[{"data":1,"prerenderedAt":572},["ShallowReactive",2],{"method-eigenfactors2019":3},{"method":4,"reference":55,"equipment":73,"figures":74,"results":75},{"id":5,"label":6,"shortName":7,"title":8,"year":9,"era":10,"cluster":11,"scope":12,"keyIdeaZh":13,"keyIdeaEn":14,"fulltextStatus":15,"publicationStatus":16,"recommendation":17,"constructionRelevance":18,"validationEnvironment":19,"strengths":21,"limitations":25,"sensors":32,"platform":34,"estimator":35,"association":36,"timeModel":37,"deskew":38,"loopClosure":18,"globalOptimization":39,"mapRepresentation":40,"prior":41,"outputGeometry":42,"compute":43,"codeUrl":44,"codeLicense":45,"relatedVersions":46},"eigenfactors2019","Ferrer, 2019","Eigen-Factors (EF)","Eigen-Factors: Plane Estimation for Multi-Frame and Time-Continuous Point Cloud Alignment",2019,"recent","C06","registration_component","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。","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.","full_text_reviewed","peer_reviewed_published","background","not_reported",[20],"simulation",[22,23,24],"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)",[26,27,28,29,30,31],"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",[33],"generic 3D point clouds (lidar and RGB-D motivated in Sec. I); evaluated only on synthetic planar point clouds",[20],"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\u002F(N_all H), beta = 0.7), compared with plain gradient descent (Sec. IV-C, IV-D, V)","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)","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)","not_reported (synthetic point clouds; no in-scan motion compensation described)","fixed time-window multi-frame alignment of all poses that observe common planes; no pose graph, loop closure or global map (Sec. IV, VI)","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)","coarse initial trajectory from pairwise alignment (origin to subsequent poses); the author states EFs are sensitive to initialization (Sec. V)","optimized trajectory (time-continuous interpolation) with implicitly estimated planes; no exported map product (Sec. IV-B, V)","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",null,"not_verified",[47,51],{"relation":48,"title":49,"doi_or_url":50},"journal_extension","Eigen-factors a bilevel optimization for plane SLAM of 3D point clouds (Autonomous Robots 49(1), 2025; Ferrer, Iarosh, Kornilova)","10.1007\u002Fs10514-025-10189-5",{"relation":52,"title":53,"doi_or_url":54},"preprint","Research Square preprint of the journal extension","10.21203\u002Frs.3.rs-4601229\u002Fv1",{"id":5,"kind":56,"shortName":7,"title":8,"authors":57,"year":9,"venue":59,"venueType":60,"publisher":61,"volumeIssuePages":62,"doi":63,"arxivId":44,"url":64,"firstPublicDate":65,"publicationStatus":16,"metadataStatus":66,"fulltextStatus":15,"era":10,"classicReason":67,"codeUrl":44,"cluster":11,"topics":68,"mdpi":69,"verification":70,"label":6,"fulltextRoute":71,"versionRead":72,"addedByCensus":69},"method",[58],"Gonzalo Ferrer","2019 IEEE\u002FRSJ International Conference on Intelligent Robots and Systems (IROS)","conference","IEEE","pp. 1278-1284","10.1109\u002Firos40897.2019.8967573","https:\u002F\u002Fdoi.org\u002F10.1109\u002FIROS40897.2019.8967573","2019-11","metadata_verified","not_applicable",[11],false,"corrected","author