[{"data":1,"prerenderedAt":137},["ShallowReactive",2],{"method-arun1987svd":3},{"method":4,"reference":38,"equipment":58,"figures":65,"results":66},{"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":23,"sensors":26,"platform":27,"estimator":28,"association":29,"timeModel":30,"deskew":30,"loopClosure":31,"globalOptimization":31,"mapRepresentation":30,"prior":32,"outputGeometry":33,"compute":34,"codeUrl":35,"codeLicense":36,"relatedVersions":37},"arun1987svd","Arun et al., 1987","SVD closed-form rigid fit (Arun-Huang-Blostein)","Least-Squares Fitting of Two 3-D Point Sets",1987,"classic","C02","registration_component","此文處理已知點對應關係時，兩組三維點之間的最小平方剛體擬合。作者先以兩組點的質心分離平移與旋轉，再對去質心點對構成的 3×3 矩陣做奇異值分解（SVD），以 VUᵀ 作為旋轉，平移由質心差求得，屬於非迭代的封閉解。若所得矩陣的行列式為負，代表得到的是鏡射：點共面時將 V 的第三欄變號即可得到旋轉，其餘情況只會在雜訊極大時出現，作者建議改用類似 RANSAC 的方法。在 VAX 11\u002F780 的模擬中，SVD 法每次執行的 CPU 時間與四元數法相近，明顯短於迭代法。","Closed-form least-squares rigid fit of corresponded 3-D point sets: centroids decouple translation, R = V U^T from the SVD of a 3x3 matrix with a reflection check; CPU time comparable to the quaternion method and below an iterative method in VAX simulations.","full_text_reviewed","peer_reviewed_published","background","not_reported（僅以隨機點集做數值模擬，未涉及建物或工地）",[20],"simulation",[22],"[\"noniterative closed-form solution (Sec. I, III)\", \"CPU time comparable to the quaternion method (37.0 to 54.6 ms versus 26.6 to 48.3 ms per run) and well below the iterative method (94.2 to 135.0 ms) for 3 to 30 correspondences on a VAX 11\u002F780 (Sec. VII, Table I)\", \"coplanar degeneracy is detectable from a zero singular value and resolvable (Sec. IV)\"]",[24,25],"[\"requires known point correspondences (Sec. I problem statement)\", \"SVD can return a reflection","with no zero singular value this happens only under very large noise, where the authors judge least squares inappropriate and suggest a RANSAC-like technique (Sec. V, VI)\", \"colinear points give infinitely many rotations and reflections (Sec. IV)\", \"sensitivity to outliers is not quantified in the paper (inference)\"]",[],[],"noniterative closed form: centroids decouple translation, H = sum q_i q'_i^t (3x3), SVD H = U L V^t, R = V U^t when det = +1 (sign of third column of V changed in the coplanar case), then T = p' - R p (Sec. II, III-A, IV, VI)","not_applicable (assumes known correspondences)","not_applicable","none","known correspondences","rigid rotation and translation","computer simulations on a VAX 11\u002F780, programs in C with IMSL subroutines; SVD method 37.0 to 54.6 ms CPU time per run for 3 to 30 correspondences (Sec. VII, Table I)",null,"not_verified",[],{"id":5,"kind":39,"shortName":7,"title":8,"authors":40,"year":9,"venue":44,"venueType":45,"publisher":46,"volumeIssuePages":47,"doi":48,"arxivId":35,"url":49,"firstPublicDate":50,"publicationStatus":16,"metadataStatus":51,"fulltextStatus":15,"era":10,"classicReason":52,"codeUrl":35,"cluster":11,"topics":53,"mdpi":54,"verification":55,"label":6,"fulltextRoute":56,"versionRead":57,"addedByCensus":54},"component",[41,42,43],"K. S. Arun","T. S. Huang","S. D. Blostein","IEEE Transactions on Pattern Analysis and Machine Intelligence","journal","IEEE","PAMI-9(5):698-700","10.1109\u002Ftpami.1987.4767965","https:\u002F\u002Fapi.crossref.org\u002Fworks\u002F10.1109\u002FTPAMI.1987.4767965","1987-09","metadata_verified","necessary technical node: closed-form SVD rigid fit of corresponded 3-D point sets (Sec. III) is the inner solve of point-to-point ICP; besl1992icp cites it among the SVD solutions (Sec. II, ref. [1]) although it uses the quaternion solve itself, and rusinkiewicz2001variants Sec. 3.5 also cites it.",[11],false,"corrected","NTU institutional (curl)","version of record, IEEE TPAMI PAMI-9(5):698-700, September 1987 (3-page correspondence), PDF with embedded text layer",[59],{"category":60,"model":61,"canonical":61,"role":62,"dataset":35,"specs":63,"locator":64},"compute","VAX 11\u002F780","compute for runtime","programs written in C; IMSL subroutines LSVDF and EIGRS","Sec. VII, Table I",[],{"totalRows":67,"groupCount":68,"groups":69,"others":136},6,1,[70],{"slug":71,"group":72,"sourceId":5,"sourceLabel":6,"table":73,"selfRows":67,"metrics":74,"seqs":79,"entrants":93,"cells":99,"outcomes":130,"locators":131,"hardware":132,"wordings":133,"notes":134},"arun1987svd-table-i","arun1987svd:Table I","Table I",[75],{"label":76,"unit":77,"statistic":78,"alignment":31},"CPU time per run","ms","not_reported",[80,83,85,87,89,91],{"dataset":81,"sequence":82,"environment":20},"synthetic point sets (Sec. VII)","N = 3 point correspondences",{"dataset":81,"sequence":84,"environment":20},"N = 7 point correspondences",{"dataset":81,"sequence":86,"environment":20},"N = 11 point correspondences",{"dataset":81,"sequence":88,"environment":20},"N = 16 point correspondences",{"dataset":81,"sequence":90,"environment":20},"N = 20 point correspondences",{"dataset":81,"sequence":92,"environment":20},"N = 30 point correspondences",[94,97],{"name":95,"methodId":5,"linkable":96,"proposed":96,"self":96},"SVD algorithm (proposed)",true,{"name":98,"methodId":35,"linkable":54,"proposed":54,"self":54},"quaternion algorithm (Faugeras and Hebert [4])",[100,104,106,108,110,113,115,118,120,123,125,128],[101,101,101,102,103,101,101,103,101],0,54.6,-1,[68,101,101,105,103,101,101,103,101],26.6,[101,101,68,107,103,101,101,103,101],41.6,[68,101,68,109,103,101,101,103,101],32.4,[101,101,111,112,103,101,101,103,101],2,37,[68,101,111,114,103,101,101,103,101],41,[101,101,116,117,103,101,101,103,101],3,39.4,[68,101,116,119,103,101,101,103,101],45.6,[101,101,121,122,103,101,101,103,101],4,40.4,[68,101,121,124,103,101,101,103,101],45.2,[101,101,126,127,103,101,101,103,101],5,44.2,[68,101,126,129,103,101,101,103,101],48.3,[],[73],[61],[],[135],"Simulation: N random 3-D points in a 6x6x6 cube, rotated 75 deg about axis (0.6, 0.7, 0.39), translated by (80, 60, 70), Gaussian noise std 0.5 per coordinate; C programs with IMSL (LSVDF for SVD, EIGRS for quaternion eigen analysis); iterative method started from zero and solved to 7-digit accuracy",[],1790510665932]