SLAM 點雲圖鑑Point clouds for construction
M-01 · 2016

FGR

FGR 先以 FPFH 特徵的雙向最近鄰建立候選對應，再以互為最近鄰檢驗與三元組邊長比例檢驗（τ = 0.9）提高內點比例；之後對這組固定不變的對應直接最佳化單一穩健目標，同時對齊表面並使錯誤對應失效，內迴圈不更新對應，也不做最近點查詢。目標採縮放 Geman-McClure 穩健估計函數，藉 Black-Rangarajan 對偶交替更新線過程變數與位姿，並以逐步非凸化將 μ 從最大表面直徑的平方每四次迭代減半，直到真對應距離門檻的平方。作者報告在合成資料、UWA 與 Choi 等人的場景基準上，精度可比或優於既有全域配準流程；在單執行緒 Intel Core i7-5960X 上，合成距離影像每對平均 0.22 s，比最快的既有全域方法 CZK 快約 50 倍；此方法並可延伸為多片點雲聯合配準。

配準元件經典已讀全文同儕審查已出版點雲配準元件

閱讀版本
Version of record: ECCV 2016 Part II, LNCS 9906, pp. 766-782, © Springer International Publishing AG 2016 (17-page chapter PDF from Springer Link); the author PDF on vladlen.info (16 pages) was also read and its numbers are identical to the version of record.
全文取得途徑
國立臺灣大學機構訂閱
本頁內容

FGR optimizes a robust Geman-McClure objective over FPFH correspondences with graduated non-convexity, aligning partially overlapping surfaces without initialization.

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synthetic range images (AIM@SHAPE Bimba, Dancing Children, Chinese Dragon; Berkeley Angel; Stanford Bunny) with added 3D Gaussian noise、UWA object and scene benchmark data (acquisition sensor not stated in the paper)、Choi et al. scene fragments whose high-frequency noise and low-frequency distortion simulate consumer depth camera scans; Augmented ICL-NUIM sequences (living room and office) used for multi-way registration
原文測試平台offline evaluation on synthetic data and public benchmarks; no physical platform
狀態估計scaled Geman-McClure robust objective optimized via Black-Rangarajan line-process duality with alternating updates and graduated non-convexity (Sec. 3.1-3.2); pose step is a Gauss-Newton solve on a locally linearized 6-vector mapped back to SE(3); mu starts at D^2 (largest surface diameter) and is halved every four iterations down to delta^2; alignment is validated once after convergence (Sec. 3.2, Algorithm 1)
資料關聯FPFH nearest neighbours in feature space in both directions, filtered by a reciprocity test and a tuple test on three random pairs (edge-length ratios within tau = 0.9 and 1/tau); correspondences stay fixed during optimization (Sec. 3.3, Algorithm 1)
時間表示不適用
去畸變不適用
迴圈閉合none
全域最佳化multi-way joint registration: one objective over all fragment poses with robust terms on pairwise correspondences and L2 odometry terms (lambda = 2 in experiments), solved by alternating line-process and 6|T|-variable Gauss-Newton updates without intermediate pairwise alignments (Sec. 4, Sec. 5.2)
地圖表示surfaces / point clouds
先驗資訊none for pairwise registration; the multi-way variant incorporates initial odometry transformations between consecutive fragments as L2 backbone terms
可輸出幾何rigid transformation(s)
計算需求Pairwise experiments (Sec. 5.1), single thread on an Intel Core i7-5960X at 3.00 GHz: 0.22 s average per synthetic pair (Table 2), 0.5 s per UWA test (Table 4), 0.2 s per Choi benchmark pair (Table 5); most time is spent on FPFH computation and correspondence building, optimization stays below 30 ms for more than 20,000 points, and validation takes about 3.3% of runtime (Sec. 5.1). Multi-way registration: 82 s average per Augmented ICL-NUIM sequence (Table 6); Sec. 5.2 does not restate the hardware

