bsds数据集

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<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://csdnimg.cn/release/download_crawler_static/css/base.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css"><link rel="stylesheet" href="https://csdnimg.cn/release/download_crawler_static/10998346/raw.css"><script src="https://csdnimg.cn/release/download_crawler_static/js/compatibility.min.js"></script><script src="https://csdnimg.cn/release/download_crawler_static/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://csdnimg.cn/release/download_crawler_static/10998346/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc0 ls0 ws0">Contour<span class="_"> </span>Detection<span class="_"> </span>and</div><div class="t m0 x3 h3 y3 ff2 fs1 fc0 sc0 ls0 ws0">Hierarchical<span class="_"> </span>Image<span class="_"> </span>Segmentation</div><div class="t m0 x4 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">P<span class="_ _0"></span>ablo<span class="_"> </span>Arbel</div><div class="t m0 x5 h4 y5 ff2 fs2 fc0 sc0 ls0 ws0">&#180;</div><div class="t m0 x6 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">aez,<span class="_"> </span><span class="ff3">Member<span class="_ _0"></span>,<span class="_ _1"> </span>IEEE,<span class="_ _1"> </span><span class="ff2">Michael<span class="_"> </span>Maire,<span class="_"> </span></span>Member<span class="_ _0"></span>,<span class="_ _1"> </span>IEEE,</span></div><div class="t m0 x7 h4 y6 ff2 fs2 fc0 sc0 ls0 ws0">Charless<span class="_"> </span>Fo<span class="_ _0"></span>wlkes<span class="_ _0"></span>,<span class="_"> </span><span class="ff3">Member<span class="_ _0"></span>,<span class="_ _1"> </span>IEEE,<span class="_ _2"> </span><span class="ff2">and<span class="_"> </span>Jitendra<span class="_"> </span>Malik,<span class="_"> </span></span>F<span class="_ _0"></span>ellow<span class="_ _3"></span>,<span class="_ _1"> </span>IEEE.</span></div><div class="t m0 x8 h5 y7 ff4 fs3 fc0 sc0 ls0 ws0">Abstract<span class="ff2">&#8212;This<span class="_ _2"> </span>paper<span class="_ _2"> </span>investigates<span class="_ _1"> </span>two<span class="_ _4"> </span>fundamental<span class="_ _2"> </span>problems<span class="_ _2"> </span>in<span class="_ _2"> </span>computer<span class="_ _4"> </span>vision:<span class="_ _2"> </span>contour<span class="_ _2"> </span>detection<span class="_ _4"> </span>and<span class="_ _2"> </span>image<span class="_ _4"> </span>segmentation.<span class="_ _2"> </span>We</span></div><div class="t m0 x8 h6 y8 ff2 fs3 fc0 sc0 ls0 ws0">present<span class="_ _2"> </span>state-of-the-ar<span class="_ _5"></span>t<span class="_ _2"> </span>algor<span class="_ _5"></span>ithms<span class="_ _2"> </span>for<span class="_ _1"> </span>both<span class="_ _4"> </span>of<span class="_ _4"> </span>these<span class="_ _4"> </span>tasks.<span class="_ _2"> </span>Our<span class="_ _4"> </span>contour<span class="_ _4"> </span>detector<span class="_ _2"> </span>combines<span class="_ _4"> </span>multiple<span class="_ _4"> </span>local<span class="_ _2"> </span>cues<span class="_ _4"> </span>into<span class="_ _4"> </span>a<span class="_ _4"> </span>globalization</div><div class="t m0 x8 h6 y9 ff2 fs3 fc0 sc0 ls0 ws0">framew<span class="_ _0"></span>ork<span class="_ _4"> </span>based<span class="_ _2"> </span>on<span class="_ _2"> </span>spectral<span class="_ _2"> </span>cluster<span class="_ _5"></span>ing.