SLAM 點雲圖鑑Point clouds for construction
M-01 · 2021

BALM

BALM 將光達束調整（LiDAR bundle adjustment, BA）定義為最小化各特徵點到其所屬邊緣或平面的距離，並證明邊緣與平面參數可用封閉解消去，使最佳化只剩下掃描位姿，因而可以納入大量稠密平面與邊緣特徵。作者推導代價函數對位姿的一階與二階解析導數，並提出自適應體素化（adaptive voxelization），以八元樹遞迴切分空間，直到每個體素只含單一平面或邊緣。此 BA 被整合為 LOAM 架構的後端，在滑動視窗內做局部地圖精修。

離線地圖精修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
arXiv v2 (2021-01-13); IEEE RA-L version of record 6(2):3184-3191 not read
全文取得途徑
arXiv 預印本
本頁內容

BALM formulates LiDAR BA as point-to-edge/plane distance minimization in which feature parameters are eliminated in closed form, leaving a pose-only optimization; adaptive voxelization supplies correspondences, and the BA runs as a sliding-window back-end of LOAM.

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
原文測試平台handheld、wheeled UGV
狀態估計sliding-window local BA over scan poses with closed-form elimination of edge/plane parameters and analytical first/second-order derivatives (second-order approximation, LM-type iterations)
資料關聯edge and plane feature points (LOAM-style extraction) grouped by adaptive voxelization from a default voxel size down to a minimal size (sizes given only as examples: 1 m and 0.125 m) using an eigenvalue test on the point covariance; separate voxel maps for edges and planes stored as hash-indexed octrees; voxels with repeated eigenvalues are skipped and dense voxels may average points per scan; scan-to-map odometry matches each point to the nearest voxel plane or edge instead of five nearest points (Sec. IV Remarks 1-4, Sec. V, Sec. VI-D)
時間表示discrete poses
去畸變not compensated in the scan-to-map odometry front-end (authors state this in Sec. VII)
迴圈閉合none
全域最佳化none (local sliding-window BA as LOAM back-end map refinement)
地圖表示adaptive voxel map of edge and plane features (hash table of octrees); points outside the window summarized by recursive covariance statistics
先驗資訊none
可輸出幾何registered LiDAR feature point-cloud map and refined scan poses; no other exportable product reported
計算需求three parallel threads (feature extraction, 10 Hz scan-to-map odometry, map refinement); local BA over the 20 most recent scans triggered every 5 scans (2 Hz map output); laptop CPU i7-10750H with 16 GiB memory; local BA plus voxel-map update completes within 100 ms in most cases, so it can nearly keep pace with 10 Hz odometry (Sec. V, VI, VI-D, Fig. 9b)

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
LiDARLivox Horizon方法輸入未標示25 deg x 82 deg FoV; handheld(Liu & Zhang, 2021, Sec. VI-A)
LiDARLivox Mid-40歸入：Livox MID40方法輸入未標示small 40 deg FoV; mounted on a UGV(Liu & Zhang, 2021, Sec. VI-B)
LiDARVelodyne VLP-16資料集感測器LeGO-LOAM VLP-16 sample datasample data offered by LeGO-LOAM on GitHub(Liu & Zhang, 2021, Sec. VI-C)
載具平台UGV (model not reported)方法輸入未標示carries the Livox Mid-40 in the indoor corridor test(Liu & Zhang, 2021, Sec. VI-B)
運算硬體i7-10750H執行運算平台未標示laptop computer with CPU i7-10750H and 16 GiB memory; all experiments(Liu & Zhang, 2021, Sec. VI)

作者報告的優勢與限制

優勢

  • Eliminating feature parameters reduces the optimization dimension so that large numbers of dense plane/edge features can be used (Sec. I contributions)
  • Local BA lowered LOAM drift in handheld Livox Horizon, UGV Livox Mid-40 and VLP-16 tests (Sec. VI-A to VI-C, Tables I-II)
  • Voxel-based correspondence search reduced scan-to-map time relative to kd-tree nearest-point search in the authors' comparison (Sec. VI-D, Fig. 9a)

