[{"data":1,"prerenderedAt":448},["ShallowReactive",2],{"method-yang2020gnc":3},{"method":4,"reference":49,"equipment":69,"figures":77,"results":78},{"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":22,"limitations":25,"sensors":28,"platform":29,"estimator":31,"association":32,"timeModel":33,"deskew":33,"loopClosure":34,"globalOptimization":35,"mapRepresentation":33,"prior":36,"outputGeometry":37,"compute":38,"codeUrl":39,"codeLicense":40,"relatedVersions":41},"yang2020gnc","Yang et al., 2020b","GNC (GNC-GM \u002F GNC-TLS)","Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection",2020,"recent","C03","estimation_framework_or_library","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。","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.","full_text_reviewed","peer_reviewed_published","main_body","not_reported（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 yang2021teaser、lim2025kissmatcher），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）。",[20,21],"simulation","public_benchmark",[23,24],"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)",[26,27],"(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",[],[20,30],"public benchmark data (Stanford Bunny, PASCAL+ car-2 mesh, INTEL and CSAIL pose graphs, FG3DCar images)","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 \u002F 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 \u002F (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","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","not_applicable","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","robust PGO with GNC-GM or GNC-TLS on top of SE-Sync, without an initial guess (Sec. V-B)","none (no initial guess required)","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","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)","https:\u002F\u002Fgithub.com\u002Fborglab\u002Fgtsam\u002Fblob\u002Fdevelop\u002Fgtsam\u002Fnonlinear\u002FGncOptimizer.h","BSD (simplified) for GTSAM per repository LICENSE; applies to the later library implementation",[42,46],{"relation":43,"title":44,"doi_or_url":45},"preprint","arXiv 1909.08605 (v1 2019-09-18; v4 2020-06-11 read)","https:\u002F\u002Farxiv.org\u002Fabs\u002F1909.08605",{"relation":47,"title":48,"doi_or_url":39},"code_release","GTSAM GncOptimizer (later library implementation by Shi, Carlone and Dellaert that cites this paper; not released with the paper)",{"id":5,"kind":50,"shortName":7,"title":8,"authors":51,"year":9,"venue":56,"venueType":57,"publisher":58,"volumeIssuePages":59,"doi":60,"arxivId":61,"url":45,"firstPublicDate":62,"publicationStatus":16,"metadataStatus":63,"fulltextStatus":15,"era":10,"classicReason":33,"codeUrl":39,"cluster":11,"topics":64,"mdpi":65,"verification":66,"label":6,"fulltextRoute":67,"versionRead":68,"addedByCensus":65},"method",[52,53,54,55],"Heng Yang","Pasquale Antonante","Vasileios Tzoumas","Luca Carlone","IEEE Robotics and Automation Letters","journal","IEEE","5(2):1127-1134","10.1109\u002Flra.2020.2965893","1909.08605","2019-09-18","metadata_verified",[11],false,"corrected","arXiv","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\u002F136232 (dc.eprint.version 'Author's final manuscript'). The IEEE Xplore version of record was not opened.",[70],{"category":71,"model":72,"canonical":72,"role":73,"dataset":74,"specs":75,"locator":76},"compute","desktop computer","compute for runtime",null,"not_reported (no model, CPU or memory given)","Sec. V-C (SOS SDP solved with