<span class="_ _1"> </span>Our<span class="_ _4"> </span>segmentation<span class="_ _2"> </span>algorithm<span class="_ _4"> </span>consists<span class="_ _2"> </span>of<span class="_ _2"> </span>gener<span class="_ _5"></span>ic<span class="_ _1"> </span>machiner<span class="_ _5"></span>y<span class="_ _2"> </span>for<span class="_ _1"> </span>transforming<span class="_ _2"> </span>the<span class="_ _2"> </span>output<span class="_ _2"> </span>of</div><div class="t m0 x8 h6 ya ff2 fs3 fc0 sc0 ls0 ws0">any<span class="_ _6"> </span>contour<span class="_ _6"> </span>detector<span class="_ _6"> </span>into<span class="_ _1"> </span>a<span class="_ _6"> </span>hierarchical<span class="_ _6"> </span>region<span class="_ _6"> </span>tree.<span class="_ _6"> </span>In<span class="_ _1"> </span>this<span class="_ _6"> </span>manner<span class="_ _0"></span>,<span class="_ _6"> </span>we<span class="_ _6"> </span>reduce<span class="_ _1"> </span>the<span class="_ _6"> </span>problem<span class="_"> </span>of<span class="_ _1"> </span>image<span class="_ _6"> </span>segmentation<span class="_ _6"> </span>to<span class="_ _1"> </span>that<span class="_"> </span>of<span class="_ _1"> </span>contour</div><div class="t m0 x8 h6 yb ff2 fs3 fc0 sc0 ls0 ws0">detection.<span class="_ _1"> </span>Extensive<span class="_ _1"> </span>experimental<span class="_ _1"> </span>ev<span class="_ _0"></span>aluation<span class="_ _1"> </span>demonstrates<span class="_ _1"> </span>that<span class="_ _2"> </span>both<span class="_ _1"> </span>our<span class="_ _2"> </span>contour<span class="_ _1"> </span>detection<span class="_ _2"> </span>and<span class="_ _1"> </span>segmentation<span class="_ _1"> </span>methods<span class="_ _2"> </span>signi&#64257;cantly</div><div class="t m0 x8 h6 yc ff2 fs3 fc0 sc0 ls0 ws0">outperform<span class="_ _7"> </span>competing<span class="_ _7"> </span>algorithms.<span class="_ _7"> </span>The<span class="_ _7"> </span>automatically<span class="_ _7"> </span>generated<span class="_ _7"> </span>hierarchical<span class="_ _7"> </span>segmentations<span class="_ _7"> </span>can<span class="_ _7"> </span>be<span class="_ _7"> </span>interactively<span class="_ _7"> </span>re&#64257;ned<span class="_ _7"> </span>by<span class="_ _7"> </span>user-</div><div class="t m0 x8 h6 yd ff2 fs3 fc0 sc0 ls0 ws0">speci&#64257;ed<span class="_"> </span>annotations.<span class="_"> </span>Computation<span class="_"> </span>at<span class="_"> </span>m<span class="_ _0"></span>ultiple<span class="_"> </span>image<span class="_"> </span>resolutions<span class="_"> </span>provides<span class="_"> </span>a<span class="_"> </span>means<span class="_"> </span>of<span class="_"> </span>coupling<span class="_ _8"> </span>our<span class="_"> </span>system<span class="_"> </span>to<span class="_"> </span>recognition<span class="_"> </span>applications.</div><div class="t m0 x9 h7 ye ff5 fs2 fc0 sc0 ls0 ws0">F</div><div class="t m0 xa h8 yf ff4 fs4 fc0 sc0 ls0 ws0">1<span class="_ _9"> </span>I<span class="_ _5"></span><span class="fs5">N<span class="_ _5"></span>T<span class="_ _5"></span>R<span class="_ _5"></span>O<span class="_ _5"></span>D<span class="_ _5"></span>U<span class="_ _a"></span>C<span class="_ _5"></span>T<span class="_ _5"></span>I<span class="_ _5"></span>O<span class="_ _a"></span>N</span></div><div class="t m0 xa h9 y10 ff1 fs6 fc0 sc0 ls0 ws0">This<span class="_ _7"> </span>paper<span class="_ _b"> </span>presents<span class="_ _7"> </span>a<span class="_ _b"> </span>uni&#64257;ed<span class="_ _7"> </span>approach<span class="_ _7"> </span>to<span class="_ _b"> </span>contour<span class="_ _7"> </span>de-</div><div class="t m0 xa h9 y11 ff1 fs6 fc0 sc0 ls0 ws0">tection<span class="_ _4"> </span>and<span class="_ _4"> </span>image<span class="_ _4"> </span>segmentation.