[{"data":1,"prerenderedAt":262},["ShallowReactive",2],{"method-gelfand2003stable":3},{"method":4,"reference":49,"equipment":71,"figures":85,"results":86},{"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":27,"sensors":32,"platform":35,"estimator":38,"association":39,"timeModel":40,"deskew":40,"loopClosure":41,"globalOptimization":41,"mapRepresentation":42,"prior":43,"outputGeometry":44,"compute":45,"codeUrl":46,"codeLicense":47,"relatedVersions":48},"gelfand2003stable","Gelfand et al., 2003","Geometrically stable sampling","Geometrically stable sampling for the ICP algorithm",2003,"classic","C02","registration_component","作者以點對平面 ICP 線性化後的 6x6 共變異數矩陣（力與力矩項）分析幾何穩定性：特徵值偏小的特徵向量對應兩曲面可相互滑動的螺旋運動，並以條件數作為穩定度指標。取樣時先以稀疏隨機樣本估計重疊區的特徵向量，再依各點對每個特徵向量的約束量排序，貪婪補強目前最弱的方向，使條件數接近 1。合成溝槽平面的條件數由 66.1 降至 3.7（選取 30% 點），Forma Urbis Romae 碎片掃描中均勻取樣無法對齊的溝槽得以正確對齊。與長廊、隧道等幾何退化場景的關聯屬推論。","Detects pose uncertainty in ICP and selects samples that constrain potentially unstable transformations, addressing featureless-region failures.","full_text_reviewed","peer_reviewed_published","background","not_reported（與長廊、隧道等退化幾何的關聯屬推論）",[20,21],"simulation","controlled_experiment",[23,24,25,26],"condition number reduced from 66.1 to 3.7 (incised plane) and from 26.9 to 4.1 (incised sphere) with 30% of points (Figs. 4, 6)","aligns grooves that uniform sampling misaligns; on the sphere it is the only method that finds the correct pose (Sec. 5, Figs. 5, 7)","Forma Urbis Romae fragment converged in 25 iterations where uniform sampling failed; after global relaxation maximum residual 0.3 mm vs over 1 mm with uniform sampling (Sec. 5, Fig. 10)","handles both translational and rotational instability, unlike normal-space sampling (Sec. 1, 3)",[28,29,30,31],"noisy areas can look like features and attract samples; smoothing helps only when features are larger than the noise, otherwise sampling fails (Sec. 5, Fig. 11)","all eigenvectors are constrained equally; leverage of geometry outside the overlap is ignored (Sec. 6)","pairwise only; stability of multi-scan global relaxation not addressed (Sec. 6)","3x to 5x slower per iteration than uniform sampling in the reported implementation (Sec. 4)",[33,34],"range-scanned meshes of Forma Urbis Romae fragments (scanner not named in the paper)","synthetic noisy meshes (incised plane and sphere)",[36,37],"simulation (synthetic meshes)","static range scans of Forma Urbis Romae fragments","point-to-plane ICP linearized for small rotations; the 6x6 covariance matrix C of per-pair torque (p x n) and force (n) terms defines the normal equations; stability measured by the condition number of C (ratio of extreme eigenvalues, target close to 1), computed with points and normals of P after centring and scaling the points to unit mean distance","covariance sampling: estimate eigenvectors of C from several hundred random points in the overlap (overlap test by mesh-boundary check of closest points), build six binned lists of candidate points sorted by |x_k . v_i|, and greedily pick the next point from the list of the currently least-constrained eigenvector; closest points on Q then feed point-to-plane minimization; for Forma Urbis Romae meshes overlapping by 25%, several hundred random points sufficed to stabilize the eigenvector estimate","not_applicable","none","triangle meshes or point sets with normals (normals averaged from adjacent faces or supplied externally)","initial pose required (ICP)","sampling strategy and pose-uncertainty indication","5 s per ICP iteration with stable sampling vs 1.5 s with uniform sampling on a 400 MHz Pentium II (300,000-point meshes, 10% subsampled); about 5x uniform-sampling cost per iteration with the delayed overlap test and about 3x with seed-point