SLAM 點雲圖鑑Point clouds for construction
M-01 · 2019

Eigen-Factors (EF)

Eigen-Factors 將每個平面由多個位姿觀測到的點累積為 4×4 齊次點矩陣，平面擬合誤差等於該矩陣的最小特徵值；平面參數不必列為狀態變數，因此複雜度與點數無關，只取決於平面數與位姿數。作者以李代數推導最小特徵值對各位姿的封閉形式梯度，並以簡化的 Nesterov 加速梯度法最佳化軌跡，另提出在 SE(3) 上內插的連續時間軌跡版本。實驗只使用合成平面點雲，且只評估連續時間版本，因為離散多位姿版本會過度擬合。此方法後來成為 BALM2 比較實驗中的平面式多影格配準基準之一。

配準元件近十年已讀全文同儕審查已出版全域一致性、場所辨識與長期建圖

閱讀版本
author's version PDF (7 pages, PDF created 2019-11-18) linked from the official code repository README and hosted on the Skoltech site; IEEE IROS 2019 version of record (pp. 1278-1284) not read, so page-level equivalence is not confirmed
全文取得途徑
作者自存版本
本頁內容

Eigen-Factors accumulate each plane's multi-pose points into 4x4 homogeneous matrices whose minimum eigenvalue is the plane-fit error, derive closed-form SE(3) pose gradients, optimize with a Nesterov-type momentum method, and evaluate a time-continuous interpolated trajectory on synthetic data only.

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generic 3D point clouds (lidar and RGB-D motivated in Sec. I); evaluated only on synthetic planar point clouds
原文測試平台simulation
狀態估計first-order optimization: closed-form gradient of the minimum eigenvalue of each plane's accumulated 4x4 homogeneous point matrix Q with respect to SE(3) poses (Lie algebra, left-hand perturbation), minimized with a simplified Nesterov Accelerated Gradient momentum method (alpha = 0.2/(N_all H), beta = 0.7), compared with plain gradient descent (Sec. IV-C, IV-D, V)
資料關聯requires a preprocessing segmentation of planes (Sec. I); (inference) the synthetic evaluation samples points per plane, so plane membership appears to be known rather than estimated (Sec. V)
時間表示discrete per-frame poses and a time-continuous variant that interpolates poses on SE(3) between the identity and one optimized final pose (Sec. IV-E); only the continuous-time version was evaluated because the discrete version over-fitted and produced trajectory discontinuities (Sec. V, VI)
去畸變原文未報告 (synthetic point clouds; no in-scan motion compensation described)
迴圈閉合原文未報告
全域最佳化fixed time-window multi-frame alignment of all poses that observe common planes; no pose graph, loop closure or global map (Sec. IV, VI)
地圖表示non-parametric plane landmarks: each plane kept only as per-pose 4x4 matrices S_t of homogeneous points, so raw points and plane parameters need not be stored (Sec. IV-B)
先驗資訊coarse initial trajectory from pairwise alignment (origin to subsequent poses); the author states EFs are sensitive to initialization (Sec. V)
可輸出幾何optimized trajectory (time-continuous interpolation) with implicitly estimated planes; no exported map product (Sec. IV-B, V)
計算需求complexity independent of the number of points and dependent on numbers of planes and poses (abstract, Sec. IV-B); C++ with Open3D; the single-threaded EF implementation is reported faster than the multi-core Open3D ICP variants, with execution time growing linearly with the number of poses (Sec. V, Fig. 5); hardware not reported

使用設備

尚未收錄此方法的設備紀錄；設備資料仍在分批查證，沒有紀錄不代表原文未使用任何設備。

作者報告的優勢與限制

優勢

  • Complexity independent of point count; each plane summarized by 4x4 matrices without information loss (abstract, Sec. IV-B)
  • Trajectory RMSE kept improving as more observations (poses) were added (Sec. V, Fig. 3)
  • For longer trajectories the last-pose error fell below point-to-plane ICP, which only aligns the first and last clouds (Sec. V, Fig. 4)

