[{"data":1,"prerenderedAt":280},["ShallowReactive",2],{"method-rusinkiewicz2019symmetric":3},{"method":4,"reference":40,"equipment":57,"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":25,"platform":28,"estimator":29,"association":30,"timeModel":31,"deskew":31,"loopClosure":32,"globalOptimization":32,"mapRepresentation":33,"prior":34,"outputGeometry":35,"compute":36,"codeUrl":37,"codeLicense":38,"relatedVersions":39},"rusinkiewicz2019symmetric","Rusinkiewicz, 2019","Symmetric ICP","A symmetric objective function for ICP",2019,"recent","C02","registration_component","此文提出對稱化的 ICP 目標函數：以對應點兩側法向量的和作為誤差方向，並把旋轉拆成兩半，以相反方向分別作用於兩個表面。只要兩點與其法向量落在同一個局部二次曲面（2D 為圓弧）上，殘差即為零，因此比只在平面上為零的點對平面誤差保留更多沿表面滑動的自由度，卻不需估計曲率。作者以 Rodrigues 公式推導線性化，每次迭代仍只解一個線性最小平方問題，對應正確時結果是精確的。在 dragon 模型、部分重疊的 bunny 掃描與一組 TUM RGB-D 室內掃描上，每次迭代的誤差下降都快於點對點、點對平面、雙平面與二次近似法；bunny 收斂範圍實驗中，Levenberg-Marquardt 版本在 20 次迭代時收斂範圍最寬。論文沒有報告執行時間，也沒有使用 LiDAR 或大尺度場景資料。","Symmetric ICP measures the pair residual along the sum of both normals and splits the rotation between the two surfaces, so the error vanishes whenever the pair lies on a locally quadratic patch; one linear solve per iteration, exact for exact correspondences, with faster per-iteration convergence and a wider basin on object-scale scans.","full_text_reviewed","peer_reviewed_published","supplementary","not_reported（僅以 dragon 模型、bunny 掃描與一組 TUM RGB-D 室內辦公室掃描測試，未涉及營建場域或 LiDAR 資料）",[20],"public_benchmark",[22],"per-iteration error decreases faster than point-to-point, point-to-plane, two-plane and quadratic objectives on the dragon model, a partially overlapping bunny pair and a TUM RGB-D office pair (Sec. 4.3, Fig. 4); linearization verified exact up to roundoff for exact correspondences (Sec. 4.2); LM-Symmetric gives the widest convergence basin at 20 iterations and comes within a few percent of two-plane at 500 iterations (Sec. 4.4); e.g. at 20 iterations with 60 deg rotation and 10% translation, 82% success for Symmetric vs 62% point-to-plane and 2% point-to-point (Fig. 5)",[24],"only object-scale data were used: dragon mesh, bunny range scans of Turk and Levoy (bun000 and bun090 overlap about 23% IOU) and one Kinect scan pair whose noise narrows the gap between variants; no LiDAR, large-scene or SLAM data (Sec. 4.3); plain E_symm has a basin comparable to the quadratic and LM point-to-plane variants and below two-plane at 500 iterations (Sec. 4.4); only a simple outlier-rejection scheme was tested, with robust l_p norms, denoising and descriptor matching left to future work (Sec. 4.3, 5); no timing numbers; still a local method needing an initial alignment (reviewer inference from Sec. 2 and 4.4)",[26,27],"[\"range scans and meshes (dragon model, Curless and Levoy 1996","bunny range scans bun000, bun090 and other overlapping pairs, Turk and Levoy 1994)\", \"RGB-D (Kinect scans from TUM RGB-D freiburg1_xyz)\"]",[],"E_symm = sum_i [(R p_i - R^-1 q_i + t) . (n_p,i + n_q,i)]^2: the rotation is split so that each surface is rotated by half the angle in opposite directions, with normals kept fixed (the rotated-normals variant E_symm-RN behaves similarly and is dropped for simplicity); linearized from the Rodrigues formula with a~ = a tan(theta) into one linear least-squares solve per iteration, interpreted as a Gauss-Newton step with Gibbs rotation parameters, exact when correspondences are exact; a Levenberg-Marquardt variant (LM-Symmetric) is also evaluated","both normals enter the residual (Sec. 3.2; if oriented normals are unavailable they are flipped to agree, footnote 1); in the convergence-basin test all variants sample points from both meshes and take Euclidean closest points on the other mesh (Sec. 4.4); the dragon self-alignment test uses no outlier rejection, while the partially overlapping bunny test and the basin test reject pairs with negative normal dot product and pairs farther than 2.5 sigma (sigma = 1.4826 x median distance) at each iteration (Sec. 4.3, 4.4)","not_applicable","none","3D models \u002F surfaces","initial pose required","rigid transformation","almost no added computation per iteration relative to point-to-plane, one linear least-squares