crawling",null,"not_verified",[],{"id":5,"kind":50,"shortName":7,"title":8,"authors":51,"year":9,"venue":56,"venueType":57,"publisher":58,"volumeIssuePages":59,"doi":60,"arxivId":46,"url":61,"firstPublicDate":62,"publicationStatus":16,"metadataStatus":63,"fulltextStatus":15,"era":10,"classicReason":64,"codeUrl":46,"cluster":11,"topics":65,"mdpi":67,"verification":68,"label":6,"fulltextRoute":69,"versionRead":70,"addedByCensus":67},"component",[52,53,54,55],"N. Gelfand","L. Ikemoto","S. Rusinkiewicz","M. Levoy","Fourth International Conference on 3-D Digital Imaging and Modeling (3DIM 2003)","conference","IEEE","pp. 260-267","10.1109\u002Fim.2003.1240258","https:\u002F\u002Fapi.crossref.org\u002Fworks\u002F10.1109\u002FIM.2003.1240258","2003","metadata_verified","evaluation\u002Funcertainty method: pose-uncertainty detection and constraint-aware point selection are precursors of degeneracy\u002Flocalizability analysis cited by tuna2024xicp (ref. [38]).",[11,66],"C13",false,"confirmed","author copy","Stanford author copy (8 pages) read in full; percentages lost in its text layer (30%, 10%, 25%) read from rendered page crops; IEEE Xplore version of record (3DIM 2003, pp. 260-267, 0-7695-1991-1\u002F03 © 2003 IEEE) opened in Chrome under NTU access to confirm key values (66.1, 26.9, 25 iterations, 400MHz Pentium II, 1.5 s)",[72,78],{"category":73,"model":74,"canonical":74,"role":75,"dataset":46,"specs":76,"locator":77},"compute","400MHz Pentium II","compute for runtime","400 MHz","Sec. 5",{"category":79,"model":80,"canonical":80,"role":81,"dataset":82,"specs":83,"locator":84},"other","range scanner used for Forma Urbis Romae scans (model not named in the paper)","dataset sensor","Forma Urbis Romae","meshes of about 300,000 points","Sec. 5; Acknowledgements",[],{"totalRows":87,"groupCount":88,"groups":89,"others":233},18,9,[90,139,172,203],{"slug":91,"group":92,"sourceId":93,"sourceLabel":94,"table":95,"selfRows":96,"metrics":97,"seqs":110,"entrants":115,"cells":119,"outcomes":133,"locators":134,"hardware":135,"wordings":136,"notes":137},"tuna2025informed-table-3","tuna2025informed:Table 3","tuna2025informed","Tuna et al., 2025","Table 3",4,[98,103,106,108],{"label":99,"unit":100,"statistic":101,"alignment":102},"APE translation µ(σ)[m]; σ 3.24","m","mean","not_reported",{"label":104,"unit":105,"statistic":101,"alignment":102},"APE rotation µ(σ)[deg]; σ 10.24","deg",{"label":107,"unit":100,"statistic":101,"alignment":102},"RPE translation per 1 m µ(σ)[m]; σ 0.222",{"label":109,"unit":105,"statistic":101,"alignment":102},"RPE rotation per 1 m µ(σ)[deg]; σ 3.60",[111],{"dataset":112,"sequence":113,"environment":114},"ANYmal simulation","pillar traverse","simulated plane with one rectangular pillar (3-axis degeneracy)",[116],{"name":117,"methodId":5,"linkable":118,"proposed":67,"self":118},"Gelfand et al.",true,[120,124,127,130],[121,121,121,122,123,121,123,123,121],0,4.273,-1,[121,125,121,126,123,121,123,123,121],1,14.3,[121,128,121,129,123,121,123,123,121],2,0.173,[121,131,121,132,123,121,123,123,121],3,1.495,[],[95],[],[],[138],"Dynamic ANYmal simulation with Open3D SLAM in the loop; prior noise σt 0.05 m, σr 0.01 rad; EVO metrics",{"slug":140,"group":141,"sourceId":93,"sourceLabel":94,"table":142,"selfRows":131,"metrics":143,"seqs":151,"entrants":156,"cells":158,"outcomes":165,"locators":166,"hardware":167,"wordings":169,"notes":170},"tuna2025informed-table-4","tuna2025informed:Table 4","Table 4",[144,146,148],{"label":145,"unit":100,"statistic":101,"alignment":102},"RTE µ(σ)[m], per 2 m traversed (Sec. V-B); σ 0.269",{"label":147,"unit":100,"statistic":101,"alignment":102},"ATE µ(σ)[m] (translation only); σ 2.44",{"label":149,"unit":150,"statistic":101,"alignment":102},"ICP-loop computational cost µ(σ)[ms]; σ 