<span class="_ _4"> </span>Contributions<span class="_ _4"> </span>include:</div><div class="t m0 xb h9 y12 ff6 fs0 fc0 sc0 ls0 ws0">&#8226;<span class="_ _c"> </span><span class="ff1 fs6">A<span class="_ _d"> </span>high<span class="_ _d"> </span>performance<span class="_ _d"> </span>contour<span class="_ _d"> </span>detector<span class="_ _3"></span>,<span class="_ _d"> </span>combining</span></div><div class="t m0 xc h9 y13 ff1 fs6 fc0 sc0 ls0 ws0">local<span class="_ _4"> </span>and<span class="_ _4"> </span>global<span class="_ _4"> </span>image<span class="_ _4"> </span>information.</div><div class="t m0 xb h9 y14 ff6 fs0 fc0 sc0 ls0 ws0">&#8226;<span class="_ _c"> </span><span class="ff1 fs6">A<span class="_ _1"> </span>method<span class="_"> </span>to<span class="_ _1"> </span>transform<span class="_ _1"> </span>any<span class="_ _1"> </span>contour<span class="_"> </span>signal<span class="_ _1"> </span>into<span class="_ _1"> </span>a<span class="_ _1"> </span>hi-</span></div><div class="t m0 xc h9 y15 ff1 fs6 fc0 sc0 ls0 ws0">erarchy<span class="_ _1"> </span>of<span class="_ _1"> </span>r<span class="_ _0"></span>egions<span class="_ _1"> </span>while<span class="_ _1"> </span>preserving<span class="_ _1"> </span>contour<span class="_ _1"> </span>quality<span class="_ _3"></span>.</div><div class="t m0 xb h9 y16 ff6 fs0 fc0 sc0 ls0 ws0">&#8226;<span class="_ _c"> </span><span class="ff1 fs6">Extensive<span class="_ _1"> </span>quantitative<span class="_ _2"> </span>evaluation<span class="_ _2"> </span>and<span class="_ _2"> </span>the<span class="_ _1"> </span>release<span class="_ _2"> </span>of</span></div><div class="t m0 xc h9 y17 ff1 fs6 fc0 sc0 ls0 ws0">a<span class="_ _4"> </span>new<span class="_ _4"> </span>annotated<span class="_ _4"> </span>dataset.</div><div class="t m0 xb h9 y18 ff1 fs6 fc0 sc0 ls0 ws0">Figures<span class="_ _d"> </span>1<span class="_ _d"> </span>and<span class="_ _c"> </span>2<span class="_ _d"> </span>summarize<span class="_ _d"> </span>our<span class="_ _c"> </span>main<span class="_ _d"> </span>results.<span class="_ _d"> </span>The</div><div class="t m0 xa h9 y19 ff1 fs6 fc0 sc0 ls0 ws0">two<span class="_ _e"> </span>Figures<span class="_ _b"> </span>represent<span class="_ _b"> </span>the<span class="_ _e"> </span>evaluation<span class="_ _e"> </span>of<span class="_ _e"> </span>multiple<span class="_ _e"> </span>con-</div><div class="t m0 xa h9 y1a ff1 fs6 fc0 sc0 ls0 ws0">tour<span class="_ _7"> </span>detection<span class="_ _7"> </span>(Figur<span class="_ _0"></span>e<span class="_ _7"> </span>1)<span class="_ _7"> </span>and<span class="_ _f"> </span>image<span class="_ _f"> </span>segmentation<span class="_ _7"> </span>(Fig-</div><div class="t m0 xa h9 y1b ff1 fs6 fc0 sc0 ls0 ws0">ure<span class="_ _1"> </span>2)<span class="_ _4"> </span>algorithms<span class="_ _2"> </span>on<span class="_ _4"> </span>the<span class="_ _2"> </span>Berkeley<span class="_ _4"> </span>Segmentation<span class="_ _4"> </span>Dataset</div><div class="t m0 xa h9 y1c ff1 fs6 fc0 sc0 ls0 ws0">(BSDS300)<span class="_ _7"> </span>[1],<span class="_ _7"> </span>using<span class="_ _7"> </span>the<span class="_ _7"> </span>precision-r<span class="_ _0"></span>ecall<span class="_ _7"> </span>framework<span class="_ _7"> </span>in-</div><div class="t m0 xa h9 y1d ff1 fs6 fc0 sc0 ls0 ws0">troduced<span class="_ _b"> </span>in<span class="_ _e"> </span>[2].