GloptiPoly 3 in Matlab in about 80 ms)",[],{"totalRows":79,"groupCount":80,"groups":81,"others":412},36,10,[82,223,286,355],{"slug":83,"group":84,"sourceId":85,"sourceLabel":86,"table":87,"selfRows":88,"metrics":89,"seqs":94,"entrants":112,"cells":128,"outcomes":217,"locators":218,"hardware":219,"wordings":220,"notes":221},"kimeramulti2022-table-i","kimeramulti2022:Table I","kimeramulti2022","Tian et al., 2022","Table I",6,[90],{"label":91,"unit":92,"statistic":93,"alignment":93},"Absolute trajectory error (ATE) [m]","m","not_reported",[95,99,101,103,107,109],{"dataset":96,"sequence":97,"environment":98},"DCIST simulation","Medfield","photo-realistic simulation, 3 robots",{"dataset":96,"sequence":100,"environment":98},"City",{"dataset":96,"sequence":102,"environment":98},"Camp",{"dataset":104,"sequence":105,"environment":106},"EuRoC","Vicon Room 1","indoor room, 3 sequences as robots",{"dataset":104,"sequence":108,"environment":106},"Vicon Room 2",{"dataset":104,"sequence":110,"environment":111},"Machine Hall","industrial hall, 5 sequences as robots",[113,115,117,119,121,124,126],{"name":114,"methodId":74,"linkable":65,"proposed":65,"self":65},"L2 (least squares, RBCD)",{"name":116,"methodId":74,"linkable":65,"proposed":65,"self":65},"PCM",{"name":118,"methodId":74,"linkable":65,"proposed":65,"self":65},"D-GNC (NI, naive initialization)",{"name":120,"methodId":74,"linkable":65,"proposed":65,"self":65},"PCM + D-GNC",{"name":122,"methodId":85,"linkable":123,"proposed":123,"self":65},"D-GNC",true,{"name":125,"methodId":85,"linkable":123,"proposed":123,"self":65},"D-GNC (ES, early stopping)",{"name":127,"methodId":5,"linkable":123,"proposed":65,"self":123},"Centralized GNC",[129,133,136,139,142,145,148,150,152,154,156,158,160,162,163,165,167,169,171,173,175,177,179,180,182,184,186,188,190,192,194,196,198,200,202,204,206,208,209,211,213,215],[130,130,130,131,132,130,132,132,130],0,64.2,-1,[134,130,130,135,132,130,132,132,130],1,12.5,[137,130,130,138,132,130,132,132,130],2,57.4,[140,130,130,141,132,130,132,132,130],3,4.64,[143,130,130,144,132,130,132,132,130],4,3.92,[146,130,130,147,132,130,132,132,130],5,4.32,[88,130,130,149,132,130,132,132,130],3.88,[130,130,134,151,132,130,132,132,130],3.58,[134,130,134,153,132,130,132,132,130],1.57,[137,130,134,155,132,130,132,132,130],0.91,[140,130,134,157,132,130,132,132,130],1.08,[143,130,134,159,132,130,132,132,130],0.85,[146,130,134,161,132,130,132,132,130],0.76,[88,130,134,134,132,130,132,132,130],[130,130,137,164,132,130,132,132,130],11.9,[134,130,137,166,132,130,132,132,130],1.37,[137,130,137,168,132,130,132,132,130],0.97,[140,130,137,170,132,130,132,132,130],1.09,[143,130,137,172,132,130,132,132,130],0.96,[146,130,137,174,132,130,132,132,130],0.75,[88,130,137,176,132,130,132,132,130],1.33,[130,130,140,178,132,130,132,132,130],1.17,[134,130,140,134,132,130,132,132,130],[137,130,140,181,132,130,132,132,130],0.34,[140,130,140,183,132,130,132,132,130],0.45,[143,130,140,185,132,130,132,132,130],0.35,[146,130,140,187,132,130,132,132,130],0.21,[88,130,140,189,132,130,132,132,130],0.36,[130,130,143,191,132,130,132,132,130],1.87,[134,130,143,193,132,130,132,132,130],1.56,[137,130,143,195,132,130,132,132,130],0.46,[140,130,143,197,132,130,132,132,130],0.62,[143,130,143,199,132,130,132,132,130],0.47,[146,130,143,201,132,130,132,132,130],0.48,[88,130,143,203,132,130,132,132,130],0.43,[130,130,146,205,132,130,132,132,130],1.92,[134,130,146,207,132,130,132,132,130],1.76,[137,130,146,201,132