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Intel Core i7-5960X執行運算平台未標示3.00 GHz; all execution times measured with a single thread(Zhou et al., 2016, Sec. 5.1)

作者報告的優勢與限制

優勢

  • matches or exceeds accuracy of global pipelines while being at least an order of magnitude faster (abstract)
  • no initialization required (abstract)
  • Most robust to noise on synthetic pairs: average RMSE 0.008 and maximal 0.017 at sigma 0.005, against the best prior 0.017 and 0.095 (Table 1)
  • About 50 times faster than the fastest prior global method CZK (0.22 s vs 11.1 s, Table 2) and faster than PCL ICP and Sparse ICP (Table 3)
  • Highest precision (23.2%) on the Choi et al. scene benchmark (Table 5); 0.05-recall 84% on UWA (Sec. 5.1)
  • Multi-way variant matches Choi et al. accuracy (0.05 m average) while about 60 times faster (Table 6)

限制

  • depends on FPFH correspondence quality (Sec. 3.3; dependency noted, not an author-stated limitation)
  • Lower recall than CZK on the Choi et al. scene benchmark (51.1% vs 59.2%, Table 5)
  • Multi-way accuracy equals but does not exceed Choi et al. (0.05 m average; 0.05 vs 0.04 m on Living room 1 and Office 2, Table 6)
  • No author-stated limitations; evaluation limited to synthetic and benchmark data without a physical sensor platform (Sec. 5, Sec. 6)

營建工程相關證據

原文未報告

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 11 個比較組，合計 53 筆紀錄。以下列出本方法紀錄最多的 4 組，其餘 7 組列在最後，並連到性能比較頁。

Zhou et al., 2016 · Table 6 本方法 10 筆

表格設定（擷取紀錄原文）：Multi-way registration of all fragments (47 to 57 per sequence), lambda = 2; mean distance of integrated surface to ground-truth model and total time (Zhou et al., 2016, Table 6)

Mean error (meters) of reconstructed surface to ground-truth model，Augmented ICL-NUIM · Living room 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 Zhou et al., 2016 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：m；場景：indoor scenes (living room and office sequences)

資料來源作者報告值(Zhou et al., 2016, Table 6)

數值與出處
方法（原文寫法）報告值出處
Choi et al. [7]0.04 m(Zhou et al., 2016, Table 6)
Ours (FGR multi-way)本方法原文提出0.05 m(Zhou et al., 2016, Table 6)

Lim et al., 2024 · Table 6 本方法 6 筆

表格設定（擷取紀錄原文）：KITTI Seq. 00 odometry test with frame interval Delta (source i+Delta, target i); trel [%] and rrel [deg/100m] by RPG evaluation tools; c2f = global registration then local registration (G-ICP); deep-learning rows copied by the authors from the original papers; † = Seq. 00 used for training (Lim et al., 2024, Table 6)

trel，KITTI · Seq. 00, Delta = 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 Lim et al., 2024 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：%；場景：vehicle, urban driving (Velodyne HDL-64E)

資料來源作者報告值(Lim et al., 2024, Table 6)

數值與出處
方法（原文寫法）報告值出處
ICP6.88%(Lim et al., 2024, Table 6)
G-ICP1.26%(Lim et al., 2024, Table 6)
VGICP1.03%(Lim et al., 2024, Table 6)
FGR本方法2.73%(Lim et al., 2024, Table 6)
TEASER++2.11%(Lim et al., 2024, Table 6)
Quatro (Ours)原文提出1.45%(Lim et al., 2024, Table 6)
Quatro++ (Ours)原文提出1.9%(Lim et al., 2024, Table 6)
LO-Net1.47%(Lim et al., 2024, Table 6)
LO-Net+M0.78%(Lim et al., 2024, Table 6)
DMLO†0.83%(Lim et al., 2024, Table 6)
DMLO+M†0.73%(Lim et al., 2024, Table 6)
A-LOAM + StickyPillars†0.65%(Lim et al., 2024, Table 6)
SuMa0.68%(Lim et al., 2024, Table 6)
A-LOAM0.7%(Lim et al., 2024, Table 6)
Quatro-c2f (Ours)原文提出0.65%(Lim et al., 2024, Table 6)
Quatro++-c2f (Ours)原文提出0.68%(Lim et al., 2024, Table 6)