<span class="_ _10"> </span>This<span class="_ _e"> </span>benchmark<span class="_ _e"> </span>operates<span class="_ _e"> </span>by<span class="_ _e"> </span>compar-</div><div class="t m0 xa h9 y1e ff1 fs6 fc0 sc0 ls0 ws0">ing<span class="_ _1"> </span>machine<span class="_ _2"> </span>generated<span class="_ _2"> </span>contours<span class="_ _1"> </span>to<span class="_ _2"> </span>human<span class="_ _2"> </span>ground-truth</div><div class="t m0 xa h9 y1f ff1 fs6 fc0 sc0 ls0 ws0">data<span class="_ _f"> </span>(Figure<span class="_ _f"> </span>3)<span class="_ _f"> </span>and<span class="_ _f"> </span>allows<span class="_ _7"> </span>evaluation<span class="_ _f"> </span>of<span class="_ _f"> </span>segmentations</div><div class="t m0 xa h9 y20 ff1 fs6 fc0 sc0 ls0 ws0">in<span class="_ _4"> </span>the<span class="_ _4"> </span>same<span class="_ _4"> </span>framework<span class="_ _4"> </span>by<span class="_ _f"> </span>regar<span class="_ _0"></span>ding<span class="_ _4"> </span>region<span class="_ _4"> </span>boundaries</div><div class="t m0 xa h9 y21 ff1 fs6 fc0 sc0 ls0 ws0">as<span class="_ _4"> </span>contours.</div><div class="t m0 xb h9 y22 ff1 fs6 fc0 sc0 ls0 ws0">Especially<span class="_ _7"> </span>noteworthy<span class="_ _7"> </span>in<span class="_ _b"> </span>Figur<span class="_ _0"></span>e<span class="_ _7"> </span>1<span class="_ _7"> </span>is<span class="_ _b"> </span>the<span class="_ _f"> </span>contour<span class="_ _b"> </span>de-</div><div class="t m0 xa ha y23 ff1 fs6 fc0 sc0 ls0 ws0">tector<span class="_"> </span><span class="ff7">g<span class="_ _5"></span>P<span class="_ _11"> </span>b</span>,<span class="_"> </span>which<span class="_"> </span>compares<span class="_"> </span>favorably<span class="_"> </span>with<span class="_ _1"> </span>other<span class="_"> </span>leading</div><div class="t m0 xa h9 y24 ff1 fs6 fc0 sc0 ls0 ws0">techniques,<span class="_ _2"> </span>providing<span class="_ _2"> </span>equal<span class="_ _2"> </span>or<span class="_ _4"> </span>better<span class="_ _2"> </span>precision<span class="_ _2"> </span>for<span class="_ _2"> </span>most</div><div class="t m0 xa ha y25 ff1 fs6 fc0 sc0 ls0 ws0">choices<span class="_ _d"> </span>of<span class="_ _c"> </span>r<span class="_ _0"></span>ecall.<span class="_ _c"> </span>In<span class="_ _d"> </span>Figure<span class="_ _d"> </span>2,<span class="_ _d"> </span><span class="ff7">g<span class="_ _5"></span>P<span class="_ _11"> </span>b</span>-owt-ucm<span class="_ _d"> </span>provides</div><div class="t m0 xa h9 y26 ff1 fs6 fc0 sc0 ls0 ws0">universally<span class="_ _1"> </span>better<span class="_ _2"> </span>performance<span class="_ _2"> </span>than<span class="_ _1"> </span>alternative<span class="_ _2"> </span>segmen-</div><div class="t m0 xa ha y27 ff1 fs6 fc0 sc0 ls0 ws0">tation<span class="_ _2"> </span>algorithms.<span class="_ _4"> </span>W<span class="_ _3"></span>e<span class="_ _4"> </span>introduced<span class="_ _2"> </span>the<span class="_ _4"> </span><span class="ff7">g<span class="_ _5"></span>P<span class="_ _11"> </span>b<span class="_ _4"> </span></span>and<span class="_ _4"> </span><span class="ff7">g<span class="_ _5"></span>P<span class="_ _11"> </span>b</span>-owt-</div><div class="t m0 xa h9 y28 ff1 fs6 fc0 sc0 ls0 ws0">ucm<span class="_ _7"> </span>algorithms<span class="_ _b"> </span>in<span class="_ _7"> </span>[3]<span class="_ _7"> </span>and<span class="_ _b"> </span>[4],<span class="_ _7"> </span>respectively<span class="_ _12"></span>.<span class="_ _7"> </span>This<span class="_ _b"> </span>paper</div><div class="t m0 xa h9 y29 ff1 fs6 fc0 sc0 ls0 ws0">offers<span class="_ _4"> </span>comprehensive<span class="_ _f"> </span>versions<span class="_ _f"> </span>of<span class="_ _f"> </span>these<span class="_ _7"> </span>algorithms,<span class="_ _f"> </span>mo-</div><div class="t m0 xa h9 y2a ff1 fs6 fc0 sc0 ls0 ws0">tivation<span class="_ _1"> </span>behind<span class="_ _1"> </span>their<span class="_"> </span>design,<span class="_ _1"> </span>and<span class="_ _1"> </span>additional<span class="_ _1"> </span>experiments</div><div class="t m0 xa h9 y2b ff1 fs6 fc0 sc0 ls0 ws0">which<span class="_ _4"> </span>support<span class="_ _4"> </span>our<span class="_ _4"> </span>basic<span class="_ _4"> </span>claims.