• fangchj2002
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基于学习的ACM算法,通过采用SVM和神经网络来拟合图像的边界,从而快速分割
Robust_ESF.zip
  • Robust_ESF
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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/6274eb468dbc4529de780825/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/6274eb468dbc4529de780825/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">222<span class="_ _0"> </span><span class="ls1">IEEE<span class="_ _1"> </span>SIGNAL<span class="_ _1"> </span>PR<span class="_ _2"></span>OCESSING<span class="_ _1"> </span>LETTERS,<span class="_ _1"> </span>V<span class="_ _2"></span>O<span class="_"> </span>L.<span class="_ _1"> </span>23,<span class="_ _1"> </span>NO.<span class="_ _1"> </span>2,<span class="_ _1"> </span>FEBRU<span class="_ _2"></span>AR<span class="_ _2"></span>Y<span class="_ _1"> </span>2016</span></div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls2 ws0">Rob<span class="_ _2"></span>ust<span class="_ _3"> </span>Edge-Stop<span class="_ _3"> </span>Functions<span class="_ _3"> </span>for<span class="_ _3"> </span>Edge-Based<span class="_ _3"> </span>Acti<span class="_ _2"></span>v<span class="_ _2"></span>e</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls3 ws0">Contour<span class="_ _3"> </span>Models<span class="_ _4"> </span>in<span class="_ _4"> </span>Medical<span class="_ _3"> </span>Image<span class="_ _4"> </span>Segmentation</div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls4 ws0">Agus<span class="_ _5"> </span>Pratondo<span class="ff2 ls5">,<span class="_ _6"> </span>Member<span class="_ _7"></span>,<span class="_ _6"> </span>IEEE<span class="ff1 ls6">,<span class="_ _8"> </span>Chee-K<span class="_ _2"></span>ong<span class="_ _5"> </span>Chui<span class="ff2 ls7">,M<span class="_ _9"></span>e<span class="_ _9"></span>m<span class="_ _9"></span>b<span class="_ _9"></span>e<span class="_ _9"></span>r<span class="_ _a"></span>,I<span class="_ _9"></span>E<span class="_ _9"></span>E<span class="_ _9"></span>E<span class="_ _9"></span><span class="ff1 ls6">,<span class="_ _6"> </span>and<span class="_ _8"> </span>Sim-Heng<span class="_ _6"> </span>Ong<span class="ff2 ls5">,<span class="_ _5"> </span>Member<span class="_ _7"></span>,<span class="_ _6"> </span>IEEE</span></span></span></span></span></div><div class="t m0 x5 h5 y5 ff3 fs3 fc0 sc0 ls8 ws0">Abstract&#8212;<span class="ff4 ls9">Edge-based<span class="_ _1"> </span>acti<span class="_ _2"></span>ve<span class="_ _1"> </span>contour<span class="_ _1"> </span>models<span class="_ _1"> </span>are<span class="_ _1"> </span>effective<span class="_ _1"> </span>in<span class="_ _1"> </span>seg-</span></div><div class="t m0 x1 h6 y6 ff4 fs3 fc0 sc0 lsa ws0">menting<span class="_ _6"> </span>images<span class="_ _6"> </span>with<span class="_ _6"> </span>intensity<span class="_ _6"> </span>i<span class="ls9">nhomogeneity<span class="_ _5"> </span>but<span class="_ _6"> </span>often<span class="_ _6"> </span>fail<span class="_ _6"> </span>when</span></div><div class="t m0 x1 h6 y7 ff4 fs3 fc0 sc0 lsb ws0">applied<span class="_ _5"> </span>to<span class="_ _5"> </span>images<span class="_ _b"> </span>containing<span class="_ _5"> </span>poor<span class="lsc">ly<span class="_ _5"> </span>defi<span class="_ _2"></span>ned<span class="_ _b"> </span>boundarie<span class="_ _2"></span>s<span class="_"> </span>,<span class="_ _b"> </span>such<span class="_ _6"> </span>as</span></div><div class="t m0 x1 h6 y8 ff4 fs3 fc0 sc0 lsd ws0">in<span class="_ _5"> </span>medical<span class="_ _5"> </span>images.