点云特征提取 详细 实用 经典的讲述过程及方法

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点云特征提取 详细 实用 经典的讲述过程及方法
65520808FeatureExtractionFromPointClouds.rar
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内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/62d68dea864d5c73accb8912/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62d68dea864d5c73accb8912/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">submitted<span class="_"> </span>for<span class="_"> </span>publication</div><div class="t m1 x2 h3 y1 ff1 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m1 x3 h4 y2 ff2 fs2 fc0 sc0 ls0 ws0">Feature<span class="_"> </span>Extraction<span class="_"> </span>from<span class="_"> </span>P<span class="_ _0"></span>oint<span class="_"> </span>Clouds</div><div class="t m1 x4 h5 y3 ff1 fs3 fc0 sc0 ls0 ws0">Stefan<span class="_"> </span>Gumhold</div><div class="t m2 x5 h6 y4 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#58883;</span></div><div class="t m1 x6 h5 y3 ff1 fs3 fc0 sc0 ls0 ws0">Xinlong<span class="_"> </span>W<span class="_ _0"></span>ang</div><div class="t m2 x7 h6 y4 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">y</span></div><div class="t m1 x8 h5 y5 ff1 fs3 fc0 sc0 ls0 ws0">Scienti&#64257;c<span class="_"> </span>Computing<span class="_ _1"> </span>and<span class="_"> </span>Imaging<span class="_ _1"> </span>Institute</div><div class="t m1 x9 h5 y6 ff1 fs3 fc0 sc0 ls0 ws0">Univ<span class="_ _2"></span>ersity<span class="_"> </span>of<span class="_ _1"> </span>Salt<span class="_"> </span>Lake<span class="_"> </span>City<span class="_ _0"></span>,<span class="_"> </span>Utah</div><div class="t m1 xa h5 y7 ff1 fs3 fc0 sc0 ls0 ws0">Rob<span class="_"> </span>MacLeod</div><div class="t m2 xb h6 y4 ff3 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">z</span></div><div class="t m1 x1 h3 y8 ff1 fs1 fc0 sc0 ls0 ws0">Figure<span class="_ _3"> </span>1:<span class="_ _4"> </span>a)<span class="_ _3"> </span>input<span class="_ _3"> </span>point<span class="_ _3"> </span>cloud.<span class="_ _5"> </span>b)<span class="_ _3"> </span>the<span class="_ _3"> </span>neighbor<span class="_ _6"> </span>graph.<span class="_ _4"> </span>c)<span class="_ _3"> </span>point<span class="_ _6"> </span>classi&#64257;cation.<span class="_ _4"> </span>d)<span class="_ _3"> </span>crease<span class="_ _6"> </span>pattern<span class="_ _3"> </span>forming.<span class="_ _5"> </span>e)<span class="_"> </span>puri&#64257;ed<span class="_ _6"> </span>crease<span class="_ _3"> </span>pattern.<span class="_ _5"> </span>f)<span class="_"> </span>spline</div><div class="t m1 x1 h3 y9 ff1 fs1 fc0 sc0 ls0 ws0">representation<span class="_"> </span>of<span class="_"> </span>crease<span class="_"> </span>pattern</div><div class="t m1 x1 h7 ya ff2 fs5 fc0 sc0 ls0 ws0">Abstract</div><div class="t m1 x1 h3 yb ff1 fs1 fc0 sc0 ls0 ws0">This<span class="_"> </span>paper<span class="_ _6"> </span>describes<span class="_ _3"> </span>a<span class="_ _3"> </span>new<span class="_"> </span>method<span class="_ _3"> </span>to<span class="_ _3"> </span>extract<span class="_"> </span>feature<span class="_ _3"> </span>lines<span class="_ _3"> </span>directly</div><div class="t m1 x1 h3 yc ff1 fs1 fc0 sc0 ls0 ws0">from<span class="_ _4"> </span>a<span class="_ _4"> </span>surf<span class="_ _2"></span>ace<span class="_ _4"> </span>point<span class="_ _4"> </span>cloud.