SLAM 點雲圖鑑Point clouds for construction
M-01 · 2020

GNC (GNC-GM / GNC-TLS)

作者把穩健估計與離群值過程（outlier process）之間的 Black-Rangarajan 對偶，結合漸進非凸化（graduated non-convexity, GNC），讓任何在無離群值情況下已有非最小解算器（non-minimal solver）的問題，都能延伸為不需初始猜測的穩健求解。每一輪外層迭代固定控制參數 µ，先以非最小解算器做一次加權最小平方的變數更新，再做一次封閉解的權重更新，並逐步把代價函數由凸的替代函數推回 Geman-McClure 或截斷最小平方（TLS）。作者另以平方和（SOS）鬆弛提出形狀對齊的可驗證最佳非最小解算器。實驗涵蓋點雲與網格配準、位姿圖最佳化（PGO）與形狀對齊，離群值皆為人工注入；作者報告可承受約 70 至 80% 離群值，但也明言無法保證全域最佳。

估計框架或函式庫近十年已讀全文同儕審查已出版估計後端與最佳化

閱讀版本
arXiv 1909.08605v4 (2020-06-11), post-acceptance author version whose first page states acceptance in IEEE RA-L; MD5 24c32310576d8d94c8a98ed4f76a91e4 and size 3,839,760 bytes, identical to the bitstream deposited at MIT DSpace hdl 1721.1/136232 (dc.eprint.version 'Author's final manuscript'). The IEEE Xplore version of record was not opened.
全文取得途徑
arXiv 預印本
本頁內容

GNC plus Black-Rangarajan duality turns any available non-minimal solver into an initial-guess-free robust estimator; on point-cloud and mesh registration, pose-graph optimization and shape alignment with synthetic outliers it tolerates about 70 to 80% outliers without global optimality guarantees, and the paper adds a certifiably optimal SOS solver for shape alignment.

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simulation、public benchmark data (Stanford Bunny, PASCAL+ car-2 mesh, INTEL and CSAIL pose graphs, FG3DCar images)
狀態估計graduated non-convexity combined with Black-Rangarajan duality: each outer iteration fixes the control parameter mu and performs a single variable update (weighted least squares solved globally by a non-minimal solver: Horn's closed form for point-cloud registration, the certifiably optimal relaxation of Briales and Gonzalez-Jimenez for point-to-point, point-to-line and point-to-plane mesh registration, SE-Sync for PGO, the authors' SOS relaxation for shape alignment) and a single closed-form weight update, with all weights initialised to 1. GNC-GM initialises mu = 2 r_max^2 / c^2 (r_max^2 = largest residual after the first variable update), divides mu by 1.4 per outer iteration and stops when mu falls below 1; GNC-TLS initialises mu = c^2 / (2 r_max^2 - c^2), multiplies mu by 1.4 and stops when the sum of weighted residuals converges; c is set to the maximum error expected for inliers
資料關聯given putative correspondences (3D point-to-point for point-cloud registration; point-to-point, point-to-line and point-to-plane for mesh registration; 2D-3D keypoint correspondences for shape alignment) or relative-pose measurements (PGO), with outliers allowed; correspondence search and loop detection are outside the method, and all outliers in the experiments are synthetically injected into the given measurement sets
時間表示不適用
去畸變不適用
迴圈閉合in PGO tests, odometry is kept and loop closures are spoiled with random outliers (random pose pairs with random measurements); rejection works through the GNC weight updates of Sec. III-IV (weights driven toward 0 for inconsistent measurements), while Sec. V-B itself reports only trajectory error and CPU time, not per-edge weights
全域最佳化robust PGO with GNC-GM or GNC-TLS on top of SE-Sync, without an initial guess (Sec. V-B)
地圖表示不適用
先驗資訊none (no initial guess required)
可輸出幾何estimated rigid transform (point-cloud and mesh registration), pose-graph trajectory (PGO), or object scale, rotation and 2D translation under weak perspective projection (shape alignment); no map geometry
計算需求runtime hardware is not reported for registration or PGO. At 80% outliers in Bunny point-cloud registration, average runtime 218 ms (RANSAC) versus 22 ms (GNC-GM) and 23 ms (GNC-TLS) (Sec. V-A); CSAIL PGO CPU times are only plotted in Fig. 4(c), with all compared techniques implemented in C++ (Sec. V-B); the SOS shape-alignment SDP is solved with GloptiPoly 3 in Matlab in about 80 ms on an unspecified desktop computer (Sec. V-C)

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desktop computer執行運算平台未標示原文未報告 (no model, CPU or memory given)(Yang et al., 2020b, Sec. V-C (SOS SDP solved with GloptiPoly 3 in Matlab in about 80 ms))

作者報告的優勢與限制

優勢

  • Shape alignment on all 600 FG3DCar images: GNC-GM, GNC-TLS and ADAPT are robust against 70% outliers while RANSAC breaks at 60% and Zhou's convex relaxation degrades quickly
  • the proposed SOS relaxation was empirically always exact (Sec. V-C)

限制

  • (inference) In all three applications the outliers are generated synthetically (random points, incorrect correspondences, random loop closures, random 2D-3D matches) on public benchmark data
  • outliers produced by real front ends were not evaluated