Zhang et al., 2024b · Table 1 本方法 6 筆

資料集與序列ISPRS benchmark on indoor modelling · Models 01-05 (250 samples)

表格設定（擷取紀錄原文）：Coarse registration on 250 samples (50 per model) with random rigid perturbations (roll and pitch within 30 deg, yaw within 180 deg, translation within 10 m); only successful results with RE < 45 deg and TE < 10 m are included; A50, A75 and A95 quantiles of rotation and translation error against the benchmark alignment (Zhang et al., 2024b, Table 1)

RE_50, rotation error 50th percentile，ISPRS benchmark on indoor modelling · Models 01-05 (250 samples)

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 Zhang et al., 2024b 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：未對齊；單位：deg；場景：building interiors from the ISPRS indoor modelling benchmark (Models 01-05)

資料來源作者報告值(Zhang et al., 2024b, Table 1)

數值與出處
方法（原文寫法）報告值出處
GMMTree (initialised with FPFH-RANSAC)4.466 deg(Zhang et al., 2024b, Table 1)
FilterReg (initialised with FPFH-RANSAC)3.59 deg(Zhang et al., 2024b, Table 1)
GO-ICP4.178 deg(Zhang et al., 2024b, Table 1)
Super4PCS2.208 deg(Zhang et al., 2024b, Table 1)
FGR本方法27.139 deg(Zhang et al., 2024b, Table 1)
RANSAC (FPFH features)5.477 deg(Zhang et al., 2024b, Table 1)
RMMG1.673 deg(Zhang et al., 2024b, Table 1)
PLADE0.424 deg(Zhang et al., 2024b, Table 1)
DCP34.865 deg(Zhang et al., 2024b, Table 1)
PointNetLK11.741 deg(Zhang et al., 2024b, Table 1)
Ours (primitive-level coarse registration)原文提出0.272 deg(Zhang et al., 2024b, Table 1)

Zhou et al., 2016 · Table 1 本方法 6 筆

表格設定（擷取紀錄原文）：25 synthetic range-image pairs per noise level; RMSE of ground-truth correspondence distances, unit surface diameter; GoICP variants on 1,000 points (Zhou et al., 2016, Table 1)

Average RMSE，Synthetic range images (AIM@SHAPE, Berkeley Angel, Stanford Bunny) · sigma 0

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 Zhou et al., 2016 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：surface diameter；場景：synthetic

資料來源作者報告值(Zhou et al., 2016, Table 1)

數值與出處
方法（原文寫法）報告值出處
GoICP [42]0.029(Zhou et al., 2016, Table 1)
GoICP-Trimming [42]0.035(Zhou et al., 2016, Table 1)
Super 4PCS [26]0.012(Zhou et al., 2016, Table 1)
OpenCV [8] (implementation of Drost et al.)0.009(Zhou et al., 2016, Table 1)
PCL [19,34] (PCL implementation of Rusu et al.)0.003(Zhou et al., 2016, Table 1)
CZK [7] (Choi et al. variant of Rusu's algorithm)0.003(Zhou et al., 2016, Table 1)
Our approach (FGR)本方法原文提出0.003(Zhou et al., 2016, Table 1)

其他比較組

列出其餘 7 個比較組

來源

  • Zhou et al., 2016

    Qian-Yi Zhou, Jaesik Park, Vladlen Koltun（2016）Fast Global RegistrationComputer Vision – ECCV 2016 (Lecture Notes in Computer Science), pp. 766-782

    DOI 10.1007/978-3-319-46475-6_47程式碼

    同儕審查已出版已讀全文經典查證後修正

程式碼：https://github.com/isl-org/FastGlobalRegistration（授權：MIT (LICENSE file checked)）。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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