solve per iteration; no runtime, timing table or hardware reported",null,"not_verified",[],{"id":5,"kind":41,"shortName":7,"title":8,"authors":42,"year":9,"venue":44,"venueType":45,"publisher":46,"volumeIssuePages":47,"doi":48,"arxivId":37,"url":49,"firstPublicDate":50,"publicationStatus":16,"metadataStatus":51,"fulltextStatus":15,"era":10,"classicReason":31,"codeUrl":37,"cluster":11,"topics":52,"mdpi":53,"verification":54,"label":6,"fulltextRoute":55,"versionRead":56,"addedByCensus":53},"method",[43],"Szymon Rusinkiewicz","ACM Transactions on Graphics","journal","ACM","38(4):1-7","10.1145\u002F3306346.3323037","https:\u002F\u002Fapi.crossref.org\u002Fworks\u002F10.1145\u002F3306346.3323037","2019-07-12","metadata_verified",[11],false,"confirmed","author copy","author's version posted by the author at Princeton (7 pages; front page states it is the author's version and that the definitive Version of Record is ACM Trans. Graph. 38(4), Article 85, July 2019); not compared page by page with the ACM DL PDF (ACM reference line gives 8 pages)",[58],{"category":59,"model":60,"canonical":60,"role":61,"dataset":62,"specs":63,"locator":64},"rgbd","Kinect","dataset sensor","TUM RGB-D (freiburg1_xyz, timestamps 1305031104.030279 and 1305031108.503548)","not_reported (paper notes warp and scanning noise from the Kinect sensor)","Sec. 4.3",[],{"totalRows":67,"groupCount":68,"groups":69,"others":279},36,1,[70],{"slug":71,"group":72,"sourceId":5,"sourceLabel":6,"table":73,"selfRows":67,"metrics":74,"seqs":79,"entrants":106,"cells":126,"outcomes":272,"locators":273,"hardware":274,"wordings":275,"notes":276},"rusinkiewicz2019symmetric-fig-5","rusinkiewicz2019symmetric:Fig. 5","Fig. 5",[75],{"label":76,"unit":77,"statistic":78,"alignment":32},"percentage of successful ICP trials","%","mean",[80,84,86,88,90,92,94,96,98,100,102,104],{"dataset":81,"sequence":82,"environment":83},"bunny range scans (Turk and Levoy 1994)","20 iterations; rotation 20 deg, translation 10%","object-scale range scans",{"dataset":81,"sequence":85,"environment":83},"20 iterations; rotation 20 deg, translation 50%",{"dataset":81,"sequence":87,"environment":83},"20 iterations; rotation 60 deg, translation 10%",{"dataset":81,"sequence":89,"environment":83},"20 iterations; rotation 60 deg, translation 50%",{"dataset":81,"sequence":91,"environment":83},"100 iterations; rotation 20 deg, translation 10%",{"dataset":81,"sequence":93,"environment":83},"100 iterations; rotation 20 deg, translation 50%",{"dataset":81,"sequence":95,"environment":83},"100 iterations; rotation 60 deg, translation 10%",{"dataset":81,"sequence":97,"environment":83},"100 iterations; rotation 60 deg, translation 50%",{"dataset":81,"sequence":99,"environment":83},"500 iterations; rotation 20 deg, translation 10%",{"dataset":81,"sequence":101,"environment":83},"500 iterations; rotation 20 deg, translation 50%",{"dataset":81,"sequence":103,"environment":83},"500 iterations; rotation 60 deg, translation 10%",{"dataset":81,"sequence":105,"environment":83},"500 iterations; rotation 60 deg, translation 50%",[107,111,113,116,118,120,122,124],{"name":108,"methodId":109,"linkable":110,"proposed":53,"self":53},"Point-to-point","besl1992icp",true,{"name":112,"methodId":37,"linkable":53,"proposed":53,"self":53},"Quadratic (Mitra et al. 2004, on-demand)",{"name":114,"methodId":115,"linkable":110,"proposed":53,"self":53},"Point-to-plane","chen1992pointtoplane",{"name":117,"methodId":37,"linkable":53,"proposed":53,"self":53},"Two-plane",{"name":119,"methodId":5,"linkable":110,"proposed":110,"self":110},"Symmetric-RN",{"name":121,"methodId":5,"linkable":110,"proposed":110,"self":110},"Symmetric",{"name":123,"methodId":37,"linkable":53,"proposed":53,"self":53},"LM-Point-to-plane (Fitzgibbon 