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

3D ICP covariance (unscented)

作者主張 ICP 結果的不確定性取決於初始值（通常來自里程計）的不確定性，因此以無跡轉換（unscented transform）額外執行 12 次 ICP 配準來傳遞初始化不確定性，並輸出含初始值與 ICP 結果相關項的聯合共變異數；感測器白雜訊與所有點共有的校正偏差（各假設約 5 cm）則以封閉式公式另計。在 Challenging data sets 八個序列、1020 組配準上，所提方法的 NNE 為平移 4.2、旋轉 34，而 Censi 公式與 65 次 Monte Carlo 為 10^2 至 10^3 量級；在軌跡一致性上平均也優於未考慮相關項的組合，但仍略為樂觀。

配準元件近十年已讀全文同儕審查已出版誤差來源：校正、同步、畸變與退化

閱讀版本
arXiv 1909.05722v2 (27 Jan 2020, 8 pp., accepted RA-L preprint) read in full; IEEE RA-L 5(2):744-751 version of record (via NTU) compared: Tables I and II checked as rendered images and match v2
全文取得途徑
arXiv 預印本
本頁內容

Treats ICP covariance as conditional on initialization uncertainty (propagated with an unscented transform) and adds a term for sensor noise and calibration bias.

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 laser scans from a Hokuyo sensor (Challenging data sets for point cloud registration, Pomerleau et al. 2012; model number not given in the paper)
原文測試平台public dataset only: Challenging data sets for point cloud registration (8 sequences of 31 to 45 scans, 268 scans, 1020 registrations; structured to unstructured, indoor to outdoor); carrying platform not described in the paper
狀態估計unscented transform over initialization uncertainty plus closed-form sensor-noise term; point-to-plane ICP
資料關聯ICP configured as in Pomerleau et al. (2013): 95% random subsampling, kd-tree data association, point-to-plane error metric, 70% closest associations kept for outlier rejection
時間表示不適用
去畸變原文未報告
迴圈閉合不適用
全域最佳化none
地圖表示不適用
先驗資訊initialization covariance Q_ini assumed known (main tests: 0.1 m and 10 deg standard deviation, 'easy'; robustness tests with 0.5 m and 20 deg, and 1 m and 50 deg); sensor white noise and common bias each with 5 cm standard deviation
可輸出幾何registration covariance
計算需求No processor stated. Sec. IV-C reports that the 12 extra ICP registrations of the unscented transform take 6 s when run in parallel and the remaining steps less than 0.1 s; the 65-run Monte Carlo baseline is more than five times as demanding. Sec. VI calls the method real time; real-time use depends on implementation

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
LiDARHokuyo sensor (model number not given in the paper)資料集感測器Challenging data sets for point cloud registration algorithms (Pomerleau et al., IJRR 2012)white noise and bias standard deviation taken as 5 cm, the mean value reported for this sensor by Pomerleau et al. (CARPI 2012)(Brossard et al., 2020, Sec. IV-B)

作者報告的優勢與限制

優勢

  • Averaged over 8 sequences, NNE of 4.2 (translation) and 34 (rotation) versus about 10^3 for Censi's formula and 10^3 and 10^2 for 65-sample Monte Carlo; robust NNE 0.8 and 3.8 (Table 1)
  • Best average trajectory consistency (Mahalanobis distance) among CELLO-3D, ini.+ICP and the proposed covariance, with a clear gain on Apartment (2.3 and 9.8 vs 3.5 and 15) (Table 2)
  • Deterministic, needs only 12 extra ICP runs, and flags wrong ICP convergence through very large covariances (Sec. III-B, Sec. V-B)

限制

  • The closed-form part is not valid for point-to-point ICP (Sec. VI)
  • Relies on a Gaussian error assumption and cannot describe non-Gaussian ICP error distributions (Sec. V-B, V-C)
  • Requires the initialization covariance as input; with local minima the output inherits an optimistic or pessimistic Q_ini (Sec. V-B, V-C, Table 3)
  • Trajectory covariances remain slightly optimistic (Table 2 caption)