限制

  • Evaluated only on synthetic data (Sec. V, VI)
  • Discrete multi-pose version over-fits the observations, giving trajectory discontinuities; more constraints are needed (Sec. V, VI)
  • Sensitive to initialization; needs a coarse initial alignment (Sec. V)
  • For very short trajectories (2 to 4 poses) point-to-plane ICP was more accurate (Sec. V, Fig. 4)
  • Needs plane segmentation as preprocessing, so it relies on planar scenes (Sec. I)
  • (inference) Real-world robustness not established in the conference version; later journal extension not read

營建工程相關證據

原文未報告

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 4 個比較組，合計 24 筆紀錄。

Liu et al., 2023a · Table II 本方法 20 筆

表格設定（擷取紀錄原文）：ATE RMSE (m) of multi-view registration; scans deskewed by FAST-LIO2 (odometry output discarded) and downsampled from 10 Hz to 2 Hz; ICP, GICP, NDT from PCL run incrementally against the last 20 scans; the ICP trajectory is the common initialization and adaptive voxelization (root voxel 1 m Hilti, 2 m VIRAL and UrbanLoco) the common association for EF, BALM, PA and Ours (BAREG uses its own); plane features only except Ours (edge); ground truth: Hilti total station or motion capture, VIRAL Leica Nova MS60, UrbanLoco Novatel SPAN-CPT RTK/INS. Column order verified from PDF layout: Ours (float), Ours (edge), Ours (Liu et al., 2023a, Table II)

Absolute trajectory error (RMSE, meters)，Hilti SLAM Challenge 2021 · Basement1

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。

這些是 Liu et al., 2023a 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。

統計量：均方根誤差（RMSE）；對齊方式：原文未報告；單位：m；場景：handheld (Ouster OS0-64), Hilti indoor or outdoor sequence

資料來源作者報告值(Liu et al., 2023a, Table II)

數值與出處
方法（原文寫法）報告值出處
ICP (PCL, incremental)0.058 m(Liu et al., 2023a, Table II)
GICP (PCL, incremental)0.063 m(Liu et al., 2023a, Table II)
NDT (PCL, incremental)0.076 m(Liu et al., 2023a, Table II)
EF本方法0.047 m(Liu et al., 2023a, Table II)
BALM0.042 m(Liu et al., 2023a, Table II)
PA0.038 m(Liu et al., 2023a, Table II)
PA (inner)0.036 m(Liu et al., 2023a, Table II)
BAREG0.04 m(Liu et al., 2023a, Table II)
Ours (float)原文提出0.0359 m(Liu et al., 2023a, Table II)
Ours (edge)原文提出0.0361 m(Liu et al., 2023a, Table II)
Ours原文提出0.0353 m(Liu et al., 2023a, Table II)

Liu et al., 2023a · Table IV 本方法 2 筆

指標Optimization time (total, unit not stated)

表格設定（擷取紀錄原文）：Total optimization time of the BA methods on the Table II inputs (pairwise methods excluded); the table does not state the time unit; desktop Intel i7-10750H, 16 GB RAM (Sec. IV) (Liu et al., 2023a, Table IV)

Optimization time (total, unit not stated)，Hilti SLAM Challenge 2021 · Construction2

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。

這些是 Liu et al., 2023a 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。

統計量：原文未報告；對齊方式：未對齊；單位：原文未報告；場景：handheld (Ouster OS0-64), construction sequence

資料來源作者報告值(Liu et al., 2023a, Table IV)