copy","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",[],[],{"totalRows":76,"groupCount":77,"groups":78,"others":571},24,4,[79,417,478,523],{"slug":80,"group":81,"sourceId":82,"sourceLabel":83,"table":84,"selfRows":85,"metrics":86,"seqs":93,"entrants":142,"cells":169,"outcomes":411,"locators":412,"hardware":413,"wordings":414,"notes":415},"balm2-2023-table-ii","balm2_2023:Table II","balm2_2023","Liu et al., 2023a","Table II",20,[87,91],{"label":88,"unit":89,"statistic":90,"alignment":18},"Absolute trajectory error (RMSE, meters)","m","RMSE",{"label":92,"unit":89,"statistic":90,"alignment":18},"Absolute trajectory error (RMSE, meters), average over 19 sequences",[94,98,100,102,104,106,108,112,116,118,120,122,124,126,128,130,132,136,138,140],{"dataset":95,"sequence":96,"environment":97},"Hilti SLAM Challenge 2021","Basement1","handheld (Ouster OS0-64), Hilti indoor or outdoor sequence",{"dataset":95,"sequence":99,"environment":97},"Basement4",{"dataset":95,"sequence":101,"environment":97},"Campus2",{"dataset":95,"sequence":103,"environment":97},"Construction2",{"dataset":95,"sequence":105,"environment":97},"LabSurvey2",{"dataset":95,"sequence":107,"environment":97},"UzhArea2",{"dataset":109,"sequence":110,"environment":111},"Hilti 2021, VIRAL and UrbanLoco (19 sequences)","Average","mixed: handheld, UAV, car",{"dataset":113,"sequence":114,"environment":115},"NTU VIRAL","eee01","UAV (horizontal 16-channel OS1)",{"dataset":113,"sequence":117,"environment":115},"eee02",{"dataset":113,"sequence":119,"environment":115},"eee03",{"dataset":113,"sequence":121,"environment":115},"nya01",{"dataset":113,"sequence":123,"environment":115},"nya02",{"dataset":113,"sequence":125,"environment":115},"nya03",{"dataset":113,"sequence":127,"environment":115},"sbs01",{"dataset":113,"sequence":129,"environment":115},"sbs02",{"dataset":113,"sequence":131,"environment":115},"sbs03",{"dataset":133,"sequence":134,"environment":135},"UrbanLoco","0117","car on urban streets (Velodyne HDL 32E)",{"dataset":133,"sequence":137,"environment":135},"0317",{"dataset":133,"sequence":139,"environment":135},"0426-1",{"dataset":133,"sequence":141,"environment":135},"0426-2",[143,147,150,152,154,157,159,161,163,165,167],{"name":144,"methodId":145,"linkable":146,"proposed":69,"self":69},"ICP (PCL, incremental)","besl1992icp",true,{"name":148,"methodId":149,"linkable":146,"proposed":69,"self":69},"GICP (PCL, incremental)","segal2009gicp",{"name":151,"methodId":44,"linkable":69,"proposed":69,"self":69},"NDT (PCL, incremental)",{"name":153,"methodId":5,"linkable":146,"proposed":69,"self":146},"EF",{"name":155,"methodId":156,"linkable":146,"proposed":69,"self":69},"BALM","balm2021",{"name":158,"methodId":44,"linkable":69,"proposed":69,"self":69},"PA",{"name":160,"methodId":44,"linkable":69,"proposed":69,"self":69},"PA (inner)",{"name":162,"methodId":44,"linkable":69,"proposed":69,"self":69},"BAREG",{"name":164,"methodId":82,"linkable":146,"proposed":146,"self":69},"Ours (float)",{"name":166,"methodId":82,"linkable":146,"proposed":146,"self":69},"Ours (edge)",{"name":168,"methodId":82,"linkable":146,"proposed":146,"self":69},"Ours",[170,174,177,180,183,185,188,191,194,197,200,203,205,207,209,211,212,214,216,218,220,222,224,226,228,230,232,234,235,236,237,239,241,243,245,247,249,251,253,255,257,258,260,262,264,265,267,269,271,273,275,276,278,280,282,284,286,288,290,292,294,296,298,300,302,304,306,308,310,312,314,316,318,320,322,324,326,328,330,332,334,336,338,340,341,343,345,347,349,351,354,356,358,361,363,365,368,370,372,375,376,378,380,381,383,386,388,390,393,395,397,400,402,404,407,409