<span class="_ _7"> </span>No<span class="_ _4"> </span>surface<span class="_ _4"> </span>reconstruction<span class="_ _4"> </span>is<span class="_ _6"> </span>needed</div><div class="t m1 x1 h3 yd ff1 fs1 fc0 sc0 ls0 ws0">in<span class="_ _3"> </span>advance,<span class="_ _6"> </span>only<span class="_ _3"> </span>the<span class="_ _6"> </span>inexpensi<span class="_ _2"></span>ve<span class="_ _3"> </span>computation<span class="_ _6"> </span>of<span class="_ _3"> </span>a<span class="_ _6"> </span>neighbor<span class="_ _6"> </span>graph</div><div class="t m1 x1 h3 ye ff1 fs1 fc0 sc0 ls0 ws0">connecting<span class="_ _3"> </span>nearby<span class="_"> </span>points.</div><div class="t m1 xc h3 yf ff1 fs1 fc0 sc0 ls0 ws0">The<span class="_"> </span>feature<span class="_ _1"> </span>e<span class="_ _2"></span>xtraction<span class="_"> </span>is<span class="_ _1"> </span>performed<span class="_"> </span>in<span class="_ _8"> </span>two<span class="_"> </span>stages.<span class="_ _3"> </span>The<span class="_"> </span>&#64257;rst<span class="_ _8"> </span>stage</div><div class="t m1 x1 h3 y10 ff1 fs1 fc0 sc0 ls0 ws0">constists<span class="_ _3"> </span>of<span class="_ _3"> </span>assigning<span class="_ _6"> </span>a<span class="_ _3"> </span>penalty<span class="_ _6"> </span>weight<span class="_ _3"> </span>to<span class="_ _3"> </span>each<span class="_ _6"> </span>point<span class="_ _3"> </span>that<span class="_ _3"> </span>indicates</div><div class="t m1 x1 h3 y11 ff1 fs1 fc0 sc0 ls0 ws0">the<span class="_ _4"> </span>unlikelihood<span class="_ _4"> </span>that<span class="_ _4"> </span>the<span class="_ _4"> </span>point<span class="_ _4"> </span>is<span class="_ _4"> </span>part<span class="_ _4"> </span>of<span class="_ _4"> </span>a<span class="_ _4"> </span>feature<span class="_ _4"> </span>and<span class="_ _4"> </span>assigning</div><div class="t m1 x1 h3 y12 ff1 fs1 fc0 sc0 ls0 ws0">these<span class="_ _3"> </span>penalty<span class="_ _3"> </span>weights<span class="_ _3"> </span>to<span class="_ _3"> </span>the<span class="_ _3"> </span>edges<span class="_ _3"> </span>of<span class="_ _3"> </span>a<span class="_ _3"> </span>neighbor<span class="_ _3"> </span>graph.<span class="_ _4"> </span>Extracting</div><div class="t m1 x1 h3 y13 ff1 fs1 fc0 sc0 ls0 ws0">a<span class="_ _3"> </span>subgraph<span class="_ _4"> </span>of<span class="_ _3"> </span>the<span class="_ _3"> </span>neighbor<span class="_ _6"> </span>graph<span class="_ _6"> </span>that<span class="_ _6"> </span>minimizes<span class="_ _6"> </span>the<span class="_ _6"> </span>edge<span class="_ _3"> </span>penalty</div><div class="t m1 x1 h3 y14 ff1 fs1 fc0 sc0 ls0 ws0">weights<span class="_ _6"> </span>then<span class="_ _6"> </span>produces<span class="_ _6"> </span>a<span class="_ _6"> </span>set<span class="_ _6"> </span>of<span class="_ _6"> </span>feature<span class="_ _6"> </span>patterns.<span class="_ _9"> </span>The<span class="_ _6"> </span>second<span class="_ _6"> </span>stage</div><div class="t m1 x1 h3 y15 ff1 fs1 fc0 sc0 ls0 ws0">is<span class="_ _4"> </span>especially<span class="_ _4"> </span>useful<span class="_ _5"> </span>for<span class="_ _4"> </span>noisy<span class="_ _4"> </span>data.