[{"data":1,"prerenderedAt":420},["ShallowReactive",2],{"method-kazhdan2006poisson":3},{"method":4,"reference":42,"equipment":63,"figures":64,"results":65},{"id":5,"label":6,"shortName":7,"title":7,"year":8,"era":9,"cluster":10,"scope":11,"keyIdeaZh":12,"keyIdeaEn":13,"fulltextStatus":14,"publicationStatus":15,"recommendation":16,"constructionRelevance":17,"validationEnvironment":18,"strengths":21,"limitations":24,"sensors":27,"platform":28,"estimator":29,"association":29,"timeModel":29,"deskew":29,"loopClosure":29,"globalOptimization":30,"mapRepresentation":31,"prior":32,"outputGeometry":33,"compute":34,"codeUrl":35,"codeLicense":36,"relatedVersions":37},"kazhdan2006poisson","Kazhdan et al., 2006","Poisson Surface Reconstruction",2006,"classic","C12","map_representation_or_reconstruction","作者指出定向點（oriented points）的法向量可視為實體指示函數（indicator function）梯度的取樣，於是把表面重建轉為泊松方程式求解，再擷取等值面成為封閉網格。解法一次考慮全部點，不需啟發式分區與混合，因而對雜訊具韌性；並在八元樹上以局部支撐基底形成稀疏且條件良好的線性系統，另處理非均勻取樣。","Casts reconstruction from oriented points as a Poisson problem for an indicator function solved globally on an adaptive octree, then extracts a watertight isosurface.","full_text_reviewed","peer_reviewed_published","main_body","原論文以物件掃描資料（Stanford Bunny、Dragon、Happy Buddha、Forma Urbis Romae 殘片、David）示範，未涉及營建。作者自述不使用視線資訊，因此在無資料處會把分離的部件連起來（Fig. 6）；加上封閉曲面假設，在開放的室外或施工場景需額外修剪（依 Vizzo et al. 2021）。",[19,20],"public_benchmark","controlled_experiment",[22,23],"[\"Global solution without heuristic partitioning, resilient to noise (Sec. 1).\", \"Sparse, well-conditioned system via locally supported octree basis (Sec. 1, Sec. 2).\", \"Recovers sharp creases where VRIP shows 'lipping' which the authors attribute to VRIP's distance function being grown perpendicular to the view direction rather than to the surface normal (Forma Urbis fragment and Happy Buddha, Sec. 5.2, Figs. 5-6).\", \"Time and memory roughly quadratic in resolution","the David head at depth 11 (215,613,477 samples) took 1.9 h and 5.2 GB and produced 16,328,329 triangles (Sec. 5.3, Table 1).\", \"Adaptive filter width gives smoother fits than the fixed-resolution FFT method in sparsely sampled regions without losing detail elsewhere (Sec. 5.2, Fig. 7).\"]",[25,26],"[\"Does not use acquisition-modality information such as line of sight: with no samples between the Happy Buddha's feet the surface connects them, whereas VRIP carves them apart (Sec. 5.2 'Limitation of our approach', Fig. 6).\", \"On the Stanford Bunny (Poisson at depth 9) it was neither fastest nor most memory-efficient: 263 s and 310 MB, versus 28 s for the fastest method (MPU) and 186 MB for the most memory-efficient (VRIP) (Sec. 5.3, Table 2).\", \"Requires oriented normals","for the bunny they were estimated from neighbouring positions (Sec. 5.2).\", \"Follow-up by the same group reports a tendency to over-smooth the data (Kazhdan and Hoppe 2013, Sec. 1).\", \"Follow-up LiDAR work reports that the watertight assumption extrapolates surfaces where no data exist, requiring density-based trimming (Vizzo et al. 2021, Sec. III-B).\"]",[],[],"not_applicable","global Poisson solve over all oriented points (octree, multiscale)","implicit indicator function on an adaptive octree","oriented normals required","watertight triangle mesh (isosurface of the indicator function)","offline (hardware and processor type not reported); conjugate-gradient solve per octree depth in a multigrid-like scheme with block Gauss-Seidel to cap memory (Sec. 4.3); time and memory in Tables 1-2","https:\u002F\u002Fgithub.com\u002Fmkazhdan\u002FPoissonRecon","MIT (repository LICENSE; repository is the first author's and implements the later screened version)",[38],{"relation":39,"title":40,"doi_or_url":41},"follow_up_method","Screened poisson surface reconstruction (Kazhdan and Hoppe, ACM TOG 