數值與出處
方法（原文寫法）報告值出處
EF本方法硬體：desktop Intel i7-10750H, 16 GB RAM1415.18(Liu et al., 2023a, Table IV)
BALM硬體：desktop Intel i7-10750H, 16 GB RAM412(Liu et al., 2023a, Table IV)
PA硬體：desktop Intel i7-10750H, 16 GB RAM335.7(Liu et al., 2023a, Table IV)
PA (inner)硬體：desktop Intel i7-10750H, 16 GB RAM313.23(Liu et al., 2023a, Table IV)
BAREG硬體：desktop Intel i7-10750H, 16 GB RAM231.48(Liu et al., 2023a, Table IV)
Ours (float)原文提出硬體：desktop Intel i7-10750H, 16 GB RAM33.04(Liu et al., 2023a, Table IV)
Ours (edge)原文提出硬體：desktop Intel i7-10750H, 16 GB RAM47.34(Liu et al., 2023a, Table IV)
Ours原文提出硬體：desktop Intel i7-10750H, 16 GB RAM47.12(Liu et al., 2023a, Table IV)

Liu et al., 2023a · Supplementary Table VII 本方法 1 筆

指標Absolute trajectory error (RMSE, meters)

資料集與序列KITTI odometry · Mean (00-10)

表格設定（擷取紀錄原文）：Supplementary application: global BA over all KITTI poses initialised with MULLS odometry (loop closure enabled); CT-ICP with loop closure as reference; ATE RMSE (m); Mean over sequences 00-10 only (Liu et al., 2023a, Supplementary Table VII)

Absolute trajectory error (RMSE, meters)，KITTI odometry · Mean (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。

這些是 Liu et al., 2023a 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。

統計量：均方根誤差（RMSE）；對齊方式：原文未報告；單位：m；場景：KITTI odometry sequences 00-10; environment not described in this paper

資料來源作者報告值(Liu et al., 2023a, Supplementary Table VII)

數值與出處
方法（原文寫法）報告值出處
MULLS1.63 m(Liu et al., 2023a, Supplementary Table VII)
CT-ICP1.4 m(Liu et al., 2023a, Supplementary Table VII)
EF本方法1.55 m(Liu et al., 2023a, Supplementary Table VII)
BALM1.48 m(Liu et al., 2023a, Supplementary Table VII)
PA (inner)1.37 m(Liu et al., 2023a, Supplementary Table VII)
BAREG1.42 m(Liu et al., 2023a, Supplementary Table VII)
Our原文提出1.34 m(Liu et al., 2023a, Supplementary Table VII)

Liu et al., 2023a · Table III 本方法 1 筆

指標Occupied cells increment over Ours (inc.), 0.1 m cells

資料集與序列Hilti SLAM Challenge 2021 · Construction2

表格設定（擷取紀錄原文）：Occupied 0.1 m cells of the registered point-cloud map (fewer is better, no reference map needed); all columns except Ours are increments over the Ours count ('inc.'), Ours is the base count (Liu et al., 2023a, Table III)

Occupied cells increment over Ours (inc.), 0.1 m cells，Hilti SLAM Challenge 2021 · Construction2

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。

這些是 Liu et al., 2023a 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。

統計量：原文未報告；對齊方式：未對齊；單位：cells；場景：handheld (Ouster OS0-64), construction sequence

資料來源作者報告值(Liu et al., 2023a, Table III)

數值與出處
方法（原文寫法）報告值出處
ICP (PCL, incremental)6235 cells(Liu et al., 2023a, Table III)
GICP (PCL, incremental)9371 cells(Liu et al., 2023a, Table III)
NDT (PCL, incremental)10032 cells(Liu et al., 2023a, Table III)
EF本方法6397 cells(Liu et al., 2023a, Table III)
BALM1789 cells(Liu et al., 2023a, Table III)
PA1047 cells(Liu et al., 2023a, Table III)
PA (inner)394 cells(Liu et al., 2023a, Table III)
BAREG986 cells(Liu et al., 2023a, Table III)
Ours (float)原文提出95 cells(Liu et al., 2023a, Table III)
Ours (edge)原文提出181 cells(Liu et al., 2023a, Table III)

來源

  • Ferrer, 2019

    Gonzalo Ferrer（2019）Eigen-Factors: Plane Estimation for Multi-Frame and Time-Continuous Point Cloud Alignment2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1278-1284

    DOI 10.1109/iros40897.2019.8967573

    同儕審查已出版已讀全文近十年查證後修正

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