Point-to-plane ICP (Chen-Medioni)
此文為點對平面 ICP 的原始期刊版本。作者假設兩個視角已有近似配準，在 P 上以規則格點挑選平滑區域的控制點，沿 P 在該點的法向線與數位曲面 Q 求交（以切平面迭代近似，通常 3 至 5 次），再以 Q 在交點的切平面為目標，最小化控制點到切平面的有號距離平方和，不需要點對點對應。實驗以結構光測距儀取得莫札特半身像、牙齒模型與木塊的距離影像；多視角建模時把新視角對已合併的全部資料配準，以減少逐對配準的誤差累積。
本頁內容
Original journal version of point-to-plane ICP: control points in smooth regions of P are paired, via intersection of the P-normal line with surface Q, with the tangent plane of Q, and squared point-to-tangent-plane distances are minimized iteratively from an approximate initial pose; applied to multi-view range-image object modelling.
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 | structured-light range finder after Sato and Inokuchi: projector with a programmable liquid crystal mask and a CCD camera, space coding with projected stripe patterns and triangulation; accuracy about 1 mm; range images at 0.5 mm spatial resolution stored as 32-bit floats |
|---|---|
| 原文測試平台 | rotary table (objects rotated on a turntable; object laid down for top and bottom views) |
| 狀態估計 | iterative least squares: at each iteration find T minimizing the sum of squared signed distances from transformed control points to the tangent planes of Q at the normal-line intersection points (Eq. 10), compose T^k = T T^(k-1), stop when the change measure of Eq. 11 falls below epsilon_c (0.01 in tests); cost per iteration linear in the number of control points |
| 資料關聯 | no point-to-point correspondence: for each control point p_i on P the line along the P-normal is intersected with digital surface Q by a Newton-like tangent-plane iteration (typically 3 to 5 iterations, stop within one sampling unit), and the tangent plane of Q at that intersection is the target; control points (usually 50 to 200) are taken on a regular grid in smooth areas (9x9 plane-fit residual below half a sampling unit) |
| 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 | no joint optimization; in multi-view modelling each new view is registered against the merged data of all previously integrated views instead of only its neighbour, to avoid accumulated error |
| 地圖表示 | object-centred cylindrical or spherical coordinate map; views are reparameterized by interpolation and averaged in overlaps, with outlier handling |
| 先驗資訊 | approximate initial transformation required: from the rotary-table set-up for side views, user-estimated rotation angles for top and bottom views, identity matrix in the two-view tests |
| 可輸出幾何 | 6-DoF rigid transformation between range views; integrated object model as a spherical coordinate map, rendered views and wireframe |
| 計算需求 | Symbolics 3620 Lisp Machine: 20 s for the Mozart pair (82 control points, 7 iterations) and 15 s for the tooth pair (88 control points, 6 iterations), whole process from control point selection to output |
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 |
|---|---|---|---|---|---|
| 載具平台 | rotary table | 方法輸入 | 未標示 | 4 to 8 side views (8 views at 45 deg in the results) plus top and bottom views | (Chen & Medioni, 1992, pp. 152-153) |
| 運算硬體 | Symbolics 3620 Lisp Machine | 執行運算平台 | 未標示 | 原文未報告 | (Chen & Medioni, 1992, p. 152) |
| 其他 | range finder set-up described by Sato and Inokuchi (projector with programmable liquid crystal mask and CCD camera) | 方法輸入 | 未標示 | space coding with projected stripe pattern and triangulation; accuracy in the neighbourhood of 1 mm; spatial resolution of range images 0.5 mm | (Chen & Medioni, 1992, p. 146; p. 151) |