<span class="_ _a"> </span>It<span class="_ _4"> </span>recovers<span class="_ _4"> </span>feature<span class="_ _4"> </span>lines<span class="_ _4"> </span>and</div><div class="t m1 x1 h3 y16 ff1 fs1 fc0 sc0 ls0 ws0">junctions<span class="_ _4"> </span>by<span class="_ _6"> </span>&#64257;tting<span class="_ _4"> </span>wedges<span class="_ _4"> </span>to<span class="_ _6"> </span>the<span class="_ _4"> </span>crease<span class="_ _4"> </span>lines<span class="_ _6"> </span>and<span class="_ _4"> </span>corners<span class="_ _4"> </span>to<span class="_ _6"> </span>the</div><div class="t m1 x1 h3 y17 ff1 fs1 fc0 sc0 ls0 ws0">junctions.</div><div class="t m1 xc h3 y18 ff1 fs1 fc0 sc0 ls0 ws0">As<span class="_"> </span>the<span class="_ _3"> </span>method<span class="_ _6"> </span>works<span class="_"> </span>on<span class="_ _3"> </span>the<span class="_ _3"> </span>local<span class="_"> </span>neighbor<span class="_ _6"> </span>graph<span class="_ _3"> </span>only<span class="_ _2"></span>,<span class="_"> </span>it<span class="_ _3"> </span>is<span class="_"> </span>fast</div><div class="t m1 x1 h3 y19 ff1 fs1 fc0 sc0 ls0 ws0">and<span class="_ _4"> </span>automatically<span class="_ _6"> </span>adapts<span class="_ _4"> </span>to<span class="_ _6"> </span>the<span class="_ _4"> </span>sampling<span class="_ _4"> </span>resolution.<span class="_ _b"> </span>This<span class="_ _6"> </span>makes</div><div class="t m1 x1 h3 y1a ff1 fs1 fc0 sc0 ls0 ws0">the<span class="_"> </span>approach<span class="_ _3"> </span>ideal<span class="_"> </span>as<span class="_"> </span>a<span class="_"> </span>preprocessing<span class="_ _3"> </span>step<span class="_"> </span>in<span class="_"> </span>mesh<span class="_"> </span>generation.</div><div class="t m1 x1 h8 y1b ff4 fs1 fc0 sc0 ls0 ws0">CR<span class="_ _a"> </span>Categories:<span class="_ _c"> </span><span class="ff1">I.4.6<span class="_ _a"> </span>Segmentation<span class="_ _a"> </span>[Edge<span class="_ _d"> </span>and<span class="_ _d"> </span>feature</span></div><div class="t m1 x1 h3 y1c ff1 fs1 fc0 sc0 ls0 ws0">detection]&#8212;;</div><div class="t m1 x1 h8 y1d ff4 fs1 fc0 sc0 ls0 ws0">Keyw<span class="_ _2"></span>ords:<span class="_ _b"> </span><span class="ff1">feature<span class="_ _3"> </span>detection,<span class="_"> </span>scattered<span class="_"> </span>data</span></div><div class="t m1 x1 h7 y1e ff2 fs5 fc0 sc0 ls0 ws0">1<span class="_ _e"> </span>Introduction</div><div class="t m1 x1 h3 y1f ff1 fs1 fc0 sc0 ls0 ws0">In<span class="_ _6"> </span>this<span class="_ _6"> </span>paper<span class="_ _6"> </span>we<span class="_ _6"> </span>consider<span class="_ _6"> </span>the<span class="_ _4"> </span>feature<span class="_ _3"> </span>detection<span class="_ _f"> </span>and<span class="_ _6"> </span>reconstruction</div><div class="t m1 x1 h3 y20 ff1 fs1 fc0 sc0 ls0 ws0">problem<span class="_"> </span>for<span class="_"> </span>the<span class="_"> </span>case<span class="_ _8"> </span>of<span class="_"> </span>the<span class="_"> </span>input<span class="_ _8"> </span>surface<span class="_"> </span>being<span class="_"> </span>described<span class="_"> </span>by<span class="_"> </span>a<span class="_ _8"> </span>point</div><div class="t m1 x1 h3 y21 ff1 fs1 fc0 sc0 ls0 ws0">cloud.