</div><div class="t m0 xb h9 y2c ff1 fs6 fc0 sc0 ls0 ws0">W<span class="_ _3"></span>e<span class="_ _2"> </span>begin<span class="_ _f"> </span>with<span class="_ _4"> </span>a<span class="_ _4"> </span>review<span class="_ _4"> </span>of<span class="_ _4"> </span>the<span class="_ _4"> </span>extensive<span class="_ _4"> </span>literature<span class="_ _4"> </span>on</div><div class="t m0 xa h9 y2d ff1 fs6 fc0 sc0 ls0 ws0">contour<span class="_ _4"> </span>detection<span class="_ _4"> </span>and<span class="_ _4"> </span>image<span class="_ _4"> </span>segmentation<span class="_ _4"> </span>in<span class="_ _4"> </span>Section<span class="_ _4"> </span>2.</div><div class="t m0 xd hb y2e ff8 fs3 fc0 sc0 ls0 ws0">&#8226;<span class="_ _c"> </span><span class="ff9">P<span class="_ _3"></span>.<span class="_"> </span>Arbel<span class="_ _5"></span>&#180;<span class="_ _13"></span>aez<span class="_"> </span>and<span class="_"> </span>J.<span class="_"> </span>Malik<span class="_ _6"> </span>ar<span class="_ _0"></span>e<span class="_"> </span>with<span class="_ _6"> </span>the<span class="_"> </span>Department<span class="_"> </span>of<span class="_"> </span>Electrical<span class="_"> </span>Engineering</span></div><div class="t m0 xb hc y2f ff9 fs3 fc0 sc0 ls0 ws0">and<span class="_ _6"> </span>Computer<span class="_ _6"> </span>Science,<span class="_ _1"> </span>University<span class="_ _6"> </span>of<span class="_ _6"> </span>California<span class="_ _6"> </span>at<span class="_ _1"> </span>Berkeley<span class="_ _0"></span>,<span class="_ _6"> </span>Berkeley,<span class="_ _6"> </span>CA</div><div class="t m0 xb hb y30 ff9 fs3 fc0 sc0 ls0 ws0">94720.<span class="_ _1"> </span>E-mail:<span class="_ _6"> </span><span class="ff8">{</span>arbelaez,malik<span class="ff8">}</span>@eecs.berkeley.edu</div><div class="t m0 xd hb y31 ff8 fs3 fc0 sc0 ls0 ws0">&#8226;<span class="_ _c"> </span><span class="ff9">M.<span class="_ _4"> </span>Maire<span class="_ _f"> </span>is<span class="_ _f"> </span>with<span class="_ _f"> </span>the<span class="_ _f"> </span>Department<span class="_ _f"> </span>of<span class="_ _f"> </span>Electrical<span class="_ _4"> </span>Engineering,<span class="_ _f"> </span>California</span></div><div class="t m0 xb hc y32 ff9 fs3 fc0 sc0 ls0 ws0">Institute<span class="_"> </span>of<span class="_ _6"> </span>T<span class="_ _3"></span>echnology<span class="_ _0"></span>,<span class="_"> </span>Pasadena,<span class="_ _6"> </span>CA<span class="_"> </span>91125.<span class="_ _6"> </span>E-mail:<span class="_"> </span>mmaire@caltech.edu</div><div class="t m0 xd hb y33 ff8 fs3 fc0 sc0 ls0 ws0">&#8226;<span class="_ _c"> </span><span class="ff9">C.<span class="_ _4"> </span>Fowlkes<span class="_ _4"> </span>is<span class="_ _4"> </span>with<span class="_ _4"> </span>the<span class="_ _4"> </span>Department<span class="_ _4"> </span>of<span class="_ _f"> </span>Computer<span class="_ _4"> </span>Science,<span class="_ _4"> </span>University<span class="_ _4"> </span>of</span></div><div class="t m0 xb hc y34 ff9 fs3 fc0 sc0 ls0 ws0">California<span class="_ _1"> </span>at<span class="_ _6"> </span>Irvine,<span class="_ _1"> </span>Irvine,<span class="_ _1"> </span>CA<span class="_ _6"> </span>92697.<span class="_ _1"> </span>E-mail:<span class="_ _1"> </span>fowlkes@ics.uci.edu</div><div class="t m0 xe ha y10 ff1 fs6 fc0 sc0 ls0 ws0">Section<span class="_ _f"> </span>3<span class="_ _f"> </span>covers<span class="_ _4"> </span>the<span class="_ _f"> </span>development<span class="_ _f"> </span>of<span class="_ _f"> </span>the<span class="_ _f"> </span><span class="ff7">g<span class="_ _5"></span>P<span class="_ _11"> </span>b<span class="_ _f"> </span></span>contour</div><div class="t m0 xf h9 y11 ff1 fs6 fc0 sc0 ls0 ws0">detector<span class="_ _3"></span>.