<span class="_ _5"> </span>T<span class="_ _2"></span>radi<span class="_ _2"></span>tional<span class="_ _5"> </span>edg<span class="lse">e-stop<span class="_ _5"> </span>functions<span class="_ _5"> </span>(ESFs)<span class="_ _5"> </span>utilize</span></div><div class="t m0 x1 h6 y9 ff4 fs3 fc0 sc0 lsf ws0">only<span class="_ _c"> </span>gradient<span class="_ _c"> </span>inf<span class="_ _d"></span>ormation,<span class="_ _c"> </span>which<span class="_ _c"> </span>fails<span class="_ _c"> </span>to<span class="_ _c"> </span>stop<span class="_ _c"> </span>contour<span class="_ _c"> </span>evolution<span class="_ _1"> </span>at</div><div class="t m0 x1 h6 ya ff4 fs3 fc0 sc0 ls10 ws0">such<span class="_ _c"> </span>boundaries<span class="_ _c"> </span>because<span class="_ _6"> </span>of<span class="_ _1"> </span>th<span class="_"> </span>e<span class="_ _e"> </span>small<span class="_ _c"> </span>gradient<span class="_ _e"> </span>magnitudes.<span class="_ _c"> </span>T<span class="_ _2"></span>o<span class="_ _c"> </span>ad-</div><div class="t m0 x1 h6 yb ff4 fs3 fc0 sc0 ls11 ws0">dress<span class="_ _c"> </span>this<span class="_ _c"> </span>problem,<span class="_ _c"> </span>we<span class="_ _e"> </span>propose<span class="_ _c"> </span>a<span class="_ _e"> </span>framework<span class="_ _c"> </span>to<span class="_ _e"> </span>construct<span class="_ _c"> </span>a<span class="_ _e"> </span>group</div><div class="t m0 x1 h6 yc ff4 fs3 fc0 sc0 ls12 ws0">of<span class="_ _6"> </span>ESFs<span class="_ _6"> </span>for<span class="_ _6"> </span>edge-based<span class="_ _e"> </span>active<span class="_ _6"> </span>contour<span class="_ _e"> </span>models<span class="_ _5"> </span>to<span class="_ _6"> </span>segment<span class="_ _6"> </span>objects</div><div class="t m0 x1 h6 yd ff4 fs3 fc0 sc0 ls13 ws0">with<span class="_ _5"> </span>poorly<span class="_ _5"> </span>defined<span class="_ _6"> </span>boundaries.<span class="_ _5"> </span><span class="lsa">In<span class="_ _5"> </span>our<span class="_ _5"> </span>framework,<span class="_ _5"> </span>which<span class="_ _6"> </span>incor-</span></div><div class="t m0 x1 h6 ye ff4 fs3 fc0 sc0 lse ws0">porates<span class="_ _e"> </span>gradient<span class="_ _6"> </span>information<span class="_ _6"> </span>as<span class="_ _e"> </span>w<span class="_ _f"></span>ell<span class="_ _e"> </span>as<span class="_ _6"> </span>probability<span class="_ _6"> </span>scores<span class="_ _e"> </span>from<span class="_ _e"> </span>a</div><div class="t m0 x1 h6 yf ff4 fs3 fc0 sc0 ls14 ws0">standard<span class="_ _1"> </span>classifier<span class="_ _7"></span>,<span class="_ _1"> </span>the<span class="_ _1"> </span>ESF<span class="_ _1"> </span>can<span class="_ _1"> </span>be<span class="_ _c"> </span>constructed<span class="_ _1"> </span>from<span class="_ _1"> </span>any<span class="_ _1"> </span>classif<span class="_ _2"></span>ica-</div><div class="t m0 x1 h6 y10 ff4 fs3 fc0 sc0 ls15 ws0">tion<span class="_ _e"> </span>algorithm<span class="_ _6"> </span>and<span class="_ _6"> </span>applied<span class="_ _e"> </span>to<span class="_ _6"> </span>any<span class="_ _6"> </span>edge-based<span class="_ _6"> </span>model<span class="_ _e"> </span>using<span class="_ _6"> </span>a<span class="_ _6"> </span>level</div><div class="t m0 x1 h6 y11 ff4 fs3 fc0 sc0 ls16 ws0">set<span class="_ _1"> </span>method.<span class="_ _1"> </span>Experiments<span class="_ _1"> </span>on<span class="_ _1"> </span>medical<span class="_ _1"> </span>images<span class="_ _1"> </span>using<span class="_ _1"> </span>the<span class="_ _1"> </span>distance<span class="_ _1"> </span>reg-</div><div class="t m0 x1 h6 y12 ff4 fs3 fc0 sc0 lsb ws0">ularized<span class="_ _6"> </span>level<span class="_ _e"> </span>set<span class="_ _5"> </span>f<span class="_ _2"></span>or<span class="_ _5"> </span>edge-based<span class="_ _6"> </span>active<span class="_ _6"> </span>contour<span class="_ _5"> </span>models<span class="_ _6"> </span>as<span class="_ _6"> </span>well<span class="_ _6"> </span>as</div><div class="t m0 x1 h6 y13 ff4 fs3 fc0 sc0 ls16 ws0">the<span class="_ _c"> </span>k-nearest<span class="_ _c"> </span>neighbours<span class="_ _c"> </span>and<span class="_ _e"> </span>the<span class="_ _c"> </span><span class="lsd">support<span class="_ _e"> </span>vector<span class="_ _c"> </span>machine<span class="_ _c"> </span>conf<span class="_ _2"></span>irm</span></div><div class="t m0 x1 h6 y14 ff4 fs3 fc0 sc0 ls17 ws0">the<span class="_ _c"> </span>effectiveness<span class="_ _c"> </span>of<span class="_ _e"> </span>the<span class="_ _e"> </span>proposed<span class="_ _c"> </span>approach.