<span class="_ _5"> </span>Figure<span class="_ _6"> </span>2<span class="_ _3"> </span>illustrates<span class="_ _6"> </span>for<span class="_ _3"> </span>the<span class="_ _6"> </span>surface<span class="_ _3"> </span>of<span class="_ _6"> </span>the<span class="_ _3"> </span>well<span class="_ _6"> </span>known<span class="_ _3"> </span>Stan-</div><div class="t m1 x1 h3 y22 ff1 fs1 fc0 sc0 ls0 ws0">ford<span class="_ _3"> </span>bunny<span class="_ _6"> </span>the<span class="_ _3"> </span>different<span class="_ _3"> </span>types<span class="_ _6"> </span>of<span class="_ _6"> </span>feature<span class="_ _6"> </span>elements<span class="_ _3"> </span>that<span class="_ _6"> </span>we<span class="_ _6"> </span>want<span class="_ _3"> </span>to</div><div class="t m1 x1 h3 y23 ff1 fs1 fc0 sc0 ls0 ws0">extract.<span class="_ _5"> </span>The<span class="_ _3"> </span>crease<span class="_ _3"> </span>pattern,<span class="_ _6"> </span>shown<span class="_ _3"> </span>in<span class="_ _6"> </span>dark<span class="_ _3"> </span>blue,<span class="_ _6"> </span>consists<span class="_ _3"> </span>of<span class="_ _6"> </span>crease</div><div class="t m1 x1 h3 y24 ff1 fs1 fc0 sc0 ls0 ws0">lines<span class="_ _4"> </span>that<span class="_ _4"> </span>either<span class="_ _5"> </span>terminate<span class="_ _4"> </span>in<span class="_ _4"> </span>junctions<span class="_ _5"> </span>or<span class="_ _4"> </span>singleton<span class="_ _5"> </span>ends<span class="_ _4"> </span>or<span class="_ _4"> </span>they</div><div class="t m1 x1 h3 y25 ff1 fs1 fc0 sc0 ls0 ws0">close<span class="_ _f"> </span>to<span class="_ _f"> </span>form<span class="_ _4"> </span>a<span class="_ _f"> </span>loop.<span class="_ _10"> </span>The<span class="_ _f"> </span>border<span class="_ _4"> </span>pattern<span class="_ _f"> </span>consists<span class="_ _f"> </span>only<span class="_ _4"> </span>of<span class="_ _f"> </span>border</div><div class="t m1 x1 h3 y26 ff1 fs1 fc0 sc0 ls0 ws0">loops.<span class="_ _7"> </span>Input<span class="_ _f"> </span>points<span class="_ _4"> </span>that<span class="_ _f"> </span>lay<span class="_ _4"> </span>on<span class="_ _4"> </span>a<span class="_ _f"> </span>crease<span class="_ _4"> </span>are<span class="_ _f"> </span>called<span class="_ _4"> </span>crease<span class="_ _4"> </span>points,</div><div class="t m1 x1 h3 y27 ff1 fs1 fc0 sc0 ls0 ws0">points<span class="_"> </span>on<span class="_ _3"> </span>the<span class="_ _3"> </span>border<span class="_ _3"> </span>loops<span class="_ _3"> </span>are<span class="_"> </span>border<span class="_ _3"> </span>points.<span class="_ _f"> </span>At<span class="_ _3"> </span>a<span class="_"> </span>junction<span class="_ _3"> </span>the<span class="_ _3"> </span>cor-</div><div class="t m1 x1 h3 y28 ff1 fs1 fc0 sc0 ls0 ws0">responding<span class="_ _4"> </span>data<span class="_ _4"> </span>point<span class="_ _4"> </span>is<span class="_ _4"> </span>called<span class="_ _4"> </span>a<span class="_ _4"> </span>corner<span class="_ _4"> </span>or<span class="_ _4"> </span>junction<span class="_ _5"> </span>point<span class="_ _f"> </span>and<span class="_ _4"> </span>at</div><div class="t m1 x1 h3 y29 ff1 fs1 fc0 sc0 ls0 ws0">singleton<span class="_"> </span>ends<span class="_"> </span>we<span class="_"> </span>&#64257;nd<span class="_"> </span>end<span class="_"> </span>points.