<span class="_ _10"> </span>W<span class="_ _3"></span>e<span class="_ _10"> </span>couple<span class="_ _d"> </span>multiscale<span class="_ _10"> </span>local<span class="_ _10"> </span>brightness,<span class="_ _10"> </span>color<span class="_ _0"></span>,</div><div class="t m0 xf h9 y35 ff1 fs6 fc0 sc0 ls0 ws0">and<span class="_ _2"> </span>texture<span class="_ _1"> </span>cues<span class="_ _4"> </span>to<span class="_ _2"> </span>a<span class="_ _2"> </span>powerful<span class="_ _2"> </span>globalization<span class="_ _4"> </span>framework</div><div class="t m0 xf h9 y36 ff1 fs6 fc0 sc0 ls0 ws0">using<span class="_ _b"> </span>spectral<span class="_ _7"> </span>clustering.<span class="_ _b"> </span>The<span class="_ _b"> </span>local<span class="_ _7"> </span>cues,<span class="_ _b"> </span>computed<span class="_ _b"> </span>by</div><div class="t m0 xf h9 y37 ff1 fs6 fc0 sc0 ls0 ws0">applying<span class="_ _b"> </span>oriented<span class="_ _b"> </span>gradient<span class="_ _b"> </span>operators<span class="_ _b"> </span>at<span class="_ _b"> </span>every<span class="_ _b"> </span>location</div><div class="t m0 xf h9 y38 ff1 fs6 fc0 sc0 ls0 ws0">in<span class="_ _f"> </span>the<span class="_ _7"> </span>image,<span class="_ _f"> </span>de&#64257;ne<span class="_ _7"> </span>an<span class="_ _f"> </span>af&#64257;nity<span class="_ _f"> </span>matrix<span class="_ _f"> </span>representing<span class="_ _4"> </span>the</div><div class="t m0 xf h9 y39 ff1 fs6 fc0 sc0 ls0 ws0">similarity<span class="_ _b"> </span>between<span class="_ _7"> </span>pixels.<span class="_ _b"> </span>From<span class="_ _7"> </span>this<span class="_ _b"> </span>matrix,<span class="_ _b"> </span>we<span class="_ _7"> </span>derive</div><div class="t m0 xf h9 y3a ff1 fs6 fc0 sc0 ls0 ws0">a<span class="_ _f"> </span>generalized<span class="_ _f"> </span>eigenproblem<span class="_ _4"> </span>and<span class="_ _7"> </span>solve<span class="_ _f"> </span>for<span class="_ _f"> </span>a<span class="_ _f"> </span>&#64257;xed<span class="_ _f"> </span>num-</div><div class="t m0 xf h9 y3b ff1 fs6 fc0 sc0 ls0 ws0">ber<span class="_ _7"> </span>of<span class="_ _7"> </span>eigenvectors<span class="_ _7"> </span>which<span class="_ _b"> </span>encode<span class="_ _f"> </span>contour<span class="_ _7"> </span>information.</div><div class="t m0 xf h9 y3c ff1 fs6 fc0 sc0 ls0 ws0">Using<span class="_ _2"> </span>a<span class="_ _2"> </span>classi&#64257;er<span class="_ _2"> </span>to<span class="_ _2"> </span>recombine<span class="_ _2"> </span>this<span class="_ _2"> </span>signal<span class="_ _2"> </span>with<span class="_ _4"> </span>the<span class="_ _2"> </span>local</div><div class="t m0 xf h9 y3d ff1 fs6 fc0 sc0 ls0 ws0">cues,<span class="_ _e"> </span>we<span class="_ _e"> </span>obtain<span class="_ _e"> </span>a<span class="_ _e"> </span>large<span class="_ _b"> </span>improvement<span class="_ _e"> </span>over<span class="_ _e"> </span>alternative</div><div class="t m0 xf h9 y3e ff1 fs6 fc0 sc0 ls0 ws0">globalization<span class="_ _4"> </span>schemes<span class="_ _4"> </span>built<span class="_ _4"> </span>on<span class="_ _4"> </span>top<span class="_ _4"> </span>of<span class="_ _4"> </span>similar<span class="_ _4"> </span>cues.