作者報告的優勢與限制
優勢
- estimated rotations -15.06 deg (actual -15 deg) and -19.75 deg (actual -20 deg) (p. 152)
- error histograms comparable to the data resolution: std 0.6523 mm (Mozart) and 0.3219 mm (tooth) (Figs. 5d, 6e)
- points may slide within the tangent plane, so constraints from different control points are less conflicting and convergence is faster than with fixed control-point pairs (p. 148)
- works on free-form objects with few detectable features (pp. 151-153)
限制
- an approximate initial transformation must be supplied (p. 153)
- the cylindrical or spherical representation cannot directly handle more complex objects (p. 153)
- no measure yet to ensure a good spatial distribution of control points (p. 150)
- line-surface intersection fails when the projection falls outside Q or the normal is nearly perpendicular to the z axis (p. 149)
- small uncovered areas remain near the poles of the spherical maps (p. 153)
營建工程相關證據
原文未報告
原文驗證環境：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 12 個比較組，合計 143 筆紀錄。以下列出本方法紀錄最多的 4 組，其餘 8 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)本方法 | 0.06 m | (Pomerleau et al., 2013, Table 6 (top)) |
| point-to-point ICP (libpointmatcher baseline, 75% trimmed) | 0.13 m | (Pomerleau et al., 2013, Table 6 (top)) |
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)本方法 | 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 | 5.17% | (Wang et al., 2021c, Table 1) |
| ICP-po2pl本方法 | 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) |
Rusinkiewicz, 2019 · Fig. 5 本方法 12 筆
指標percentage of successful ICP trials
表格設定（擷取紀錄原文，這些數值分屬表中不同部分）：(Rusinkiewicz, 2019, Fig. 5)
- Numerals printed in Fig. 5 heatmap cells: % of 1000 random initial transforms (given rotation about a random axis, translation as fraction of mesh size), averaged over all bunny scan pairs with IOU > 20%, that end within 1% of mesh size of ground truth; 4 of 24 cells per variant and iteration budget transcribed
- Same setting as other Fig. 5 rows
percentage of successful ICP trials，bunny range scans (Turk and Levoy 1994) · 20 iterations; rotation 20 deg, translation 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 Rusinkiewicz, 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(Rusinkiewicz, 2019, Fig. 5)
| 方法（原文寫法） | 報告值 | 出處 |
|---|---|---|
| Point-to-point | 22% | (Rusinkiewicz, 2019, Fig. 5) |
| Quadratic (Mitra et al. 2004, on-demand) | 98% | (Rusinkiewicz, 2019, Fig. 5) |
| Point-to-plane本方法 | 99% | (Rusinkiewicz, 2019, Fig. 5) |
| Two-plane | 99% | (Rusinkiewicz, 2019, Fig. 5) |
| Symmetric-RN原文提出 | 99% | (Rusinkiewicz, 2019, Fig. 5) |
| Symmetric原文提出 | 99% | (Rusinkiewicz, 2019, Fig. 5) |
| LM-Point-to-plane (Fitzgibbon 2001) | 99% | (Rusinkiewicz, 2019, Fig. 5) |
| LM-Symmetric原文提出 | 99% | (Rusinkiewicz, 2019, Fig. 5) |
其他比較組
列出其餘 8 個比較組
- Chen & Medioni, 1992 · Fig. 5d and Fig. 6e histogram labels
- Zhang et al., 2024b · Table 2
- Zhou et al., 2016 · Table 3
- Chen & Medioni, 1992 · Text p. 152
- Pomerleau et al., 2013 · Text Sec. 5.2.4
- Magnusson et al., 2015 · Fig. 3 (execution-time table)
- Zhang et al., 2024a · Table 8
- Zhang et al., 2024a · Table 9
來源
Chen & Medioni, 1992
（1992）Object modelling by registration of multiple range imagesImage and Vision Computing, 10(3):145-155
DOI 10.1016/0262-8856(92)90066-c
同儕審查已出版已讀全文經典查證後修正
相關版本
- 會議版：Object modeling by registration of multiple range images (Proc. 1991 IEEE ICRA, pp. 2724-2729) 10.1109/ROBOT.1991.132043