<span class="_ _3"> </span>The<span class="_"> </span>feature<span class="_"> </span>extraction<span class="_"> </span>algorithm</div><div class="t m2 xc h6 y2a ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">&#58883;</span></div><div class="t m1 xd h9 y2b ff1 fs6 fc0 sc0 ls0 ws0">stefan@gumhold.com</div><div class="t m2 xc h6 y2c ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">y</span></div><div class="t m1 xd h9 y2d ff1 fs6 fc0 sc0 ls0 ws0">wangxl@cs.utah.edu</div><div class="t m2 xc h6 y2e ff5 fs4 fc0 sc0 ls0 ws0"><span class="fc1 sc0">z</span></div><div class="t m1 xd h9 y2f ff1 fs6 fc0 sc0 ls0 ws0">macleod@cvrti.utah.edu</div><div class="t m1 xe h3 y30 ff1 fs1 fc0 sc0 ls0 ws0">Figure<span class="_"> </span>2:<span class="_ _6"> </span>dif<span class="_ _2"></span>ferent<span class="_"> </span>elements<span class="_"> </span>in<span class="_"> </span>the<span class="_"> </span>crease<span class="_"> </span>and<span class="_ _3"> </span>border<span class="_"> </span>patterns</div><div class="t m1 xf h3 y31 ff1 fs1 fc0 sc0 ls0 ws0">that<span class="_ _f"> </span>we<span class="_ _f"> </span>describe<span class="_ _4"> </span>here<span class="_ _4"> </span>is<span class="_ _f"> </span>fully<span class="_ _f"> </span>automated<span class="_ _4"> </span>and<span class="_ _4"> </span>no<span class="_ _4"> </span>seed<span class="_ _f"> </span>or<span class="_ _4"> </span>junction</div><div class="t m1 xf h3 y32 ff1 fs1 fc0 sc0 ls0 ws0">points<span class="_"> </span>need<span class="_"> </span>to<span class="_"> </span>be<span class="_ _3"> </span>marked<span class="_"> </span>by<span class="_"> </span>the<span class="_"> </span>user<span class="_ _2"></span>.</div><div class="t m1 x10 h3 y33 ff1 fs1 fc0 sc0 ls0 ws0">Figure<span class="_ _4"> </span>1<span class="_ _4"> </span>illustrates<span class="_ _4"> </span>our<span class="_ _4"> </span>feature<span class="_ _4"> </span>extraction<span class="_ _4"> </span>pipeline.<span class="_ _d"> </span>The<span class="_ _4"> </span>input</div><div class="t m1 xf h3 y34 ff1 fs1 fc0 sc0 ls0 ws0">is<span class="_ _6"> </span>a<span class="_ _6"> </span>point<span class="_ _6"> </span>cloud<span class="_ _f"> </span>a);<span class="_ _4"> </span>in<span class="_ _6"> </span>this<span class="_ _6"> </span>case<span class="_ _f"> </span>the<span class="_ _f"> </span>underlying<span class="_ _f"> </span>surface<span class="_ _6"> </span>is<span class="_ _6"> </span>a<span class="_ _f"> </span>model</div><div class="t m1 xf h3 y35 ff1 fs1 fc0 sc0 ls0 ws0">of<span class="_ _3"> </span>the<span class="_ _6"> </span>human<span class="_ _6"> </span>torso.<span class="_ _9"> </span>In<span class="_ _3"> </span>the<span class="_ _6"> </span>analysis<span class="_ _6"> </span>stage<span class="_ _6"> </span>we<span class="_ _3"> </span>construct<span class="_ _6"> </span>a<span class="_ _6"> </span>neighbor</div><div class="t m1 xf h3 y36 ff1 fs1 fc0 sc0 ls0 ws0">graph<span class="_ _3"> </span>b)<span class="_ _6"> </span>on<span class="_ _3"> </span>the<span class="_ _6"> </span>point<span class="_ _3"> </span>cloud<span class="_ _6"> </span>that<span class="_ _3"> </span>re&#64258;ects<span class="_ _3"> </span>proximity<span class="_ _2"></span>.