</div><div class="t m0 x5 h5 y15 ff3 fs3 fc0 sc0 lsc ws0">Index<span class="_ _10"> </span>T<span class="_ _11"></span>erms&#8212;<span class="ff4 lsa">Edge-based<span class="_ _10"> </span>active<span class="_ _10"> </span>contour<span class="_ _7"></span>,<span class="_ _12"> </span>edge-stop<span class="_ _10"> </span>function,</span></div><div class="t m0 x1 h6 y16 ff4 fs3 fc0 sc0 lsa ws0">gradient<span class="_ _c"> </span>information,<span class="_ _c"> </span>image<span class="_ _c"> </span>segm<span class="ls18">entation,<span class="_ _c"> </span>probability<span class="_ _c"> </span>score.</span></div><div class="t m0 x6 h7 y17 ff1 fs4 fc0 sc0 ls19 ws0">I.<span class="_ _4"> </span>I<span class="fs5 ls1a">NTR<span class="_ _2"></span>O<span class="_"> </span>DUCTION</span></div><div class="t m0 x1 h8 y18 ff4 fs6 fc0 sc0 ls0 ws0">I</div><div class="t m0 x7 h7 y19 ff1 fs4 fc0 sc0 ls1b ws0">MA<span class="_ _2"></span>G<span class="_ _f"></span>E<span class="_ _5"> </span>segmentatio<span class="_"> </span>n<span class="_ _b"> </span>plays<span class="_ _b"> </span>an<span class="_ _5"> </span>importan<span class="_ _f"></span>t<span class="_ _5"> </span>role<span class="_ _b"> </span>in<span class="_ _b"> </span>computer</div><div class="t m0 x7 h7 y1a ff1 fs4 fc0 sc0 ls1c ws0">vision<span class="_ _13"> </span>and<span class="_ _13"> </span>m</div><div class="t m0 x8 h7 y1b ff1 fs4 fc0 sc0 ls1d ws0">edical<span class="_ _13"> </span>image<span class="_ _8"> </span>analysis.<span class="_ _13"> </span>Many<span class="_ _8"> </span>segmentation</div><div class="t m0 x1 h7 y1c ff1 fs4 fc0 sc0 ls1e ws0">methods<span class="_ _e"> </span>have<span class="_ _e"> </span>been<span class="_ _e"> </span>propo<span class="_"> </span>sed<span class="_ _6"> </span>but<span class="_ _e"> </span>none<span class="_ _e"> </span>is<span class="_ _6"> </span>univ<span class="_ _2"></span>e<span class="_"> </span>rsally<span class="_ _6"> </span>applicable</div><div class="t m0 x1 h7 y1d ff1 fs4 fc0 sc0 ls1f ws0">[1],<span class="_ _e"> </span>[2],<span class="_ _6"> </span>especially<span class="_ _6"> </span>for<span class="_ _6"> </span>medical<span class="_ _6"> </span>im<span class="_"> </span>ages.<span class="_ _6"> </span>The<span class="_ _6"> </span>use<span class="_ _6"> </span>of<span class="_ _6"> </span>energy<span class="_ _e"> </span>min-</div><div class="t m0 x1 h7 y1e ff1 fs4 fc0 sc0 ls20 ws0">imiza</div><div class="t m0 x9 h7 y1f ff1 fs4 fc0 sc0 ls21 ws0">tion<span class="_ _5"> </span>in<span class="_ _b"> </span>image<span class="_ _5"> </span>segmentation<span class="_ _5"> </span>has<span class="_ _b"> </span>been<span class="_ _5"> </span>intensiv<span class="_ _2"></span>ely<span class="_ _b"> </span>studied,</div><div class="t m0 x1 h7 y20 ff1 fs4 fc0 sc0 ls22 ws0">starting<span class="_ _c"> </span>from<span class="_ _c"> </span>the<span class="_ _e"> </span>snake<span class="_ _c"> </span>model<span class="_ _c"> </span>[3].<span class="_ _c"> </span>Am<span class="_"> </span>ong<span class="_ _e"> </span>energy<span class="_ _c"> </span>minimization</div><div class="t m0 x1 h7 y21 ff1 fs4 fc0 sc0 ls22 ws0">approaches,<span class="_ _12"> </span>the<span class="_ _12"> </span>level<span class="_ _12"> </span>set<span class="_ _12"> </span>method<span class="_ _12"> </span>(LSM)<span class="_ _13"> </span>has<span class="_ _12"> </span>received<span class="_ _12"> </span>much</div><div class="t m0 x1 h7 y22 ff1 fs4 fc0 sc0 ls22 ws0">at</div><div class="t m0 x2 h7 y23 ff1 fs4 fc0 sc0 ls1a ws0">tention<span class="_ _14"> </span>and<span class="_ _14"> </span>is<span class="_ _14"> </span>used<span class="_ _14"> </span>to<span class="_ _14"> </span>minimize<span class="_ _14"> </span>an<span class="_ _14"> </span>ener<span class="_ _2"></span>gy<span class="_ _14"> </span>functional<span class="_ _14"> </span>when</div><div class="t m0 x1 h7 y24 ff1 fs4 fc0 sc0 ls1e ws0">segmenting<span class="_ _6"> </span>an<span class="_ _5"> </span>object<span class="_ _6"> </span>[4]&#8211;[10<span class="_"> </span>].