</div><div class="t m0 xe h9 y3f ff1 fs6 fc0 sc0 ls0 ws0">T<span class="_ _3"></span>o<span class="_"> </span>produce<span class="_"> </span>high-quality<span class="_ _1"> </span>image<span class="_"> </span>segmentations,<span class="_"> </span>we<span class="_ _1"> </span>link</div><div class="t m0 xf h9 y40 ff1 fs6 fc0 sc0 ls0 ws0">this<span class="_ _2"> </span>contour<span class="_ _2"> </span>detector<span class="_ _2"> </span>with<span class="_ _2"> </span>a<span class="_ _2"> </span>generic<span class="_ _4"> </span>grouping<span class="_ _1"> </span>algorithm</div><div class="t m0 xf h9 y41 ff1 fs6 fc0 sc0 ls0 ws0">described<span class="_ _1"> </span>in<span class="_ _2"> </span>Section<span class="_ _2"> </span>4<span class="_ _2"> </span>and<span class="_ _2"> </span>consisting<span class="_ _2"> </span>of<span class="_ _1"> </span>two<span class="_ _2"> </span>steps.<span class="_ _2"> </span>First,</div><div class="t m0 xf h9 y42 ff1 fs6 fc0 sc0 ls0 ws0">we<span class="_ _d"> </span>introduce<span class="_ _10"> </span>a<span class="_ _d"> </span>new<span class="_ _d"> </span>image<span class="_ _d"> </span>transformation<span class="_ _10"> </span>called<span class="_ _d"> </span>the</div><div class="t m0 xf h9 y43 ff1 fs6 fc0 sc0 ls0 ws0">Oriented<span class="_ _4"> </span>W<span class="_ _3"></span>atershed<span class="_ _f"> </span>T<span class="_ _3"></span>ransform<span class="_ _4"> </span>for<span class="_ _f"> </span>constructing<span class="_ _4"> </span>a<span class="_ _f"> </span>set<span class="_ _f"> </span>of</div><div class="t m0 xf h9 y44 ff1 fs6 fc0 sc0 ls0 ws0">initial<span class="_ _f"> </span>regions<span class="_ _4"> </span>from<span class="_ _f"> </span>an<span class="_ _f"> </span>oriented<span class="_ _f"> </span>contour<span class="_ _7"> </span>signal.<span class="_ _f"> </span>Second,</div><div class="t m0 xf h9 y45 ff1 fs6 fc0 sc0 ls0 ws0">using<span class="_ _b"> </span>an<span class="_ _7"> </span>agglomerative<span class="_ _b"> </span>clustering<span class="_ _b"> </span>procedur<span class="_ _0"></span>e,<span class="_ _b"> </span>we<span class="_ _b"> </span>form</div><div class="t m0 xf h9 y46 ff1 fs6 fc0 sc0 ls0 ws0">these<span class="_ _2"> </span>regions<span class="_ _2"> </span>into<span class="_ _4"> </span>a<span class="_ _2"> </span>hierarchy<span class="_ _2"> </span>which<span class="_ _4"> </span>can<span class="_ _2"> </span>be<span class="_ _4"> </span>repr<span class="_ _0"></span>esented</div><div class="t m0 xf h9 y47 ff1 fs6 fc0 sc0 ls0 ws0">by<span class="_ _f"> </span>an<span class="_ _7"> </span>Ultrametric<span class="_ _7"> </span>Contour<span class="_ _f"> </span>Map,<span class="_ _7"> </span>the<span class="_ _7"> </span>real-valued<span class="_ _4"> </span>image</div><div class="t m0 xf h9 y48 ff1 fs6 fc0 sc0 ls0 ws0">obtained<span class="_ _10"> </span>by<span class="_ _10"> </span>weighting<span class="_ _10"> </span>each<span class="_ _10"> </span>boundary<span class="_ _10"> </span>by<span class="_ _10"> </span>its<span class="_ _10"> </span>scale<span class="_ _e"> </span>of</div><div class="t m0 xf h9 y49 ff1 fs6 fc0 sc0 ls0 ws0">disappearance.<span class="_ _1"> </span>W<span class="_ _3"></span>e<span class="_ _1"> </span>provide<span class="_"> </span>experiments<span class="_ _2"> </span>on<span class="_ _1"> </span>the<span class="_ _1"> </span>BSDS300</div><div class="t m0 xf h9 y4a ff1 fs6 fc0 sc0 ls0 ws0">as<span class="_ _2"> </span>well<span class="_ _4"> </span>as<span class="_ _4"> </span>the<span class="_ _4"> </span>BSDS500,<span class="_ _4"> </span>a<span class="_ _4"> </span>superset<span class="_ _4"> </span>newly<span class="_ _4"> </span>released<span class="_ _2"> </span>here.