營建工程相關證據

原文未報告

原文驗證環境：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 3 個比較組，合計 26 筆紀錄。

Brossard et al., 2020 · Table 2 本方法 16 筆

表格設定（擷取紀錄原文）：Trajectory consistency: Mahalanobis distance of compounded ICP trajectories to ground truth, averaged over 40 initial trajectories per sequence; target 1, below 1 pessimistic; CELLO-3D reproduced from Landry et al. with a slightly different ICP setting (Brossard et al., 2020, Table 2)

Mah. dist. trans.，Challenging data sets for point cloud registration (Pomerleau et al. 2012) · Apartment

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 Brossard et al., 2020 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：平均值（mean）；對齊方式：未對齊；單位：無單位；場景：per-sequence type not stated in the paper

資料來源作者報告值(Brossard et al., 2020, Table 2)

數值與出處
方法（原文寫法）報告值出處
CELLO-3D0.2(Brossard et al., 2020, Table 2)
ini.+ICP (fusion without cross-covariance)3.5(Brossard et al., 2020, Table 2)
proposed (full ML covariance, Eq. 15)本方法原文提出2.3(Brossard et al., 2020, Table 2)

Brossard et al., 2020 · Table 1 本方法 8 筆

資料集與序列Challenging data sets for point cloud registration (Pomerleau et al. 2012) · average of 8 sequences

表格設定（擷取紀錄原文）：ICP covariance consistency averaged over 8 sequences, 1020 registrations x 1000 initializations; Q_ini 0.1 m and 10 deg; noise and bias SD 5 cm; NNE target 1; starred = robust statistics after removing extreme quantiles; baselines printed as orders of magnitude (Brossard et al., 2020, Table 1)

NNE trans.，Challenging data sets for point cloud registration (Pomerleau et al. 2012) · average of 8 sequences

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 Brossard et al., 2020 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：平均值（mean）；對齊方式：未對齊；單位：無單位；場景：structured to unstructured, indoor to outdoor

資料來源作者報告值(Brossard et al., 2020, Table 1)

數值與出處
方法（原文寫法）報告值出處
Q_censi (closed-form, Censi 2007)1000有附註註記（擷取紀錄）：printed only as order of magnitude 10^3(Brossard et al., 2020, Table 1)
Q_monte carlo (65 Monte Carlo ICP samples)1000有附註註記（擷取紀錄）：printed only as order of magnitude 10^3(Brossard et al., 2020, Table 1)
proposed本方法原文提出4.2(Brossard et al., 2020, Table 1)

Brossard et al., 2020 · Text Sec. IV-C 本方法 2 筆

資料集與序列Challenging data sets for point cloud registration (Pomerleau et al. 2012) · per registration pair

表格設定（擷取紀錄原文）：Execution time of the covariance computation per registration pair (Algorithm 1) (Brossard et al., 2020, Text Sec. IV-C)

time for the 12 unscented-transform ICP registrations, computed in parallel，Challenging data sets for point cloud registration (Pomerleau et al. 2012) · per registration pair

這張表在此指標與資料序列只列出本方法一筆，沒有可並列的其他方法，因此不畫圖，數值與出處見下表。這是 Brossard et al., 2020 在此表設定下報告的數值（author-reported results），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：s

數值與出處
方法（原文寫法）報告值出處
proposed本方法原文提出6 s(Brossard et al., 2020, Sec. IV-C)

來源

  • Brossard et al., 2020

    Martin Brossard, Silvere Bonnabel, Axel Barrau（2020）A New Approach to 3D ICP Covariance EstimationIEEE Robotics and Automation Letters, 5(2), pp. 744-751

    DOI 10.1109/lra.2020.2965391arXiv 1909.05722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/CAOR-MINES-ParisTech/3d-icp-cov（授權：MIT）。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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