</div><div class="t m0 xa h7 y25 ff1 fs4 fc0 sc0 ls23 ws0">Generally<span class="_ _11"></span>,<span class="_ _4"> </span>image<span class="_ _4"> </span>se<span class="_ _2"></span>gm<span class="_"> </span>entation<span class="_ _4"> </span>models<span class="_ _4"> </span>using<span class="_ _15"> </span>LSMs<span class="_ _15"> </span>can</div><div class="t m0 x1 h7 y26 ff1 fs4 fc0 sc0 ls24 ws0">be<span class="_ _8"> </span>classified<span class="_ _13"> </span>as<span class="_ _8"> </span>edge-based<span class="_ _8"> </span>models<span class="_ _13"> </span>or<span class="_ _8"> </span>region-based<span class="_ _13"> </span>models</div><div class="t m0 x1 h7 y27 ff1 fs4 fc0 sc0 ls24 ws0">[11]&#8211;[13].<span class="_ _b"> </span>The<span class="_ _b"> </span>former<span class="_ _14"> </span>utilizes<span class="_ _b"> </span>ed<span class="ls25">ge<span class="_ _b"> </span>inform<span class="_ _f"></span>ation<span class="_ _b"> </span>[6]<span class="_ _14"> </span>while<span class="_ _b"> </span>the</span></div><div class="t m0 x1 h7 y28 ff1 fs4 fc0 sc0 ls1f ws0">latter<span class="_ _b"> </span>employs<span class="_ _b"> </span>a<span class="_ _b"> </span>region<span class="_ _5"> </span>descript<span class="_ _f"></span><span class="ls23">or<span class="_ _b"> </span>to<span class="_ _b"> </span>control<span class="_ _b"> </span>the<span class="_ _b"> </span>displacement</span></div><div class="t m0 xb h9 y29 ff1 fs5 fc0 sc0 ls26 ws0">Manuscript<span class="_ _1"> </span>recei<span class="_ _2"></span>ved<span class="_ _1"> </span>October<span class="_ _1"> </span>18,<span class="_ _16"> </span>2015;<span class="_ _16"> </span><span class="ls27">revised<span class="_ _16"> </span>D<span class="_"> </span>ecem<span class="_ _f"></span>ber<span class="_ _16"> </span>02,<span class="_ _1"> </span>2015;<span class="_ _1"> </span>accepted</span></div><div class="t m0 x1 h9 y2a ff1 fs5 fc0 sc0 ls28 ws0">December<span class="_ _16"> </span>04,<span class="_ _16"> </span>2015.<span class="_ _16"> </span>Dat<span class="_ _2"></span>e<span class="_ _16"> </span>of<span class="_ _16"> </span>publication<span class="_ _16"> </span>December<span class="_ _16"> </span>11,<span class="_ _16"> </span>2015;<span class="_ _17"> </span>date<span class="_ _16"> </span>of<span class="_ _17"> </span>current<span class="_ _16"> </span>ver-</div><div class="t m0 x1 h9 y2b ff1 fs5 fc0 sc0 ls29 ws0">sion<span class="_ _1"> </span>December<span class="_ _1"> </span>23,<span class="_ _1"> </span>2015.<span class="_ _1"> </span>This<span class="_ _16"> </span>work<span class="_ _1"> </span>was<span class="_ _1"> </span>supported<span class="_ _1"> </span>in<span class="_ _1"> </span>part<span class="_ _1"> </span>by<span class="_ _1"> </span>the<span class="_ _1"> </span>A*ST<span class="_ _11"></span>AR<span class="_ _1"> </span>Sin-</div><div class="t m0 x1 h9 y2c ff1 fs5 fc0 sc0 ls2a ws0">gapore-China<span class="_ _1"> </span>Joint<span class="_ _1"> </span>Research<span class="_ _c"> </span>Programme<span class="_ _c"> </span>under<span class="_ _1"> </span>Grant<span class="_ _c"> </span>12105009;<span class="_ _1"> </span>and<span class="_ _c"> </span>by<span class="_ _1"> </span>WBS</div><div class="t m0 x1 h9 y2d ff1 fs5 fc0 sc0 ls2a ws0">Grant<span class="_ _c"> </span>R265-000-467-305.<span class="_ _c"> </span>The<span class="_ _c"> </span>associate<span class="_ _c"> </span>editor<span class="_ _c"> </span>coordinatin<span class="_ _2"></span>g<span class="_ _e"> </span>the<span class="_ _c"> </span>revie<span class="_ _2"></span>w<span class="_ _e"> </span>of<span class="_ _c"> </span>this</div><div class="t m0 x1 h9 y2e ff1 fs5 fc0 sc0 ls2b ws0">manuscript<span class="_ _1"> </span>and<span class="_ _c"> </span>appro<span class="_ _2"></span>ving<span class="_ _c"> </span>it<span class="_ _1"> </span>for<span class="_ _c"> </span>publication<span class="_ _1"> </span>was<span class="_ _1"> </span>Prof.