,130,132,132,130],[140,130,146,210,132,130,132,132,130],0.7,[143,130,146,212,132,130,132,132,130],0.41,[146,130,146,214,132,130,132,132,130],0.49,[88,130,146,216,132,130,132,132,130],0.52,[],[87],[],[],[222],"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",{"slug":224,"group":225,"sourceId":85,"sourceLabel":86,"table":226,"selfRows":88,"metrics":227,"seqs":232,"entrants":239,"cells":245,"outcomes":280,"locators":281,"hardware":282,"wordings":283,"notes":284},"kimeramulti2022-table-ii","kimeramulti2022:Table II","Table II",[228],{"label":229,"unit":230,"statistic":93,"alignment":231},"Runtime [sec] of robust PGO","s","none",[233,234,235,236,237,238],{"dataset":96,"sequence":97,"environment":98},{"dataset":96,"sequence":100,"environment":98},{"dataset":96,"sequence":102,"environment":98},{"dataset":104,"sequence":105,"environment":106},{"dataset":104,"sequence":108,"environment":106},{"dataset":104,"sequence":110,"environment":111},[240,242,244],{"name":241,"methodId":85,"linkable":123,"proposed":123,"self":65},"D-GNC distributed",{"name":243,"methodId":85,"linkable":123,"proposed":123,"self":65},"D-GNC distributed (ES)",{"name":127,"methodId":5,"linkable":123,"proposed":65,"self":123},[246,248,250,252,254,256,258,260,262,263,265,267,269,271,272,274,276,278],[130,130,130,247,132,130,132,132,130],29.2,[134,130,130,249,132,130,132,132,130],5.9,[137,130,130,251,132,130,132,132,130],4.4,[130,130,134,253,132,130,132,132,130],22.1,[134,130,134,255,132,130,132,132,130],4.5,[137,130,134,257,132,130,132,132,130],3.2,[130,130,137,259,132,130,132,132,130],43.2,[134,130,137,261,132,130,132,132,130],9.1,[137,130,137,251,132,130,132,132,130],[130,130,140,264,132,130,132,132,130],8.9,[134,130,140,266,132,130,132,132,130],2.2,[137,130,140,268,132,130,132,132,130],3.1,[130,130,143,270,132,130,132,132,130],11.7,[134,130,143,257,132,130,132,132,130],[137,130,143,273,132,130,132,132,130],1.7,[130,130,146,275,132,130,132,132,130],20.5,[134,130,146,277,132,130,132,132,130],2.5,[137,130,146,279,132,130,132,132,130],6.3,[],[226],[],[],[285],"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",{"slug":287,"group":288,"sourceId":85,"sourceLabel":86,"table":289,"selfRows":88,"metrics":290,"seqs":293,"entrants":309,"cells":317,"outcomes":349,"locators":350,"hardware":351,"wordings":352,"notes":353},"kimeramulti2022-table-v","kimeramulti2022:Table V","Table V",[291],{"label":292,"unit":92,"statistic":93,"alignment":231},"end-to-end error [m]",[294,298,300,302,305,307],{"dataset":295,"sequence":296,"environment":297},"Medfield outdoor dataset (authors' own)","Robot 0 (600 m)","outdoor campus with similar-looking scenes, Clearpath Jackal UGV",{"dataset":295,"sequence":299,"environment":297},"Robot 1 (860 m)",{"dataset":295,"sequence":301,"environment":297},"Robot 2 (728 m)",{"dataset":303,"sequence":304,"environment":297},"Stata outdoor dataset (authors' own)","Robot 0 (515 m)",{"dataset":303,"sequence":306,"environment":297},"Robot 1 (570 m)",{"dataset":303,"sequence":308,"environment":297},"Robot 2 (610 