文未報告 | (Segal et al., 2009, Sec. IV (p. 4)) |
作者報告的優勢與限制
優勢
- outperforms standard ICP and point-to-plane on simulated and real data (abstract, Sec. IV)
- less sensitive to the max match distance d_max because inconsistent correspondences are down-weighted, and in the simulated scenes accuracy is not sensitive to overestimated d_max (Sec. IV, Fig. 5)
- on real Velodyne data GICP with its worst-case d_max performs roughly as well as point-to-plane with its best-case d_max (Sec. IV, p. 8)
- removes some local minima seen with point-to-plane in Velodyne scan pairs about 30 m apart (Sec. IV, Figs. 6 to 7)
限制
- assumes locally planar surfaces
- high-frequency real data raises incorrect correspondences sharing orientation, not handled by the model (Sec. IV)
- outlier terms and slack distributions left for future work (Sec. IV to V)
- real-data ground truth came from pairwise constraint-based SLAM (standard ICP on scans spaced an order of magnitude closer) with GPS and IMU, which the authors call not a perfect method but a reasonable baseline (Sec. IV, p. 5)
- results given only as plots, without runtime (reviewer observation)
營建工程相關證據
原文未報告（模擬室內走廊與郊區道路車載資料，未涉及營建場域）
原文驗證環境：模擬
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 19 個比較組，合計 138 筆紀錄。以下列出本方法紀錄最多的 4 組，其餘 15 組列在最後，並連到性能比較頁。
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) | 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)本方法 | 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) | 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)本方法 | 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) |
Stückler & Behnke, 2014 · Table 1 本方法 22 筆
指標median relative pose error (RPE) in mm
表格設定（擷取紀錄原文）：Incremental (frame-to-frame) registration on TUM Freiburg sequences; median translational relative pose error in mm (maximum values in brackets in the table not extracted); warp is the OpenCV reimplementation (Stückler & Behnke, 2014, Table 1)
median relative pose error (RPE) in mm，TUM RGB-D (Freiburg) · fr1 360
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 Stückler & Behnke, 2014 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(Stückler & Behnke, 2014, Table 1)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| Ours (MRSMap)原文提出 | 5.1 mm | (Stückler & Behnke, 2014, Table 1) |
| Warp [17] (OpenCV) | 5.9 mm | (Stückler & Behnke, 2014, Table 1) |
| GICP [5]本方法 | 18.8 mm | (Stückler & Behnke, 2014, Table 1) |
| 3D-NDT [7] | 7.8 mm | (Stückler & Behnke, 2014, Table 1) |
| Fovis [12] | 7.1 mm | (Stückler & Behnke, 2014, Table 1) |
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) | 5.17% | (Li et al., 2019, Table 1) |
| ICP-po2pl (PCL) | 1.55% | (Li et al., 2019, Table 1) |
| GICP [30]本方法 | 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 | 5.17% | (Wang et al., 2021c, Table 1) |
| ICP-po2pl | 1.55% | (Wang et al., 2021c, Table 1) |
| GICP [19]本方法 | 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 15 個比較組
- Razlaw et al., 2015 · Table III
- Koide, 2024 · Text BENCHMARK.md Accuracy
- Liu et al., 2023a · Table II
- Koide et al., 2021b · Table II
- Lim et al., 2024 · Table 6
- Koide et al., 2021b · Table I
- Deng et al., 2023 · Table 3
- Deng et al., 2023 · Table 5
- Koide et al., 2021b · Text Sec. IV-A
- Lim et al., 2025 · Table I
- Stückler & Behnke, 2014 · Table 2
- Liu et al., 2023a · Table III
- Lee et al., 2025a · Table III
- Zhang et al., 2024a · Table 8
- Zhang et al., 2024a · Table 9
來源
Segal et al., 2009
（2009）Generalized-ICPRobotics: Science and Systems V
同儕審查已出版已讀全文經典查證後修正