<span class="_ _1"> </span>Arrate<span class="_ _c"> </span>Munoz-Barrutia.</div><div class="t m0 xb h9 y2f ff1 fs5 fc0 sc0 ls2c ws0">A.<span class="_ _c"> </span>Pratondo<span class="_ _c"> </span>is<span class="_ _e"> </span>with<span class="_ _c"> </span>the<span class="_ _e"> </span>Department<span class="_ _c"> </span>of<span class="_ _c"> </span>Information<span class="_ _c"> </span>Systems,<span class="_ _e"> </span>School<span class="_ _c"> </span>of<span class="_ _c"> </span>Ap-</div><div class="t m0 x1 h9 y30 ff1 fs5 fc0 sc0 ls2d ws0">plied<span class="_ _6"> </span>Science,<span class="_ _5"> </span>T<span class="_ _2"></span>elkom<span class="_ _5"> </span>Univ<span class="_ _d"></span>ersity<span class="_ _11"></span>,<span class="_ _b"> </span>Bandung,<span class="_ _6"> </span>Indonesia<span class="_ _5"> </span>40257,<span class="_ _5"> </span>and<span class="_ _5"> </span>also<span class="_ _5"> </span>with</div><div class="t m0 x1 h9 y31 ff1 fs5 fc0 sc0 ls2e ws0">the<span class="_ _6"> </span>Department<span class="_ _5"> </span>of<span class="_ _6"> </span>Electrical<span class="_ _6"> </span>and<span class="_ _6"> </span>Com<span class="_ _f"></span>puter<span class="_ _6"> </span>Engineerin<span class="_"> </span>g,<span class="_ _6"> </span>N<span class="_ _f"></span>ational<span class="_ _6"> </span>University</div><div class="t m0 x1 h9 y32 ff1 fs5 fc0 sc0 ls2f ws0">of<span class="_ _c"> </span>Singap<span class="_ _2"></span>ore,<span class="_ _c"> </span>Singapore<span class="_ _1"> </span>(e-mail:<span class="_ _c"> </span>agus.pr<span class="_ _2"></span>atondo.id@ieee.or<span class="_ _2"></span>g).</div><div class="t m0 xb h9 y33 ff1 fs5 fc0 sc0 ls30 ws0">C.-K.<span class="_ _16"> </span>C<span class="_"> </span>hui<span class="_ _1"> </span>is<span class="_ _16"> </span>w<span class="_ _f"></span>ith<span class="_ _16"> </span>the<span class="_ _1"> </span>Department<span class="_ _1"> </span>of<span class="_ _16"> </span>Mech<span class="_"> </span><span class="ls1e">anical<span class="_ _1"> </span>Engineering,<span class="_ _16"> </span>N<span class="_ _f"></span>ational<span class="_ _16"> </span>Uni-</span></div><div class="t m0 x1 h9 y34 ff1 fs5 fc0 sc0 ls31 ws0">versi<span class="_ _d"></span>ty<span class="_ _1"> </span>of<span class="_ _c"> </span>Singapore,<span class="_ _1"> </span>Singapore<span class="_ _1"> </span>117575<span class="_ _c"> </span>(e-mail:<span class="_ _1"> </span>mpecck@nus.edu.sg<span class="_ _2"></span>).</div><div class="t m0 xb h9 y35 ff1 fs5 fc0 sc0 ls32 ws0">S-H.<span class="_ _e"> </span>Ong<span class="_ _6"> </span>is<span class="_ _e"> </span>with<span class="_ _6"> </span>the<span class="_ _e"> </span>Department<span class="_ _6"> </span>of<span class="_ _e"> </span>Electrical<span class="_ _6"> </span>and<span class="_ _e"> </span>Computer<span class="_ _e"> </span>Engineering,</div><div class="t m0 x1 h9 y36 ff1 fs5 fc0 sc0 ls2b ws0">National<span class="_ _e"> </span>Universi<span class="_ _d"></span>ty<span class="_ _6"> </span>of<span class="_ _6"> </span>Singapore,<span class="_ _e"> </span>Singapore<span class="_ _6"> </span>117583<span class="_ _6"> </span>(e-mail:<span class="_ _6"> </span>eleongsh@nus.</div><div class="t m0 x1 h9 y37 ff1 fs5 fc0 sc0 ls2b ws0">edu.sg).</div><div class="t m0 xb h9 y38 ff1 fs5 fc0 sc0 ls33 ws0">Color<span class="_ _1"> </span>versions<span class="_ _1"> </span>of<span class="_ _1"> </span>one<span class="_ _c"> </span>or<span class="_ _1"> </span>more<span class="_ _1"> </span>of<span class="_ _1"> </span>the<span class="_ _c"> </span>figures<span class="_ _1"> </span>in<span class="_ _1"> </span>this<span class="_ _1"> </span>paper<span class="_ _1"> </span>are<span class="_ _c"> </span>a<span class="_ _2"></span>vailable<span class="_ _1"> </span>onlin<span class="_ _f"></span>e</div><div class="t m0 x1 h9 y39 ff1 fs5 fc0 sc0 ls30 ws0">at<span class="_ _c"> </span>http://ieeexplore.ieee.org.