],[171,171,171,172,173,171,173,173,171],0,0.058,-1,[175,171,171,176,173,171,173,173,171],1,0.063,[178,171,171,179,173,171,173,173,171],2,0.076,[181,171,171,182,173,171,173,173,171],3,0.047,[77,171,171,184,173,171,173,173,171],0.042,[186,171,171,187,173,171,173,173,171],5,0.038,[189,171,171,190,173,171,173,173,171],6,0.036,[192,171,171,193,173,171,173,173,171],7,0.04,[195,171,171,196,173,171,173,173,171],8,0.0359,[198,171,171,199,173,171,173,173,171],9,0.0361,[201,171,171,202,173,171,173,173,171],10,0.0353,[171,171,175,204,173,171,173,173,171],0.084,[175,171,175,206,173,171,173,173,171],0.089,[178,171,175,208,173,171,173,173,171],0.098,[181,171,175,210,173,171,173,173,171],0.071,[77,171,175,172,173,171,173,173,171],[186,171,175,213,173,171,173,173,171],0.048,[189,171,175,215,173,171,173,173,171],0.045,[192,171,175,217,173,171,173,173,171],0.054,[195,171,175,219,173,171,173,173,171],0.0444,[198,171,175,221,173,171,173,173,171],0.0448,[201,171,175,223,173,171,173,173,171],0.0443,[171,171,178,225,173,171,173,173,171],0.105,[175,171,178,227,173,171,173,173,171],0.109,[178,171,178,229,173,171,173,173,171],0.124,[181,171,178,231,173,171,173,173,171],0.08,[77,171,178,233,173,171,173,173,171],0.066,[186,171,178,172,173,171,173,173,171],[189,171,178,217,173,171,173,173,171],[192,171,178,176,173,171,173,173,171],[195,171,178,238,173,171,173,173,171],0.0535,[198,171,178,240,173,171,173,173,171],0.053,[201,171,178,242,173,171,173,173,171],0.0531,[171,171,181,244,173,171,173,173,171],0.108,[175,171,181,246,173,171,173,173,171],0.104,[178,171,181,248,173,171,173,173,171],0.113,[181,171,181,250,173,171,173,173,171],0.086,[77,171,181,252,173,171,173,173,171],0.068,[186,171,181,254,173,171,173,173,171],0.06,[189,171,181,256,173,171,173,173,171],0.059,[192,171,181,176,173,171,173,173,171],[195,171,181,259,173,171,173,173,171],0.0563,[198,171,181,261,173,171,173,173,171],0.0577,[201,171,181,263,173,171,173,173,171],0.0553,[171,171,77,233,173,171,173,173,171],[175,171,77,266,173,171,173,173,171],0.069,[178,171,77,268,173,171,173,173,171],0.072,[181,171,77,270,173,171,173,173,171],0.046,[77,171,77,272,173,171,173,173,171],0.025,[186,171,77,274,173,171,173,173,171],0.019,[189,171,77,274,173,171,173,173,171],[192,171,77,277,173,171,173,173,171],0.023,[195,171,77,279,173,171,173,173,171],0.0185,[198,171,77,281,173,171,173,173,171],0.0189,[201,171,77,283,173,171,173,173,171],0.0181,[171,171,186,285,173,171,173,173,171],0.182,[175,171,186,287,173,171,173,173,171],0.191,[178,171,186,289,173,171,173,173,171],0.211,[181,171,186,291,173,171,173,173,171],0.161,[77,171,186,293,173,171,173,173,171],0.141,[186,171,186,295,173,171,173,173,171],0.122,[189,171,186,297,173,171,173,173,171],0.121,[192,171,186,299,173,171,173,173,171],0.127,[195,171,186,301,173,171,173,173,171],0.1205,[198,171,186,303,173,171,173,173,171],0.1102,[201,171,186,305,173,171,173,173,171],0.1171,[171,175,189,307,173,171,173,173,171],0.411,[175,175,189,309,173,171,173,173,171],0.41,[178,175,189,311,173,171,173,173,171],0.412,[181,175,189,313,173,171,173,173,171],0.268,[77,175,189,315,173,171,173,173,171],0.221,[186,175,189,317,173,171,173,173,171],0.186,[189,175,189,319,173,171,173,173,171],0.179,[192,175,189,321,173,171,173,173,171],0.203,[195,175,189,323,173,171,173,173,171],0.1775,[198,175,189,325,173,171,173,173,171],0.1826,[201,175,189,327,173,171,173,173,171],0.1763,[181,171,192,329,173,171,173,173,171],0.102,[77,171,192,331,173,171,173,173,171],0.073,[201,171,192,333