營建工程相關證據

原文未報告（僅用標準位姿圖與電腦視覺基準）。其 GNC 已被 TEASER++ 與 KISS-Matcher 等配準方法採用（見 C02 紀錄 Yang et al., 2021、Lim et al., 2025），與工地點雲的全域配準及迴圈驗證間接相關（推論）。Sec. V-A 以點對點、點對線與點對面對應把取樣點雲配準到網格模型，形式上接近掃描點雲對 BIM 模型的配準（推論，論文未提及營建）。

原文驗證環境：模擬、公開基準

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 10 個比較組，合計 36 筆紀錄。以下列出本方法紀錄最多的 4 組，其餘 6 組列在最後，並連到性能比較頁。

Tian et al., 2022 · Table I 本方法 6 筆

指標Absolute trajectory error (ATE) [m]

表格設定（擷取紀錄原文）：ATE in meters against ground truth for distributed trajectory estimators on Kimera-VIO odometry plus putative loops; fixed isotropic covariance (0.01 rad, 0.1 m); probability threshold 50%; statistic of the ATE not stated (Tian et al., 2022, Table I)

Absolute trajectory error (ATE) [m]，DCIST simulation · Medfield

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 Tian et al., 2022 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：原文未報告；單位：m；場景：photo-realistic simulation, 3 robots

資料來源作者報告值(Tian et al., 2022, Table I)

數值與出處
方法（原文寫法）報告值出處
L2 (least squares, RBCD)64.2 m(Tian et al., 2022, Table I)
PCM12.5 m(Tian et al., 2022, Table I)
D-GNC (NI, naive initialization)57.4 m(Tian et al., 2022, Table I)
PCM + D-GNC4.64 m(Tian et al., 2022, Table I)
D-GNC原文提出3.92 m(Tian et al., 2022, Table I)
D-GNC (ES, early stopping)原文提出4.32 m(Tian et al., 2022, Table I)
Centralized GNC本方法3.88 m(Tian et al., 2022, Table I)

Tian et al., 2022 · Table II 本方法 6 筆

指標Runtime [sec] of robust PGO

表格設定（擷取紀錄原文）：Communication usage (total of place recognition, geometric verification and distributed PGO) versus centralized baselines transmitting images or keypoints, and runtime of the robust PGO solver; hardware not reported (Tian et al., 2022, Table II)

Runtime [sec] of robust PGO，DCIST simulation · Medfield

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 Tian et al., 2022 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：s；場景：photo-realistic simulation, 3 robots

資料來源作者報告值(Tian et al., 2022, Table II)

數值與出處
方法（原文寫法）報告值出處
D-GNC distributed原文提出29.2 s(Tian et al., 2022, Table II)
D-GNC distributed (ES)原文提出5.9 s(Tian et al., 2022, Table II)
Centralized GNC本方法4.4 s(Tian et al., 2022, Table II)

Tian et al., 2022 · Table V 本方法 6 筆

指標end-to-end error [m]

表格設定（擷取紀錄原文）：Outdoor datasets without ground truth: each robot starts and ends at the same place; end-to-end position error; Kimera-Multi uses D-GNC (Stata with full variable updates), centralized uses GNC in GTSAM (Tian et al., 2022, Table V)

end-to-end error [m]，Medfield outdoor dataset (authors' own) · Robot 0 (600 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。

這些是 Tian et al., 2022 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：m；場景：outdoor campus with similar-looking scenes, Clearpath Jackal UGV

資料來源作者報告值(Tian et al., 2022, Table V)

數值與出處
方法（原文寫法）報告值出處
Kimera-VIO18.74 m(Tian et al., 2022, Table V)
Kimera-Multi原文提出0.01 m(Tian et al., 2022, Table V)
Centralized本方法0.01 m(Tian et al., 2022, Table V)

Wang et al., 2026 · Table VIII 本方法 4 筆

指標F1

表格設定（擷取紀錄原文）：Loop closure outlier rejection on RING++ candidates; correctness judged against the framework's optimized trajectory (pose distance below 5 m); PCM and GNC parameter sweeps, Best-F1 setting reported; only F1 extracted (Wang et al., 2026, Table VIII)

F1，S3E · Campus 1

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 Wang et al., 2026 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：%；場景：multi-robot campus or tunnel

資料來源作者報告值(Wang et al., 2026, Table VIII)

數值與出處
方法（原文寫法）報告值出處
Ours (loop processing module)原文提出92.2%(Wang et al., 2026, Table VIII)
PCM Best-F186.5%(Wang et al., 2026, Table VIII)
GNC Best-F1本方法85.7%(Wang et al., 2026, Table VIII)

其他比較組

列出其餘 6 個比較組

來源

  • Yang et al., 2020b

    Heng Yang, Pasquale Antonante, Vasileios Tzoumas, Luca Carlone（2020）Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier RejectionIEEE Robotics and Automation Letters, 5(2):1127-1134

    DOI 10.1109/lra.2020.2965893arXiv 1909.08605程式碼

    同儕審查已出版已讀全文近十年查證後修正

程式碼：https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/GncOptimizer.h（授權：BSD (simplified) for GTSAM per repository LICENSE; applies to the later library implementation）。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。

回到方法圖鑑

SLAM 點雲圖鑑

本站為綜述論文《SLAM-Based Point Clouds for Construction: A Review》研究過程的互動說明文件。互動圖為教學模擬，不代表任何特定系統的實測表現；方法描述、數值與結論以所引原始文獻為準。

內容基準日 2026-09-25 · 研究與網站製作使用 AI 輔助工具，見 證據標記與方法

選擇開啟Esc關閉