</div><div class="t m0 xb h9 y3a ff1 fs5 fc0 sc0 ls28 ws0">Digital<span class="_ _c"> </span>Object<span class="_ _1"> </span>Identifier<span class="_ _1"> </span>10.1109/LSP.2015.2508039</div><div class="t m0 xc h7 y5 ff1 fs4 fc0 sc0 ls1f ws0">of<span class="_ _10"> </span>the<span class="_ _12"> </span>activ<span class="_ _2"></span>e<span class="_ _12"> </span>conto<span class="_"> </span>ur<span class="_ _12"> </span>[14],<span class="_ _12"> </span>[15].<span class="_ _12"> </span>Edge-based<span class="_ _12"> </span>models<span class="_ _12"> </span>are<span class="_ _10"> </span>not</div><div class="t m0 xc h7 y3b ff1 fs4 fc0 sc0 ls34 ws0">sensiti<span class="_ _2"></span>ve<span class="_ _b"> </span>to<span class="_ _b"> </span>inhomogeneity<span class="_ _b"> </span>of<span class="_ _5"> </span>im<span class="_"> </span>age<span class="_ _b"> </span>intensities,<span class="_ _b"> </span>i.e.,<span class="_ _b"> </span>the<span class="_ _5"> </span>over-</div><div class="t m0 xc h7 y3c ff1 fs4 fc0 sc0 ls35 ws0">lapping<span class="_ _e"> </span>of<span class="_ _6"> </span>the<span class="_ _e"> </span>in<span class="_"> </span>tensi<span class="_"> </span>ty<span class="_ _6"> </span>ranges,<span class="_ _e"> </span>but<span class="_ _e"> </span>are<span class="_ _6"> </span>sensitive<span class="_ _c"> </span>to<span class="_ _6"> </span>objects<span class="_ _e"> </span>with</div><div class="t m0 xc h7 y3d ff1 fs4 fc0 sc0 ls36 ws0">poorly<span class="_ _18"> </span>defined<span class="_ _8"> </span>boundaries.<span class="_ _18"> </span>In<span class="_ _8"> </span>im<span class="_"> </span>ages<span class="_ _18"> </span>where<span class="_ _18"> </span>the<span class="_ _18"> </span>intensities</div><div class="t m0 xc h7 y3e ff1 fs4 fc0 sc0 ls35 ws0">change<span class="_ _5"> </span>gradually<span class="_ _b"> </span>in<span class="_ _5"> </span>the<span class="_ _5"> </span>vicinity<span class="_ _b"> </span>of<span class="_ _5"> </span>a<span class="_ _5"> </span>poorly<span class="_ _5"> </span>defined<span class="_ _5"> </span>boundary<span class="_ _2"></span>,</div><div class="t m0 xc h7 y3f ff1 fs4 fc0 sc0 ls1c ws0">the<span class="_ _e"> </span>edge-stop<span class="_ _c"> </span>function<span class="_ _e"> </span>(ESF)<span class="_ _e"> </span>fails<span class="_ _c"> </span>to<span class="_ _e"> </span>stop<span class="_ _e"> </span>the<span class="_ _e"> </span>contour<span class="_ _e"> </span>[16].</div><div class="t m0 xd h7 y40 ff1 fs4 fc0 sc0 ls1f ws0">T<span class="_ _11"></span>o<span class="_ _b"> </span>ov<span class="_ _2"></span>erco<span class="_"> </span>me<span class="_ _b"> </span>the<span class="_ _b"> </span>limitation<span class="_ _5"> </span>of<span class="_ _b"> </span>the<span class="_ _5"> </span>traditional<span class="_ _b"> </span>ESFs<span class="_ _b"> </span>in<span class="_ _5"> </span>edge-</div><div class="t m0 xc h7 y41 ff1 fs4 fc0 sc0 ls1f ws0">based<span class="_ _5"> </span>activ<span class="_ _2"></span>e<span class="_ _5"> </span>con<span class="_"> </span>tou<span class="_"> </span>r<span class="_ _5"> </span>m<span class="_"> </span>odels,<span class="_ _5"> </span>w<span class="_"> </span>e<span class="_ _5"> </span>pro<span class="_ _f"></span>pose<span class="_ _5"> </span>a<span class="_ _5"> </span>framew<span class="_ _d"></span>ork<span class="_ _5"> </span>to<span class="_ _5"> </span>con-</div><div class="t m0 xc h7 y42 ff1 fs4 fc0 sc0 ls37 ws0">struct<span class="_ _6"> </span>a<span class="_ _6"> </span>group<span class="_ _5"> </span>of<span class="_ _6"> </span>robust<span class="_ _6"> </span>ESFs<span class="_ _6"> </span>that<span class="_ _6"> </span>utilize<span class="_ _5"> </span>probability<span class="_ _6"> </span>scores<span class="_ _5"> </span>in-</div><div class="t m0 xc h7 y43 ff1 fs4 fc0 sc0 ls38 ws0">stead<span class="_ _b"> </span>of<span class="_ _b"> </span>the<span class="_ _14"> </span>predicted<span class="_ _b"> </span>class<span class="_ _b"> </span>labels<span class="_ _b"> </span>from<span class="_ _14"> </span>a<span class="_ _b"> </span>classifier.