<span class="_ _5"> </span>The<span class="_ _3"> </span>classi&#64257;ca-</div><div class="t m1 xf h3 y37 ff1 fs1 fc0 sc0 ls0 ws0">tion<span class="_"> </span>stage<span class="_"> </span>that<span class="_ _3"> </span>follows<span class="_"> </span>&#64257;ts<span class="_"> </span>ellipsoids<span class="_"> </span>c)<span class="_"> </span>to<span class="_ _3"> </span>the<span class="_"> </span>neighborhoods<span class="_ _6"> </span>of<span class="_"> </span>the</div><div class="t m1 xf h3 y38 ff1 fs1 fc0 sc0 ls0 ws0">input<span class="_"> </span>points,<span class="_"> </span>approximates<span class="_ _3"> </span>the<span class="_ _3"> </span>surface<span class="_"> </span>curvature<span class="_"> </span>and<span class="_"> </span>the<span class="_ _3"> </span>maximum</div><div class="t m1 xf h3 y39 ff1 fs1 fc0 sc0 ls0 ws0">open<span class="_ _6"> </span>angle;<span class="_ _4"> </span>the<span class="_ _6"> </span>latter<span class="_ _f"> </span>is<span class="_ _6"> </span>used<span class="_ _f"> </span>to<span class="_ _6"> </span>detect<span class="_ _f"> </span>border<span class="_ _f"> </span>points.<span class="_ _11"> </span>From<span class="_ _6"> </span>these</div><div class="t m1 xf h3 y3a ff1 fs1 fc0 sc0 ls0 ws0">vertex<span class="_"> </span>properties<span class="_ _6"> </span>we<span class="_"> </span>de&#64257;ne<span class="_ _6"> </span>crease<span class="_ _3"> </span>and<span class="_ _6"> </span>border<span class="_ _3"> </span>penalty<span class="_ _6"> </span>weights<span class="_ _3"> </span>that</div><div class="t m1 xf h3 y3b ff1 fs1 fc0 sc0 ls0 ws0">measure<span class="_"> </span>the<span class="_"> </span>unlikelihood<span class="_ _3"> </span>that<span class="_"> </span>a<span class="_"> </span>speci&#64257;c<span class="_"> </span>point<span class="_"> </span>is<span class="_ _3"> </span>on<span class="_"> </span>a<span class="_"> </span>crease<span class="_"> </span>or<span class="_ _3"> </span>bor-</div><div class="t m1 xf h3 y3c ff1 fs1 fc0 sc0 ls0 ws0">der<span class="_ _3"> </span>line,<span class="_ _6"> </span>respectiv<span class="_ _2"></span>ely<span class="_ _0"></span>.<span class="_ _12"> </span>From<span class="_ _3"> </span>the<span class="_ _6"> </span>penalty<span class="_ _3"> </span>weights<span class="_ _6"> </span>at<span class="_ _3"> </span>the<span class="_ _6"> </span>vertices<span class="_ _3"> </span>we</div><div class="t m1 xf h3 y3d ff1 fs1 fc0 sc0 ls0 ws0">compute<span class="_ _6"> </span>penalty<span class="_ _6"> </span>weights<span class="_ _6"> </span>at<span class="_ _6"> </span>the<span class="_ _6"> </span>edges<span class="_ _f"> </span>of<span class="_ _6"> </span>the<span class="_ _6"> </span>neighbor<span class="_ _6"> </span>graph.<span class="_ _9"> </span>The</div><div class="t m1 xf h3 y3e ff1 fs1 fc0 sc0 ls0 ws0">feature<span class="_ _f"> </span>line<span class="_ _f"> </span>linkage<span class="_ _4"> </span>stage<span class="_ _f"> </span>&#64257;nds<span class="_ _4"> </span>spanning<span class="_ _f"> </span>patterns<span class="_ _4"> </span>in<span class="_ _f"> </span>the<span class="_ _f"> </span>neighbor</div><div class="t m1 xf h3 y3f ff1 fs1 fc0 sc0 ls0 ws0">graph<span class="_ _6"> </span>that<span class="_ _6"> </span>minimize<span class="_ _6"> </span>the<span class="_ _6"> </span>crease<span class="_ _6"> </span>or<span class="_ _6"> </span>border<span class="_ _6"> </span>penalty<span class="_ _6"> </span>weights,<span class="_ _f"> </span>respec-</div><div class="t m1 xf h3 y40 ff1 fs1 fc0 sc0 ls0 ws0">tiv<span class="_ _2"></span>ely<span class="_ _0"></span>.