2013), a later extension of the method by a subset of the authors, not a journal version of this paper","10.1145\u002F2487228.2487237",{"id":5,"kind":43,"shortName":7,"title":7,"authors":44,"year":8,"venue":48,"venueType":49,"publisher":50,"volumeIssuePages":51,"doi":52,"arxivId":53,"url":54,"firstPublicDate":55,"publicationStatus":15,"metadataStatus":56,"fulltextStatus":14,"era":9,"classicReason":57,"codeUrl":35,"cluster":10,"topics":58,"mdpi":59,"verification":60,"label":6,"fulltextRoute":61,"versionRead":62,"addedByCensus":59},"method",[45,46,47],"Michael Kazhdan","Matthew Bolitho","Hugues Hoppe","Eurographics Symposium on Geometry Processing (SGP 2006)","conference","The Eurographics Association","pp. 61-70","10.2312\u002Fsgp\u002Fsgp06\u002F061-070",null,"https:\u002F\u002Fapi.datacite.org\u002Fdois\u002F10.2312\u002FSGP\u002FSGP06\u002F061-070","2006","metadata_verified","principle reused: global indicator-function fitting from oriented points via a sparse Poisson system; used directly by PUMA and as an offline baseline by ImMesh.",[10],false,"corrected","author copy","Author-hosted PDF of the SGP 2006 paper (hhoppe.com\u002Fpoissonrecon.pdf, 10 pp., each page marked '© The Eurographics Association 2006'); Eurographics Digital Library copy not compared",[],[],{"totalRows":66,"groupCount":67,"groups":68,"others":413},35,5,[69,244,295,379],{"slug":70,"group":71,"sourceId":72,"sourceLabel":73,"table":74,"selfRows":75,"metrics":76,"seqs":84,"entrants":100,"cells":110,"outcomes":236,"locators":238,"hardware":239,"wordings":241,"notes":242},"kazhdan2013screened-table-i","kazhdan2013screened:Table I","kazhdan2013screened","Kazhdan & Hoppe, 2013","Table I",16,[77,81],{"label":78,"unit":79,"statistic":80,"alignment":80},"Time in seconds","s","not_reported",{"label":82,"unit":83,"statistic":80,"alignment":80},"Memory in MB","MB",[85,89,91,93,95,97,98,99],{"dataset":86,"sequence":87,"environment":88},"Neptune (Aim@Shape)","depth 8","object scan",{"dataset":86,"sequence":90,"environment":88},"depth 9",{"dataset":86,"sequence":92,"environment":88},"depth 10",{"dataset":86,"sequence":94,"environment":88},"depth 11",{"dataset":96,"sequence":87,"environment":88},"David (Stanford 3D Scanning Repository)",{"dataset":96,"sequence":90,"environment":88},{"dataset":96,"sequence":92,"environment":88},{"dataset":96,"sequence":94,"environment":88},[101,104,106,108],{"name":102,"methodId":5,"linkable":103,"proposed":59,"self":103},"Poisson",true,{"name":105,"methodId":53,"linkable":59,"proposed":59,"self":59},"Wavelet",{"name":107,"methodId":53,"linkable":59,"proposed":59,"self":59},"SSD",{"name":109,"methodId":72,"linkable":103,"proposed":103,"self":59},"Screened",[111,115,118,121,123,125,127,129,131,133,134,136,138,140,142,144,146,148,150,152,154,156,157,159,161,163,165,167,169,171,173,175,177,179,180,182,184,186,187,189,191,193,195,197,199,201,203,205,207,209,210,212,214,216,218,220,222,225,227,229,231,233,234],[112,112,112,113,114,112,112,114,112],0,10,-1,[116,112,112,117,114,112,112,114,112],1,3,[119,112,112,120,114,112,112,114,112],2,275,[117,112,112,122,114,112,112,114,112],14,[112,116,112,124,114,112,112,114,112],113,[116,116,112,126,114,112,112,114,112],4,[119,116,112,128,114,112,112,114,112],238,[117,116,112,130,114,112,112,114,112],133,[112,112,116,132,114,112,112,114,112],25,[116,112,116,126,114,112,112,114,112],[119,112,116,135,114,112,112,114,112],547,[117,112,116,137,114,112,112,114,112],20,[112,116,116,139,114,112,112,114,112],149,[116,116,116,141,114,112,112,114,112],11,[119,116,116,143,114,112,112,114,112],455,[117,116,116,145,114,112,112,114,112],269,[112,112,119,147,114,112,112,114,112],89,[116,112,119,149,114,112,112,114,112],6,[119,112,119,151,114,112,112,114,112],3302,[117,112,119,153,114,112,112,114,112],44,[112,116,119,155,114,112