</div><div class="t m0 xe h9 y4b ff1 fs6 fc0 sc0 ls0 ws0">Although<span class="_"> </span>the<span class="_"> </span>precision-r<span class="_ _0"></span>ecall<span class="_"> </span>framework<span class="_ _1"> </span>[2]<span class="_"> </span>has<span class="_"> </span>found</div><div class="t m0 xf h9 y4c ff1 fs6 fc0 sc0 ls0 ws0">widespread<span class="_ _b"> </span>use<span class="_ _e"> </span>for<span class="_ _b"> </span>evaluating<span class="_ _e"> </span>contour<span class="_ _e"> </span>detectors,<span class="_ _b"> </span>con-</div><div class="t m0 xf h9 y4d ff1 fs6 fc0 sc0 ls0 ws0">siderable<span class="_ _b"> </span>effort<span class="_ _e"> </span>has<span class="_ _b"> </span>also<span class="_ _e"> </span>gone<span class="_ _b"> </span>into<span class="_ _e"> </span>developing<span class="_ _e"> </span>metrics</div><div class="t m0 xf h9 y4e ff1 fs6 fc0 sc0 ls0 ws0">to<span class="_ _f"> </span>directly<span class="_ _7"> </span>measure<span class="_ _4"> </span>the<span class="_ _7"> </span>quality<span class="_ _7"> </span>of<span class="_ _7"> </span>r<span class="_ _0"></span>egions<span class="_ _7"> </span>produced<span class="_ _f"> </span>by</div><div class="t m0 xf h9 y4f ff1 fs6 fc0 sc0 ls0 ws0">segmentation<span class="_ _2"> </span>algorithms.<span class="_ _2"> </span>Noteworthy<span class="_ _2"> </span>examples<span class="_ _2"> </span>include</div><div class="t m0 xf h9 y50 ff1 fs6 fc0 sc0 ls0 ws0">the<span class="_ _4"> </span>Probabilistic<span class="_ _f"> </span>Rand<span class="_ _f"> </span>Index,<span class="_ _4"> </span>introduced<span class="_ _f"> </span>in<span class="_ _4"> </span>this<span class="_ _f"> </span>context</div><div class="t m0 xf h9 y51 ff1 fs6 fc0 sc0 ls0 ws0">by<span class="_ _d"> </span>[5],<span class="_ _d"> </span>the<span class="_ _d"> </span>V<span class="_ _3"></span>ariation<span class="_ _d"> </span>of<span class="_ _d"> </span>Information<span class="_ _c"> </span>[6],<span class="_ _d"> </span>[7],<span class="_ _d"> </span>and<span class="_ _d"> </span>the</div><div class="t m0 xf h9 y52 ff1 fs6 fc0 sc0 ls0 ws0">Segmentation<span class="_ _c"> </span>Covering<span class="_ _c"> </span>criteria<span class="_ _c"> </span>used<span class="_ _c"> </span>in<span class="_ _c"> </span>the<span class="_ _c"> </span>P<span class="_ _3"></span>ASCAL</div><div class="t m0 xf h9 y53 ff1 fs6 fc0 sc0 ls0 ws0">challenge<span class="_ _14"> </span>[8].<span class="_ _14"> </span>W<span class="_ _3"></span>e<span class="_ _14"> </span>consider<span class="_ _14"> </span>all<span class="_ _14"> </span>of<span class="_ _14"> </span>these<span class="_ _14"> </span>metrics<span class="_ _14"> </span>and</div><div class="t m0 xf ha y54 ff1 fs6 fc0 sc0 ls0 ws0">demonstrate<span class="_ _e"> </span>that<span class="_ _e"> </span><span class="ff7">g<span class="_ _5"></span>P<span class="_ _11"> </span>b</span>-owt-ucm<span class="_ _e"> </span>delivers<span class="_ _e"> </span>an<span class="_ _e"> </span>across-the-</div><div class="t m0 xf h9 y55 ff1 fs6 fc0 sc0 ls0 ws0">board<span class="_ _2"> </span>improvement<span class="_ _2"> </span>over<span class="_ _4"> </span>existing<span class="_ _4"> </span>algorithms.</div><div class="t m0 xe h9 y56 ff1 fs6 fc0 sc0 ls0 ws0">Sections<span class="_ _14"> </span>5<span class="_ _c"> </span>and<span class="_ _14"> </span>6<span class="_ _c"> </span>explore<span class="_ _c"> </span>ways<span class="_ _14"> </span>of<span class="_ _c"> </span>connecting<span class="_ _14"> </span>our</div><div class="t m0 xf h9 y57 ff1 fs6 fc0 sc0 ls0 ws0">purely<span class="_ _2"> </span>bottom-up<span class="_ _4"> </span>contour<span class="_ _4"> </span>and<span class="_ _4"> </span>segmentation<span class="_ _4"> </span>machinery</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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