,173,171,173,173,171],0.0382,[181,171,195,335,173,171,173,173,171],0.092,[77,171,195,337,173,171,173,173,171],0.062,[201,171,195,339,173,171,173,173,171],0.0356,[181,171,198,248,173,171,173,173,171],[77,171,198,342,173,171,173,173,171],0.081,[201,171,198,344,173,171,173,173,171],0.0517,[181,171,201,346,173,171,173,173,171],0.107,[77,171,201,348,173,171,173,173,171],0.082,[201,171,201,350,173,171,173,173,171],0.0362,[181,171,352,353,173,171,173,173,171],11,0.097,[77,171,352,355,173,171,173,173,171],0.067,[201,171,352,357,173,171,173,173,171],0.0468,[181,171,359,360,173,171,173,173,171],12,0.085,[77,171,359,362,173,171,173,173,171],0.074,[201,171,359,364,173,171,173,173,171],0.0413,[181,171,366,367,173,171,173,173,171],13,0.083,[77,171,366,369,173,171,173,173,171],0.077,[201,171,366,371,173,171,173,173,171],0.0385,[181,171,373,374,173,171,173,173,171],14,0.094,[77,171,373,337,173,171,173,173,171],[201,171,373,377,173,171,173,173,171],0.0377,[181,171,379,244,173,171,173,173,171],15,[77,171,379,268,173,171,173,173,171],[201,171,379,382,173,171,173,173,171],0.0427,[181,171,384,385,173,171,173,173,171],16,0.728,[77,171,384,387,173,171,173,173,171],0.625,[201,171,384,389,173,171,173,173,171],0.4956,[181,171,391,392,173,171,173,173,171],17,0.878,[77,171,391,394,173,171,173,173,171],0.732,[201,171,391,396,173,171,173,173,171],0.6488,[181,171,398,399,173,171,173,173,171],18,1.014,[77,171,398,401,173,171,173,173,171],0.875,[201,171,398,403,173,171,173,173,171],0.6886,[181,171,405,406,173,171,173,173,171],19,1.113,[77,171,405,408,173,171,173,173,171],0.924,[201,171,405,410,173,171,173,173,171],0.8223,[],[84],[],[],[416],"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\u002FINS. Column order verified from PDF layout: Ours (float), Ours (edge), Ours",{"slug":418,"group":419,"sourceId":82,"sourceLabel":83,"table":420,"selfRows":178,"metrics":421,"seqs":425,"entrants":429,"cells":438,"outcomes":471,"locators":472,"hardware":473,"wordings":475,"notes":476},"balm2-2023-table-iv","balm2_2023:Table IV","Table IV",[422],{"label":423,"unit":18,"statistic":18,"alignment":424},"Optimization time (total, unit not stated)","none",[426,428],{"dataset":95,"sequence":103,"environment":427},"handheld (Ouster OS0-64), construction sequence",{"dataset":109,"sequence":110,"environment":111},[430,431,432,433,434,435,436,437],{"name":153,"methodId":5,"linkable":146,"proposed":69,"self":146},{"name":155,"methodId":156,"linkable":146,"proposed":69,"self":69},{"name":158,"methodId":44,"linkable":69,"proposed":69,"self":69},{"name":160,"methodId":44,"linkable":69,"proposed":69,"self":69},{"name":162,"methodId":44,"linkable":69,"proposed":69,"self":69},{"name":164,"methodId":82,"linkable":146,"proposed":146,"self":69},{"name":166,"methodId":82,"linkable":146,"proposed":146,"self":69},{"name":168,"methodId":82,"linkable":146,"proposed":146,"self":69},[439,441,443,445,447,449,451,453,455,457,459,461,463,465,467,469],[171,171,171,440,173,171,171,173,171],1415.18,[175,171,171,442,173,171,171,173,171],412,[178,171,171,444,173,171,171,173,171],335.7,[181,171,171,446,173,171,171,173,171],313.23,[77,171,171,448,173,171,171,173,171],231.48,[186,171,171,450,173,171,171,173,171],33.04,[189,171,171,452,173,171,171,173,171],47.34,[192,171,171,454,173,171,171,173,171],47.12,[171,171,175,456,173,171,171,173,171],647.29,[175,171,175,458,173,171,171,173,171],232.54,[178,171,175,460,173,171,171,173,171],202.64,[181,171,175,462,173,171,171,173,171],171.11,[77,171,175,464,173,171,171,173,171],132.1,[186,171,175,466,173,171,171,173,171],18.15,[189,171,175,468,173,171,171,173,171],31.16,[192,171,175,470,173,171,171,173,171],30.58,[],[420],[474],"desktop