,112,114,112],422,[116,116,119,66,114,112,112,114,112],[119,116,119,158,114,112,112,114,112],1247,[117,116,119,160,114,112,112,114,112],604,[112,112,117,162,114,112,112,114,112],320,[116,112,117,164,114,112,112,114,112],9,[119,112,117,166,114,112,112,114,112],15441,[117,112,117,168,114,112,112,114,112],126,[112,116,117,170,114,112,112,114,112],1387,[116,116,117,172,114,112,112,114,112],118,[119,116,117,174,114,112,112,114,112],3495,[117,116,117,176,114,112,112,114,112],1622,[112,112,126,178,114,112,112,114,112],41,[116,112,126,164,114,112,112,114,112],[119,112,126,181,114,112,112,114,112],492,[117,112,126,183,114,112,112,114,112],48,[112,116,126,185,114,112,112,114,112],427,[116,116,126,141,114,112,112,114,112],[119,116,126,188,114,112,112,114,112],863,[117,116,126,190,114,112,112,114,112],454,[112,112,67,192,114,112,112,114,112],108,[116,112,67,194,114,112,112,114,112],12,[119,112,67,196,114,112,112,114,112],2355,[117,112,67,198,114,112,112,114,112],73,[112,116,67,200,114,112,112,114,112],510,[116,116,67,202,114,112,112,114,112],38,[119,116,67,204,114,112,112,114,112],1724,[117,116,67,206,114,112,112,114,112],932,[112,112,149,208,114,112,112,114,112],412,[116,112,149,137,114,112,112,114,112],[119,112,149,211,114,112,112,114,112],19158,[117,112,149,213,114,112,112,114,112],182,[112,116,149,215,114,112,112,114,112],1498,[116,116,149,217,114,112,112,114,112],151,[119,116,149,219,114,112,112,114,112],4895,[117,116,149,221,114,112,112,114,112],2194,[112,112,223,224,114,112,112,114,112],7,1710,[116,112,223,226,114,112,112,114,112],43,[117,112,223,228,114,112,112,114,112],609,[112,116,223,230,114,112,112,114,112],5318,[116,116,223,232,114,112,112,114,112],545,[119,116,223,53,112,112,112,114,112],[117,116,223,235,114,112,112,114,112],6188,[237],">8192 MB; exceeded available RAM",[74],[240],"laptop, quad-core Intel Core i7, 8 GB RAM",[],[243],"Wall-clock time and memory for Neptune and David at depths 8 to 11; screening weight alpha = 4, Neumann boundaries, samples-per-node 1; bracketed values are the new solver with alpha = 0; dagger: SSD at David depth 11 reports CPU user time because memory exceeded RAM",{"slug":245,"group":246,"sourceId":5,"sourceLabel":6,"table":247,"selfRows":194,"metrics":248,"seqs":257,"entrants":264,"cells":266,"outcomes":289,"locators":290,"hardware":291,"wordings":292,"notes":293},"kazhdan2006poisson-table-1","kazhdan2006poisson:Table 1","Table 1",[249,251,254],{"label":250,"unit":79,"statistic":80,"alignment":80},"Time (s)",{"label":252,"unit":83,"statistic":253,"alignment":80},"Peak Memory (MB)","max",{"label":255,"unit":256,"statistic":80,"alignment":80},"# of Tris.","triangles",[258,261,262,263],{"dataset":259,"sequence":260,"environment":88},"Stanford dragon","depth 7",{"dataset":259,"sequence":87,"environment":88},{"dataset":259,"sequence":90,"environment":88},{"dataset":259,"sequence":92,"environment":88},[265],{"name":102,"methodId":5,"linkable":103,"proposed":103,"self":103},[267,268,270,272,274,276,278,279,281,283,285,287],[112,112,112,149,114,112,114,114,112],[112,116,112,269,114,112,114,114,112],19,[112,119,112,271,114,112,114,114,112],21000,[112,112,116,273,114,112,114,114,112],26,[112,116,116,275,114,112,114,114,112],75,[112,119,116,277,114,112,114,114,112],90244,[112,112,119,168,114,112,114,114,112],[112,116,119,280,114,112,114,114,112],155,[112,119,119,282,114,112,114,114,112],374868,[112,112,117,284,114,112,114,114,112],633,[112,116,117,286,114,112,114,114,112],699,[112,119,117,288,114,112,114,114,112],1516806,[],[247],[],[],[294],"Dragon model reconstructed at octree depths 7 to 10; kernel depth 6 for density estimation; hardware not reported",{"slug":296,"group":297,"sourceId":5,"sourceLabel":6,"table":298,"selfRows":117,"metrics":299,"seqs":303,"entrants":307,"cells":324,"outcomes":373,"locators":374,"hardware":375,"wordings":376,"notes":377},"kazhdan2006poisson-table-2","kazhdan2006poisson:Table 