6.42","ms",[152],{"dataset":153,"sequence":154,"environment":155},"ANYmal forest experiment","forest open field","forest edge and open field (3-axis degeneracy)",[157],{"name":117,"methodId":5,"linkable":118,"proposed":67,"self":118},[159,161,163],[121,121,121,160,123,121,123,123,121],0.258,[121,125,121,162,123,121,123,123,121],2.61,[121,128,121,164,123,121,121,123,121],15.2,[],[142],[168],"desktop Intel i9 13900K, single-threaded",[],[171],"ANYmal forest to open-field run (107 m before revisit), leg-odometry prior, GNSS position ground truth; ICP-loop cost",{"slug":173,"group":174,"sourceId":93,"sourceLabel":94,"table":175,"selfRows":131,"metrics":176,"seqs":183,"entrants":188,"cells":190,"outcomes":197,"locators":198,"hardware":199,"wordings":200,"notes":201},"tuna2025informed-table-5","tuna2025informed:Table 5","Table 5",[177,179,181],{"label":178,"unit":100,"statistic":101,"alignment":102},"RTE µ(σ)[m], per 1 m traversed; σ 0.075",{"label":180,"unit":100,"statistic":101,"alignment":102},"ATE µ(σ)[m]; σ 1.28",{"label":182,"unit":150,"statistic":101,"alignment":102},"ICP registration computational cost µ(σ)[ms]; σ 4.54",[184],{"dataset":185,"sequence":186,"environment":187},"ENWIDE (Ulmberg bicycle tunnel)","Ulmberg tunnel","bicycle tunnel (one-directional degeneracy)",[189],{"name":117,"methodId":5,"linkable":118,"proposed":67,"self":118},[191,193,195],[121,121,121,192,123,121,123,123,121],0.073,[121,125,121,194,123,121,123,123,121],1.97,[121,128,121,196,123,121,121,123,121],24.321,[],[175],[168],[],[202],"Ulmberg bicycle tunnel, handheld payload, COIN-LIO prior, one-directional degeneracy over more than 80% of the run; ICP registration cost",{"slug":204,"group":205,"sourceId":5,"sourceLabel":6,"table":206,"selfRows":128,"metrics":207,"seqs":213,"entrants":216,"cells":221,"outcomes":225,"locators":226,"hardware":228,"wordings":229,"notes":230},"gelfand2003stable-text-sec-4","gelfand2003stable:Text Sec. 4","Text Sec. 4",[208,211],{"label":209,"unit":210,"statistic":102,"alignment":41},"time per iteration relative to uniform-sampling ICP","ratio",{"label":212,"unit":210,"statistic":102,"alignment":41},"time per iteration relative to conventional ICP",[214],{"dataset":102,"sequence":215,"environment":102},"implementation variants",[217,219],{"name":218,"methodId":5,"linkable":118,"proposed":118,"self":118},"stable sampling with delayed overlap test",{"name":220,"methodId":5,"linkable":118,"proposed":118,"self":118},"stable sampling with mesh or k-d tree crawling from seed points",[222,224],[121,121,121,223,123,121,123,123,121],5,[125,125,121,131,123,121,123,123,125],[],[227],"Sec. 4",[],[],[231,232],"Per-iteration cost relative to ICP with uniform sampling when meshes overlap by half their area","Per-iteration cost relative to conventional ICP",[234,239,244,250,256],{"group":235,"slug":236,"sourceLabel":6,"table":237,"selfRows":128,"datasets":238},"gelfand2003stable:Text Sec. 5","gelfand2003stable-text-sec-5","Text Sec. 5",[82],{"group":240,"slug":241,"sourceLabel":6,"table":242,"selfRows":125,"datasets":243},"gelfand2003stable:Fig. 10 caption","gelfand2003stable-fig-10-caption","Fig. 10 caption",[82],{"group":245,"slug":246,"sourceLabel":6,"table":247,"selfRows":125,"datasets":248},"gelfand2003stable:Fig. 4 caption","gelfand2003stable-fig-4-caption","Fig. 4 caption",[249],"synthetic incised plane",{"group":251,"slug":252,"sourceLabel":6,"table":253,"selfRows":125,"datasets":254},"gelfand2003stable:Fig. 6 caption","gelfand2003stable-fig-6-caption","Fig. 6 caption",[255],"synthetic incised sphere",{"group":257,"slug":258,"sourceLabel":94,"table":259,"selfRows":125,"datasets":260},"tuna2025informed:Table 6","tuna2025informed-table-6","Table 6",[261],"HEAP excavator experiment",1790510663618]