Intel i7-10750H, 16 GB RAM",[],[477],"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)",{"slug":479,"group":480,"sourceId":82,"sourceLabel":83,"table":481,"selfRows":175,"metrics":482,"seqs":484,"entrants":489,"cells":502,"outcomes":517,"locators":518,"hardware":519,"wordings":520,"notes":521},"balm2-2023-supplementary-table-vii","balm2_2023:Supplementary Table VII","Supplementary Table VII",[483],{"label":88,"unit":89,"statistic":90,"alignment":18},[485],{"dataset":486,"sequence":487,"environment":488},"KITTI odometry","Mean (00-10)","KITTI odometry sequences 00-10; environment not described in this paper",[490,493,496,497,498,499,500],{"name":491,"methodId":492,"linkable":146,"proposed":69,"self":69},"MULLS","mulls2021",{"name":494,"methodId":495,"linkable":146,"proposed":69,"self":69},"CT-ICP","cticp2022",{"name":153,"methodId":5,"linkable":146,"proposed":69,"self":146},{"name":155,"methodId":156,"linkable":146,"proposed":69,"self":69},{"name":160,"methodId":44,"linkable":69,"proposed":69,"self":69},{"name":162,"methodId":44,"linkable":69,"proposed":69,"self":69},{"name":501,"methodId":82,"linkable":146,"proposed":146,"self":69},"Our",[503,505,507,509,511,513,515],[171,171,171,504,173,171,173,173,171],1.63,[175,171,171,506,173,171,173,173,171],1.4,[178,171,171,508,173,171,173,173,171],1.55,[181,171,171,510,173,171,173,173,171],1.48,[77,171,171,512,173,171,173,173,171],1.37,[186,171,171,514,173,171,173,173,171],1.42,[189,171,171,516,173,171,173,173,171],1.34,[],[481],[],[],[522],"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",{"slug":524,"group":525,"sourceId":82,"sourceLabel":83,"table":526,"selfRows":175,"metrics":527,"seqs":531,"entrants":533,"cells":544,"outcomes":565,"locators":566,"hardware":567,"wordings":568,"notes":569},"balm2-2023-table-iii","balm2_2023:Table III","Table III",[528],{"label":529,"unit":530,"statistic":18,"alignment":424},"Occupied cells increment over Ours (inc.), 0.1 m cells","cells",[532],{"dataset":95,"sequence":103,"environment":427},[534,535,536,537,538,539,540,541,542,543],{"name":144,"methodId":145,"linkable":146,"proposed":69,"self":69},{"name":148,"methodId":149,"linkable":146,"proposed":69,"self":69},{"name":151,"methodId":44,"linkable":69,"proposed":69,"self":69},{"name":153,"methodId":5,"linkable":146,"proposed":69,"self":146},{"name":155,"methodId":156,"linkable":146,"proposed":69,"self":69},{"name":158,"methodId":44,"linkable":69,"proposed":69,"self":69},{"name":160,"methodId":44,"linkable":69,"proposed":69,"self":69},{"name":162,"methodId":44,"linkable":69,"proposed":69,"self":69},{"name":164,"methodId":82,"linkable":146,"proposed":146,"self":69},{"name":166,"methodId":82,"linkable":146,"proposed":146,"self":69},[545,547,549,551,553,555,557,559,561,563],[171,171,171,546,173,171,173,173,171],6235,[175,171,171,548,173,171,173,173,171],9371,[178,171,171,550,173,171,173,173,171],10032,[181,171,171,552,173,171,173,173,171],6397,[77,171,171,554,173,171,173,173,171],1789,[186,171,171,556,173,171,173,173,171],1047,[189,171,171,558,173,171,173,173,171],394,[192,171,171,560,173,171,173,173,171],986,[195,171,171,562,173,171,173,173,171],95,[198,171,171,564,173,171,173,173,171],181,[],[526],[],[],[570],"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",[],1790510663917]