2","Table 2",[300,301,302],{"label":250,"unit":79,"statistic":80,"alignment":80},{"label":252,"unit":83,"statistic":253,"alignment":80},{"label":255,"unit":256,"statistic":80,"alignment":80},[304],{"dataset":305,"sequence":306,"environment":88},"Stanford Bunny","raw data, 362,000 points (Poisson at depth 9)",[308,310,312,314,316,318,321,323],{"name":309,"methodId":53,"linkable":59,"proposed":59,"self":59},"Power Crust",{"name":311,"methodId":53,"linkable":59,"proposed":59,"self":59},"Robust Cocone",{"name":313,"methodId":53,"linkable":59,"proposed":59,"self":59},"FastRBF",{"name":315,"methodId":53,"linkable":59,"proposed":59,"self":59},"MPU",{"name":317,"methodId":53,"linkable":59,"proposed":59,"self":59},"Hoppe et al 1992",{"name":319,"methodId":320,"linkable":103,"proposed":59,"self":59},"VRIP","curless1996volumetric",{"name":322,"methodId":53,"linkable":59,"proposed":59,"self":59},"FFT",{"name":102,"methodId":5,"linkable":103,"proposed":103,"self":103},[325,327,329,331,333,335,337,339,341,343,345,347,349,351,353,355,357,359,361,363,365,367,369,371],[112,112,112,326,114,112,114,114,112],380,[116,112,112,328,114,112,114,114,112],892,[119,112,112,330,114,112,114,114,112],4919,[117,112,112,332,114,112,114,114,112],28,[126,112,112,334,114,112,114,114,112],70,[67,112,112,336,114,112,114,114,112],86,[149,112,112,338,114,112,114,114,112],125,[223,112,112,340,114,112,114,114,112],263,[112,116,112,342,114,112,114,114,112],2653,[116,116,112,344,114,112,114,114,112],544,[119,116,112,346,114,112,114,114,112],796,[117,116,112,348,114,112,114,114,112],260,[126,116,112,350,114,112,114,114,112],330,[67,116,112,352,114,112,114,114,112],186,[149,116,112,354,114,112,114,114,112],1684,[223,116,112,356,114,112,114,114,112],310,[112,119,112,358,114,112,114,114,112],554332,[116,119,112,360,114,112,114,114,112],272662,[119,119,112,362,114,112,114,114,112],1798154,[117,119,112,364,114,112,114,114,112],925240,[126,119,112,366,114,112,114,114,112],950562,[67,119,112,368,114,112,114,114,112],1038055,[149,119,112,370,114,112,114,114,112],910320,[223,119,112,372,114,112,114,114,112],911390,[],[298],[],[],[378],"Stanford Bunny raw data (362,000 points from ten range images), processed to fit each algorithm's input format; Poisson reconstructed at octree depth 9, resolution settings of the other seven methods not reported (VRIP used the registered scans with confidence values); running time in seconds, peak memory in MB, output triangles; hardware not reported",{"slug":380,"group":381,"sourceId":5,"sourceLabel":6,"table":382,"selfRows":117,"metrics":383,"seqs":392,"entrants":396,"cells":398,"outcomes":405,"locators":406,"hardware":409,"wordings":410,"notes":411},"kazhdan2006poisson-text-sec-5-3","kazhdan2006poisson:Text Sec. 5.3","Text Sec. 5.3",[384,387,390],{"label":385,"unit":386,"statistic":80,"alignment":80},"computation time","h",{"label":388,"unit":389,"statistic":80,"alignment":80},"RAM","GB",{"label":391,"unit":256,"statistic":80,"alignment":80},"output triangles",[393],{"dataset":394,"sequence":395,"environment":88},"David (non-rigidly aligned scans)","head, depth 11",[397],{"name":102,"methodId":5,"linkable":103,"proposed":103,"self":103},[399,401,403],[112,112,112,400,114,112,114,114,112],1.9,[112,116,112,402,114,116,114,114,112],5.2,[112,119,112,404,114,116,114,114,112],16328329,[],[407,408],"Sec. 5.3, Fig. 8","Sec. 5.3",[],[],[412],"Head of Michelangelo's David at depth 11 from 215,613,477 samples",[414],{"group":415,"slug":416,"sourceLabel":73,"table":417,"selfRows":116,"datasets":418},"kazhdan2013screened:Text Sec. 1","kazhdan2013screened-text-sec-1","Text Sec. 1",[419],"David (Digital Michelangelo, 11.4M-point subset)",1790510665696]