<span class="_ _10"> </span>A<span class="_ _4"> </span>minimum<span class="_ _f"> </span>crease<span class="_ _4"> </span>spanning<span class="_ _4"> </span>pattern<span class="_ _f"> </span>is<span class="_ _f"> </span>shown<span class="_ _4"> </span>in<span class="_ _f"> </span>d).<span class="_ _10"> </span>The</div><div class="t m1 xf h3 y41 ff1 fs1 fc0 sc0 ls0 ws0">minimum<span class="_ _6"> </span>spanning<span class="_ _6"> </span>pattern<span class="_ _6"> </span>is<span class="_ _6"> </span>similar<span class="_ _3"> </span>to<span class="_ _6"> </span>a<span class="_ _f"> </span>minimum<span class="_ _6"> </span>spanning<span class="_ _6"> </span>tree</div><div class="t m1 xf h3 y42 ff1 fs1 fc0 sc0 ls0 ws0">but<span class="_ _3"> </span>allows<span class="_ _3"> </span>for<span class="_ _6"> </span>signi&#64257;cantly<span class="_ _6"> </span>long<span class="_ _6"> </span>cycles.<span class="_ _12"> </span>A<span class="_ _6"> </span>pruning<span class="_ _6"> </span>algorithm<span class="_ _6"> </span>cuts</div><div class="t m1 xf h3 y43 ff1 fs1 fc0 sc0 ls0 ws0">off<span class="_ _3"> </span>short<span class="_ _3"> </span>branches<span class="_ _6"> </span>e).<span class="_ _12"> </span>For<span class="_ _3"> </span>noisy<span class="_ _6"> </span>data<span class="_ _6"> </span>the<span class="_ _6"> </span>resulting<span class="_ _6"> </span>crease<span class="_ _3"> </span>lines<span class="_ _6"> </span>are</div><div class="t m1 xf h3 y44 ff1 fs1 fc0 sc0 ls0 ws0">jittered<span class="_ _f"> </span>because<span class="_ _5"> </span>no<span class="_ _4"> </span>input<span class="_ _4"> </span>points<span class="_ _4"> </span>lay<span class="_ _4"> </span>directly<span class="_ _5"> </span>on<span class="_ _4"> </span>the<span class="_ _4"> </span>actual<span class="_ _4"> </span>crease</div><div class="t m1 xf h3 y45 ff1 fs1 fc0 sc0 ls0 ws0">line,<span class="_"> </span>in<span class="_"> </span>which<span class="_"> </span>case<span class="_"> </span>we<span class="_"> </span>apply<span class="_"> </span>a<span class="_ _3"> </span>crease<span class="_"> </span>line<span class="_"> </span>and<span class="_"> </span>junction<span class="_ _3"> </span>recov<span class="_ _2"></span>ery<span class="_ _3"> </span>al-</div><div class="t m1 xf h3 y46 ff1 fs1 fc0 sc0 ls0 ws0">gorithm.<span class="_ _3"> </span>This<span class="_"> </span>algorithm<span class="_"> </span>&#64257;ts<span class="_"> </span>wedges,<span class="_ _8"> </span>a<span class="_"> </span>simple<span class="_"> </span>crease<span class="_"> </span>representation</div><div class="t m1 xf h3 y47 ff1 fs1 fc0 sc0 ls0 ws0">consisting<span class="_"> </span>of<span class="_"> </span>two<span class="_"> </span>half<span class="_ _3"> </span>planes<span class="_ _3"> </span>meeting<span class="_"> </span>at<span class="_"> </span>a<span class="_"> </span>line,<span class="_ _3"> </span>to<span class="_"> </span>the<span class="_"> </span>crease<span class="_ _3"> </span>neigh-</div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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