m)",[310,313,315],{"name":311,"methodId":312,"linkable":123,"proposed":65,"self":65},"Kimera-VIO","kimera2020",{"name":314,"methodId":85,"linkable":123,"proposed":123,"self":65},"Kimera-Multi",{"name":316,"methodId":5,"linkable":123,"proposed":65,"self":123},"Centralized",[318,320,322,323,325,327,328,330,332,333,335,337,338,340,342,344,346,348],[130,130,130,319,132,130,132,132,130],18.74,[134,130,130,321,132,130,132,132,130],0.01,[137,130,130,321,132,130,132,132,130],[130,130,134,324,132,130,132,132,130],14.84,[134,130,134,326,132,130,132,132,130],0.13,[137,130,134,326,132,130,132,132,130],[130,130,137,329,132,130,132,132,130],24.55,[134,130,137,331,132,130,132,132,130],0.09,[137,130,137,331,132,130,132,132,130],[130,130,140,334,132,130,132,132,130],49.02,[134,130,140,336,132,130,132,132,130],0.03,[137,130,140,321,132,130,132,132,130],[130,130,143,339,132,130,132,132,130],24.19,[134,130,143,341,132,130,132,132,130],33.13,[137,130,143,343,132,130,132,132,130],21.56,[130,130,146,345,132,130,132,132,130],29.35,[134,130,146,347,132,130,132,132,130],1.26,[137,130,146,178,132,130,132,132,130],[],[289],[],[],[354],"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",{"slug":356,"group":357,"sourceId":358,"sourceLabel":359,"table":360,"selfRows":143,"metrics":361,"seqs":365,"entrants":376,"cells":383,"outcomes":406,"locators":407,"hardware":408,"wordings":409,"notes":410},"lemon2026-table-viii","lemon2026:Table VIII","lemon2026","Wang et al., 2026","Table VIII",[362],{"label":363,"unit":364,"statistic":93,"alignment":231},"F1","%",[366,370,372,374],{"dataset":367,"sequence":368,"environment":369},"S3E","Campus 1","multi-robot campus or tunnel",{"dataset":367,"sequence":371,"environment":369},"Dormitory",{"dataset":367,"sequence":373,"environment":369},"Library",{"dataset":367,"sequence":375,"environment":369},"Tunnel",[377,379,381],{"name":378,"methodId":358,"linkable":123,"proposed":123,"self":65},"Ours (loop processing module)",{"name":380,"methodId":74,"linkable":65,"proposed":65,"self":65},"PCM Best-F1",{"name":382,"methodId":5,"linkable":123,"proposed":65,"self":123},"GNC Best-F1",[384,386,388,390,392,394,396,397,399,401,402,404],[130,130,130,385,132,130,132,132,130],92.2,[134,130,130,387,132,130,132,132,130],86.5,[137,130,130,389,132,130,132,132,130],85.7,[130,130,134,391,132,130,132,132,130],90.5,[134,130,134,393,132,130,132,132,130],81.1,[137,130,134,395,132,130,132,132,130],82.5,[130,130,137,385,132,130,132,132,130],[134,130,137,398,132,130,132,132,130],86.9,[137,130,137,400,132,130,132,132,130],89.4,[130,130,140,391,132,130,132,132,130],[134,130,140,403,132,130,132,132,130],88.6,[137,130,140,405,132,130,132,132,130],91.6,[],[360],[],[],[411],"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",[413,419,425,431,437,443],{"group":414,"slug":415,"sourceLabel":6,"table":416,"selfRows":143,"datasets":417},"yang2020gnc:Text Sec.V-A P-REG","yang2020gnc-text-sec-v-a-p-reg","Text Sec.V-A P-REG",[418],"Stanford 3D Scanning Repository Bunny",{"group":420,"slug":421,"sourceLabel":6,"table":422,"selfRows":143,"datasets":423},"yang2020gnc:Text Sec.V-B INTEL","yang2020gnc-text-sec-v-b-intel","Text Sec.V-B INTEL",[424],"INTEL",{"group":426,"slug":427,"sourceLabel":6,"table":428,"selfRows":137,"datasets":429},"yang2020gnc:Text Sec.V-A G-REG","yang2020gnc-text-sec-v-a-g-reg","Text Sec.V-A G-REG",[430],"PASCAL+ (car-2 mesh)",{"group":432,"slug":433,"sourceLabel":6,"table":434,"selfRows":137,"datasets":435},"yang2020gnc:Text Sec.V-C","yang2020gnc-text-sec-v-c","Text Sec.V-C",[436],"FG3DCar",{"group":438,"slug":439,"sourceLabel":6,"table":440,"selfRows":134,"datasets":441},"yang2020gnc:Text Sec.V-B CSAIL","yang2020gnc-text-sec-v-b-csail","Text Sec.V-B CSAIL",[442],"CSAIL",{"group":444,"slug":445,"sourceLabel":6,"table":446,"selfRows":134,"datasets":447},"yang2020gnc:Text Sec.V-C SOS","yang2020gnc-text-sec-v-c-sos","Text Sec.V-C SOS",[93],1790510654759]