<span class="_ _5"> </span>Since<span class="_ _14"> </span>the</div><div class="t m0 xc h7 y44 ff1 fs4 fc0 sc0 ls1b ws0">scores<span class="_ _b"> </span>fall<span class="_ _b"> </span>in<span class="_ _b"> </span>[0,1],<span class="_ _b"> </span>this<span class="_ _b"> </span>task<span class="_ _14"> </span>is<span class="_ _b"> </span>similar<span class="_ _b"> </span>to<span class="_ _b"> </span>fuzzy<span class="_ _b"> </span>segmentation.</div><div class="t m0 xc h7 y45 ff1 fs4 fc0 sc0 ls39 ws0">Unlike<span class="_ _c"> </span>the<span class="_ _c"> </span>methods<span class="_ _c"> </span>of<span class="_ _c"> </span>[17],<span class="_ _c"> </span>[18],<span class="_ _c"> </span>which<span class="_ _c"> </span>rely<span class="_ _c"> </span>only<span class="_ _c"> </span>on<span class="_ _1"> </span>c<span class="_"> </span>lass<span class="_ _c"> </span>prob-</div><div class="t m0 xc h7 y46 ff1 fs4 fc0 sc0 ls36 ws0">ability<span class="_ _e"> </span>u<span class="_"> </span>sing<span class="_ _6"> </span>Bayes&#8217;<span class="_ _6"> </span>ru<span class="_"> </span>le,<span class="_ _6"> </span>our<span class="_ _6"> </span>framework<span class="_ _e"> </span>is<span class="_ _6"> </span>more<span class="_ _6"> </span>flexible<span class="_ _6"> </span>since</div><div class="t m0 xc h7 y47 ff1 fs4 fc0 sc0 ls3a ws0">it<span class="_ _c"> </span>utilizes<span class="_ _c"> </span>the<span class="_ _c"> </span>pro<span class="_ _f"></span>bability<span class="_ _c"> </span>score<span class="ls3b">s<span class="_ _c"> </span>from<span class="_ _c"> </span>any<span class="_ _c"> </span>classif<span class="_ _d"></span>ier.<span class="_ _c"> </span>At<span class="_ _c"> </span>the<span class="_ _1"> </span>same</span></div><div class="t m0 xc h7 y48 ff1 fs4 fc0 sc0 ls34 ws0">time,<span class="_ _c"> </span>we<span class="_ _1"> </span>retain<span class="_ _c"> </span>gradient<span class="_ _1"> </span>informa<span class="ls1e">tio<span class="_"> </span>n<span class="_ _c"> </span>to<span class="_ _c"> </span>terminate<span class="_ _1"> </span>contour<span class="_ _c"> </span>ev<span class="_ _2"></span>olu<span class="_"> </span>-</span></div><div class="t m0 xc h7 y49 ff1 fs4 fc0 sc0 ls3c ws0">tion<span class="_ _6"> </span>when<span class="_ _6"> </span>there<span class="_ _6"> </span>are<span class="_ _6"> </span>no<span class="_ _6"> </span>fuzzy<span class="_ _6"> </span>valu<span class="ls3d">es<span class="_ _e"> </span>due<span class="_ _6"> </span>to<span class="_ _6"> </span>d<span class="_"> </span>istin<span class="_ _f"></span>ct<span class="_ _e"> </span>bo<span class="_ _f"></span>undaries.</span></div><div class="t m0 xc h7 y4a ff1 fs4 fc0 sc0 ls23 ws0">These<span class="_ _b"> </span>ideas<span class="_ _b"> </span>differentiate<span class="_ _5"> </span>our<span class="_ _14"> </span><span class="ls3e">work<span class="_ _5"> </span>from<span class="_ _b"> </span>[19],<span class="_ _b"> </span>which<span class="_ _b"> </span>relies<span class="_ _b"> </span>on</span></div><div class="t m0 xc h7 y4b ff1 fs4 fc0 sc0 ls34 ws0">fuzzy<span class="_ _c"> </span>energy<span class="_ _c"> </span>and<span class="_ _c"> </span>is<span class="_ _c"> </span>considered<span class="_ _c"> </span>a<span class="_ _c"> </span>region-based<span class="_ _c"> </span>le<span class="_ _d"></span>vel<span class="_ _c"> </span>set<span class="_ _1"> </span>m<span class="_"> </span>ethod.</div><div class="t m0 xe h7 y4c ff1 fs4 fc0 sc0 ls3f ws0">II.<span class="_ _15"> </span>C</div><div class="t m0 xf h7 y4d ff1 fs5 fc0 sc0 ls40 ws0">ONSTR<span class="_ _2"></span>UCTION<span class="_ _5"> </span>OF<span class="_ _6"> </span><span class="fs4 ls0">N</span><span class="ls41">EW<span class="_ _5"> </span><span class="fs4 ls42">ESF</span><span class="ls0">S</span></span></div><div class="t m0 xd h7 y4e ff1 fs4 fc0 sc0 ls22 ws0">Our<span class="_ _e"> </span>new<span class="_ _c"> </span>ESFs<span class="_ _6"> </span>can<span class="_ _e"> </span>be<span class="_ _e"> </span>constructed<span class="_ _6"> </span>from<span class="_ _e"> </span>any<span class="_ _e"> </span>classification<span class="_ _c"> </span>al-</div><div class="t m0 xc h7 y4f ff1 fs4 fc0 sc0 ls23 ws0">gorithm<span class="_ _c"> </span>and<span class="_ _c"> </span>applied<span class="_ _c"> </span>to<span class="_ _e"> </span>any<span class="_ _c"> </span>edge-based<span class="_ _c"> </span>model<span class="_ _c"> </span>using<span class="_ _c"> </span>an<span class="_ _c"> </span>LSM.