[{"data":1,"prerenderedAt":182},["ShallowReactive",2],{"method-lorensen1987marchingcubes":3},{"method":4,"reference":38,"equipment":57,"figures":74,"results":75},{"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":20,"limitations":24,"sensors":28,"platform":29,"estimator":30,"association":30,"timeModel":30,"deskew":30,"loopClosure":30,"globalOptimization":31,"mapRepresentation":32,"prior":31,"outputGeometry":33,"compute":34,"codeUrl":35,"codeLicense":36,"relatedVersions":37},"lorensen1987marchingcubes","Lorensen & Cline, 1987","Marching Cubes","Marching cubes: A high resolution 3D surface construction algorithm",1987,"classic","C12","map_representation_or_reconstruction","此演算法把三維體積資料（原文為 CT、MR、SPECT 醫學影像）以相鄰兩張切片各四個像素組成邏輯立方體，依八個頂點數值是否達到門檻得到 8 位元索引，查詢由 256 種情形（利用互補與旋轉對稱歸納為 14 種樣式）建立的邊交點表決定三角面拓樸，再以線性內插定出三角形頂點，並以中央差分梯度內插出頂點法向量，藉此擷取等值面（isosurface）成為三角網格。後續 TSDF 管線（如 Voxblox、nvblox、VDBFusion、Mesh-LOAM）與 Poisson 類重建常以它或其八元樹變體把隱式場轉為可輸出的網格；體素雜湊等系統也可改以射線投射（ray casting）直接渲染表面。","Builds logical cubes from two adjacent slices, indexes each cube's 8 inside\u002Foutside vertex states into a 256-case edge table (14 patterns by complementary and rotational symmetry), places triangle vertices by linear interpolation and assigns normals from interpolated central-difference gradients.","full_text_reviewed","peer_reviewed_published","background","原論文以醫學體積資料示範，未涉及營建場域；在本主題中的角色是 TSDF 或 Poisson 管線輸出網格的共同步驟。",[],[21,22,23],"Maintains inter-slice connectivity and gradient information, which the authors link to image detail (abstract).","Reusing edge intersections from previous pixels and lines speeds the algorithm up by a factor of three (Sec. 5.1).","The cube index supports Boolean cutting, capping and texture-mapped cut planes for solid modeling (Sec. 5.2).",[25,26,27],"Follow-up work (ImMesh, Lin et al. 2023, Sec. VIII-C4) reports that marching-cubes-based meshes (TSDF, Poisson) contain sliver triangles when a facet lies nearly parallel to cube edges.","Surface models can exceed 500,000 triangles; the authors reduce counts with cut planes, connectivity and by filtering or averaging slices at some loss of detail (Sec. 5.1, 6, 8).","(reviewer observation) No quantitative geometric accuracy assessment is given; quality is shown with rendered case studies (Sec. 7).",[],[],"not_applicable","none","scalar volume (3D grid) to triangle mesh","triangle mesh of a constant-value isosurface with per-vertex unit normals from interpolated density gradients (Sec. 4)","C implementation on Sun workstations, VAX (VMS) and IBM 3081; on a VAX 11\u002F780 model creation took 100 s for 64x64x48 SPECT data and 30 min for 260x260x93 CT data, about 12 times faster on the IBM 3081; display on a GE Graphicon 700 at 10,000 triangles per second (Sec. 6)",null,"not_verified",[],{"id":5,"kind":39,"shortName":7,"title":8,"authors":40,"year":9,"venue":43,"venueType":44,"publisher":45,"volumeIssuePages":46,"doi":47,"arxivId":35,"url":48,"firstPublicDate":49,"publicationStatus":16,"metadataStatus":50,"fulltextStatus":15,"era":10,"classicReason":51,"codeUrl":35,"cluster":11,"topics":52,"mdpi":53,"verification":54,"label":6,"fulltextRoute":55,"versionRead":56,"addedByCensus":53},"component",[41,42],"William E. Lorensen","Harvey E. Cline","Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '87)","conference","ACM","pp. 163-169","10.1145\u002F37401.37422","https:\u002F\u002Fapi.crossref.org\u002Fworks\u002F10.1145\u002F37401.37422","1987-08","metadata_verified","necessary technical node: the isosurface-to-triangle extraction step reused by TSDF pipelines (Voxblox, nvblox, VDBFusion, Mesh-LOAM) and by Poisson-type reconstruction to output meshes.",[11],false,"corrected","publisher OA","ACM version of record, PDF pp. 163-169 (page headers of Computer Graphics 21(4) and SIGGRAPH '87), free-access ACM Digital Library copy",[58,64,67,70],{"category":59,"model":60,"canonical":60,"role":61,"dataset":35,"specs":62,"locator":63},"compute","VAX 11\u002F780","compute for runtime","under VMS; 100 s to 30 min per model","Sec. 6",{"category":59,"model":65,"canonical":65,"role":61,"dataset":35,"specs":66,"locator":63},"IBM 3081","under IX\u002F370; about 12 times faster than the VAX 11\u002F780",{"category":59,"model":68,"canonical":68,"role":61,"dataset":35,"specs":69,"locator":63},"Sun Workstations","under Unix; no timing reported",{"category":71,"model":72,"canonical":72,"role":61,"dataset":35,"specs":73,"locator":63},"other","General Electric Graphicon 700","display system, 10,000 triangles per second",[],{"totalRows":76,"groupCount":77,"groups":78,"others":181},7,3,[79,128,158],{"slug":80,"group":81,"sourceId":5,"sourceLabel":6,"table":82,"selfRows":83,"metrics":84,"seqs":89,"entrants":102,"cells":106,"outcomes":119,"locators":120,"hardware":124,"wordings":125,"notes":126},"lorensen1987marchingcubes-text-sec-7","lorensen1987marchingcubes:Text Sec. 7","Text Sec. 7",4,[85],{"label":86,"unit":87,"statistic":88,"alignment":30},"number of triangles","triangles","not_reported",[90,94,96,99],{"dataset":91,"sequence":92,"environment":93},"CT head (93 axial slices, 1.5 mm, 0.8 mm pixels)","bone surface","medical volume data",{"dataset":91,"sequence":95,"environment":93},"soft tissue surface",{"dataset":97,"sequence":98,"environment":93},"MR head (128 coronal slices, 1.9 mm)","largest model incl. cut surface",{"dataset":100,"sequence":101,"environment":93},"SPECT heart (29 coronal slices, 64 x 64)","blood pool surface",[103],{"name":104,"methodId":5,"linkable":105,"proposed":105,"self":105},"marching cubes",true,[107,111,114,117],[108,108,108,109,110,108,110,110,108],0,550000,-1,[108,108,112,113,110,108,110,110,108],1,375000,[108,108,115,116,110,112,110,110,108],2,330000,[108,108,77,118,110,115,110,110,108],5000,[],[121,122,123],"Sec. 7.1","Sec. 7.2","Sec. 7.3",[],[],[127],"Triangle counts of the case-study models",{"slug":129,"group":130,"sourceId":5,"sourceLabel":6,"table":131,"selfRows":115,"metrics":132,"seqs":138,"entrants":145,"cells":147,"outcomes":152,"locators":153,"hardware":154,"wordings":155,"notes":156},"lorensen1987marchingcubes-text-sec-6","lorensen1987marchingcubes:Text Sec. 6","Text Sec. 6",[133,136],{"label":134,"unit":135,"statistic":88,"alignment":30},"model creation time on VAX 11\u002F780","s",{"label":137,"unit":135,"statistic":88,"alignment":30},"model creation time on VAX 11\u002F780 (30 minutes)",[139,142],{"dataset":140,"sequence":141,"environment":93},"SPECT study","64 x 64 x 48",{"dataset":143,"sequence":144,"environment":93},"CT study","260 x 260 x 93",[146],{"name":104,"methodId":5,"linkable":105,"proposed":105,"self":105},[148,150],[108,108,108,149,110,108,108,110,108],100,[108,112,112,151,110,108,108,110,108],1800,[],[63],[60],[],[157],"Implementation times and model sizes stated in the text; no accuracy evaluation; C implementation, times depend on number of surfaces and data resolution",{"slug":159,"group":160,"sourceId":5,"sourceLabel":6,"table":161,"selfRows":112,"metrics":162,"seqs":166,"entrants":169,"cells":172,"outcomes":174,"locators":175,"hardware":177,"wordings":178,"notes":179},"lorensen1987marchingcubes-text-sec-5-1","lorensen1987marchingcubes:Text Sec. 5.1","Text Sec. 5.1",[163],{"label":164,"unit":165,"statistic":88,"alignment":30},"speed-up from coherence","x",[167],{"dataset":168,"sequence":168,"environment":93},"",[170],{"name":171,"methodId":5,"linkable":105,"proposed":105,"self":105},"marching cubes with coherence",[173],[108,108,108,77,110,108,110,110,108],[],[176],"Sec. 5.1",[],[],[180],"Speed-up from reusing edge intersections of previous pixels and lines",[],1790510665257]