限制

  • Adaptive voxelization requires good initial pose alignment (Sec. VII)
  • Odometry front-end does not compensate motion distortion or use a motion model (Sec. VII)
  • Temporal sliding window keeps redundant, highly overlapping scans; keyframes left to future work (Sec. VII)
  • With the 40 degree FoV Livox Mid-40 the scan-to-map front-end still degenerates at corridor corners (zigzag trajectory); the local BA only mitigates the resulting map inconsistency (Sec. VI-B, Fig. 7)
  • (inference) BALM itself provides only local refinement without loop closure, so large-loop drift is outside its scope

營建工程相關證據

未見營建工地驗證；作者測試為校園戶外手持、建築室內樓梯手持與 UGV 走廊轉角（Sec. VI、Fig. 2、Fig. 7），以回到起點的漂移評估，無獨立參考量測。其點到平面 BA 公式被 BALM2、HBA、LEMON-Mapping 沿用或作比較（見各紀錄），此為對工程點雲一致化的主要意義（推論）。

原文驗證環境：公開基準、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 12 個比較組，合計 40 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。

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)
EF0.047 m(Liu et al., 2023a, Table II)
BALM本方法0.042 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)

Yan et al., 2026a · Table 2 本方法 4 筆

表格設定（擷取紀錄原文）：ATE (RMSE, m) on WHU-Helmet with dataset ground-truth trajectory; LiDAR baselines use variants adapted to the Livox configuration; 'Failed' = failure to run (Yan et al., 2026a, Table 2)

ATE (m)，WHU-Helmet (WHUH) · Tunnel

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。

  • 失敗

這些是 Yan et al., 2026a 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：WHU-Helmet Tunnel sequence, 790.32 m, 1403 s

資料來源作者報告值(Yan et al., 2026a, Table 2)

數值與出處
方法（原文寫法）報告值出處
ORB-SLAM35.92 m(Yan et al., 2026a, Table 2)
VINS-Mono無數值失敗註記（擷取紀錄）：failed(Yan et al., 2026a, Table 2)
LOAM無數值失敗註記（擷取紀錄）：failed(Yan et al., 2026a, Table 2)
BALM本方法4.53 m(Yan et al., 2026a, Table 2)
LIO-Mapping5.95 m(Yan et al., 2026a, Table 2)
Fast-LIO24.21 m(Yan et al., 2026a, Table 2)
R3live++5.3 m(Yan et al., 2026a, Table 2)
COIN-LIO4.05 m(Yan et al., 2026a, Table 2)
VINS-FEN4.39 m(Yan et al., 2026a, Table 2)
This work原文提出4.04 m(Yan et al., 2026a, Table 2)

Zhou et al., 2021 · Table I 本方法 4 筆

指標keyframe ATE (m), median of 5 runs

表格設定（擷取紀錄原文）：Keyframe ATE (m), median of 5 runs, on four indoor NavVis M6 datasets (VLP-16 data only) with large rotations; ground truth = offline fused NavVis trajectory; '-' = failed to complete (Zhou et al., 2021, Table I)

keyframe ATE (m), median of 5 runs，own indoor datasets A-D (NavVis M6) · A (261.9 m)

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。

  • 失敗

這些是 Zhou 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。

統計量：中位數（median）；對齊方式：原文未報告；單位：m；場景：building interior, mobile mapping device

資料來源作者報告值(Zhou et al., 2021, Table I)

數值與出處
方法（原文寫法）報告值出處
LeGO-LOAM [8]無數值失敗註記（擷取紀錄）：failed (did not complete the sequence)(Zhou et al., 2021, Table I)
BALM [29]本方法0.34 m(Zhou et al., 2021, Table I)
pi-LSAM [22]0.082 m(Zhou et al., 2021, Table I)
Ours - LPA - GPA原文提出0.29 m(Zhou et al., 2021, Table I)
Ours - GPA原文提出0.18 m(Zhou et al., 2021, Table I)
Ours原文提出0.039 m(Zhou et al., 2021, Table I)

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硬體：desktop Intel i7-10750H, 16 GB RAM1415.18(Liu et al., 2023a, Table IV)
BALM本方法硬體：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)

其他比較組

列出其餘 8 個比較組

來源

程式碼：https://github.com/hku-mars/BALM（授權：GPL-2.0 (LICENSE file in repository; repository now hosts BALM 2.0)）。有公開程式碼不等於已被重現，也不代表目前版本與論文版本相同。

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