2001)",{"name":125,"methodId":5,"linkable":110,"proposed":110,"self":110},"LM-Symmetric",[127,131,133,136,138,140,142,144,146,147,149,151,153,155,156,158,160,161,163,165,167,169,171,173,175,176,178,180,182,184,185,187,189,191,192,193,195,196,197,198,199,201,202,203,205,207,208,209,210,212,214,215,217,218,219,220,221,223,225,227,228,229,230,231,232,234,235,236,237,238,239,240,241,244,245,247,248,249,250,251,252,254,255,256,257,258,260,261,262,264,265,266,267,268,270,271],[128,128,128,129,130,128,130,130,128],0,22,-1,[68,128,128,132,130,128,130,130,68],98,[134,128,128,135,130,128,130,130,68],2,99,[137,128,128,135,130,128,130,130,68],3,[139,128,128,135,130,128,130,130,68],4,[141,128,128,135,130,128,130,130,68],5,[143,128,128,135,130,128,130,130,68],6,[145,128,128,135,130,128,130,130,68],7,[128,128,68,145,130,128,130,130,68],[68,128,68,148,130,128,130,130,68],69,[134,128,68,150,130,128,130,130,68],66,[137,128,68,152,130,128,130,130,68],73,[139,128,68,154,130,128,130,130,68],81,[141,128,68,154,130,128,130,130,68],[143,128,68,157,130,128,130,130,68],78,[145,128,68,159,130,128,130,130,68],89,[128,128,134,134,130,128,130,130,68],[68,128,134,162,130,128,130,130,68],53,[134,128,134,164,130,128,130,130,68],62,[137,128,134,166,130,128,130,130,68],65,[139,128,134,168,130,128,130,130,68],77,[141,128,134,170,130,128,130,130,68],82,[143,128,134,172,130,128,130,130,68],58,[145,128,134,174,130,128,130,130,68],79,[128,128,137,134,130,128,130,130,68],[68,128,137,177,130,128,130,130,68],40,[134,128,137,179,130,128,130,130,68],44,[137,128,137,181,130,128,130,130,68],51,[139,128,137,183,130,128,130,130,68],59,[141,128,137,166,130,128,130,130,68],[143,128,137,186,130,128,130,130,68],47,[145,128,137,188,130,128,130,130,68],70,[128,128,139,190,130,128,130,130,68],92,[68,128,139,135,130,128,130,130,68],[134,128,139,135,130,128,130,130,68],[137,128,139,194,130,128,130,130,68],100,[139,128,139,135,130,128,130,130,68],[141,128,139,135,130,128,130,130,68],[143,128,139,135,130,128,130,130,68],[145,128,139,135,130,128,130,130,68],[128,128,141,200,130,128,130,130,68],67,[68,128,141,159,130,128,130,130,68],[134,128,141,170,130,128,130,130,68],[137,128,141,204,130,128,130,130,68],91,[139,128,141,206,130,128,130,130,68],85,[141,128,141,206,130,128,130,130,68],[143,128,141,159,130,128,130,130,68],[145,128,141,204,130,128,130,130,68],[128,128,143,211,130,128,130,130,68],49,[68,128,143,213,130,128,130,130,68],80,[134,128,143,154,130,128,130,130,68],[137,128,143,216,130,128,130,130,68],86,[139,128,143,170,130,128,130,130,68],[141,128,143,216,130,128,130,130,68],[143,128,143,213,130,128,130,130,68],[145,128,143,206,130,128,130,130,68],[128,128,145,222,130,128,130,130,68],43,[68,128,145,224,130,128,130,130,68],71,[134,128,145,226,130,128,130,130,68],68,[137,128,145,157,130,128,130,130,68],[139,128,145,226,130,128,130,130,68],[141,128,145,152,130,128,130,130,68],[143,128,145,152,130,128,130,130,68],[145,128,145,157,130,128,130,130,68],[128,128,233,135,130,128,130,130,68],8,[68,128,233,135,130,128,130,130,68],[134,128,233,135,130,128,130,130,68],[137,128,233,194,130,128,130,130,68],[139,128,233,135,130,128,130,130,68],[141,128,233,135,130,128,130,130,68],[143,128,233,135,130,128,130,130,68],[145,128,233,135,130,128,130,130,68],[128,128,242,243,130,128,130,130,68],9,88,[68,128,242,159,130,128,130,130,68],[134,128,242,246,130,128,130,130,68],83,[137,128,242,204,130,128,130,130,68],[139,128,242,206,130,128,130,130,68],[141,128,242,206,130,128,130,130,68],[143,128,242,159,130,128,130,130,68],[145,128,242,204,130,128,130,130,68],[128,128,253,168,130,128,130,130,68],10,[68,128,253,170,130,128,130,130,68],[134,128,253,170,130,128,130,130,68],[137,128,253,243,130,128,130,130,68],[139,128,253,246,130,128,130,130,68],[141,128,253,259,130,128,130,130,68],87,[143,128,253,154,130,128,130,130,68],[145,128,253,216,130,128,130,130,68],[128,128,263,224,130,128,130,130,68],11,[68,128,263,152,130,128,130,130,68],[134,128,263,148,130,128,130,130,68],[137,128,263,213,130,128,130,130,68],[139,128,263,148,130,128,130,130,68],[141,128,263,269,130,128,130,130,68],74,[143,128,263,269,130,128,130,130,68],[145,128,263,174,130,128,130,130,68],[],[73],[],[],[277,278],"Numerals printed in Fig. 5 heatmap cells: % of 1000 random initial transforms (given rotation about a random axis, translation as fraction of mesh size), averaged over all bunny scan pairs with IOU > 20%, that end within 1% of mesh size of ground truth; 4 of 24 cells per variant and iteration budget transcribed","Same setting as other Fig. 5 rows",[],1790510665971]