<span class="_ _c"> </span>In</div><div class="t m0 xc h7 y50 ff1 fs4 fc0 sc0 ls43 ws0">this<span class="_ _c"> </span>section,<span class="_ _1"> </span>we<span class="_ _c"> </span>briefly<span class="_ _c"> </span>re<span class="_ _d"></span>view<span class="_ _1"> </span>the<span class="_ _c"> </span>application<span class="_ _c"> </span>of<span class="_ _1"> </span>LSM<span class="_ _f"></span>s<span class="_ _1"> </span>to<span class="_ _c"> </span>image</div><div class="t m0 xc h7 y51 ff1 fs4 fc0 sc0 ls38 ws0">segmentation<span class="_ _6"> </span>as<span class="_ _5"> </span>well<span class="_ _5"> </span>as<span class="_ _6"> </span>selected<span class="_ _5"> </span>classification<span class="_ _6"> </span>algorithms,<span class="_ _6"> </span>i.e.,</div><div class="t m0 xc h7 y52 ff1 fs4 fc0 sc0 ls44 ws0">the</div><div class="t m0 x10 h7 y53 ff1 fs4 fc0 sc0 ls22 ws0">-nearest<span class="_ _14"> </span>neighbours<span class="_ _10"> </span>(<span class="_ _15"> </span><span class="ls45">-NN)<span class="_ _14"> </span>and<span class="_ _10"> </span>the<span class="_ _10"> </span>support<span class="_ _14"> </span>vector<span class="_ _10"> </span>ma-</span></div><div class="t m0 xc h7 y54 ff1 fs4 fc0 sc0 ls46 ws0">chine<span class="_ _5"> </span>(SVM),<span class="_ _5"> </span>and<span class="_ _5"> </span>show<span class="_ _6"> </span>how<span class="_ _5"> </span>to<span class="_ _5"> </span>construct<span class="_ _5"> </span>the<span class="_ _5"> </span>new<span class="_ _5"> </span>ESFs<span class="_ _5"> </span>using</div><div class="t m0 xc h7 y55 ff1 fs4 fc0 sc0 ls43 ws0">these<span class="_ _6"> </span>classification<span class="_ _5"> </span>algorithms.</div><div class="t m0 xc ha y56 ff2 fs4 fc0 sc0 ls47 ws0">A.<span class="_ _15"> </span>Level<span class="_ _e"> </span>Set<span class="_ _e"> </span>Methods<span class="_ _6"> </span>for<span class="_ _e"> </span>Image<span class="_ _e"> </span>Se<span class="_ _2"></span>gmentation</div><div class="t m0 xd h7 y57 ff1 fs4 fc0 sc0 ls1d ws0">In<span class="_ _c"> </span>LSMs,<span class="_ _c"> </span>a<span class="_ _c"> </span>planar<span class="_ _c"> </span>closed<span class="_ _c"> </span>c</div><div class="t m0 x11 h7 y58 ff1 fs4 fc0 sc0 ls1d ws0">urve</div><div class="t m0 x12 h7 y59 ff1 fs4 fc0 sc0 ls1f ws0">is<span class="_ _c"> </span>represented<span class="_ _c"> </span>implicitly<span class="_ _c"> </span>by</div><div class="t m0 xc h7 y5a ff1 fs4 fc0 sc0 ls39 ws0">the<span class="_ _e"> </span>zero<span class="_ _6"> </span>lev<span class="_ _d"></span>el<span class="_ _e"> </span>set<span class="_ _6"> </span>of<span class="_ _e"> </span>a<span class="_ _6"> </span>lev</div><div class="t m0 x13 h7 y5b ff1 fs4 fc0 sc0 ls48 ws0">el<span class="_ _e"> </span>set<span class="_ _e"> </span>f<span class="_"> </span>unction<span class="_ _6"> </span>(LSF)</div><div class="t m0 x14 h7 y5c ff1 fs4 fc0 sc0 ls0 ws0">:</div><div class="t m0 x15 h7 y5d ff1 fs4 fc0 sc0 ls19 ws0">(1)</div><div class="t m0 xc h7 y5e ff1 fs4 fc0 sc0 ls49 ws0">The<span class="_ _e"> </span>lev<span class="_ _d"></span>el<span class="_ _c"> </span>set<span class="_ _e"> </span>e<span class="_"> </span>qu<span class="_ _f"></span>ation<span class="_ _e"> </span>(LSE)<span class="_ _e"> </span>which<span class="_ _e"> </span>d<span class="_"> </span>efines<span class="_ _e"> </span>the<span class="_ _e"> </span>evolution<span class="_ _c"> </span>of<span class="_ _e"> </span>the</div><div class="t m0 xc h7 y5f ff1 fs4 fc0 sc0 ls45 ws0">implicit<span class="_ _6"> </span>function</div><div class="t m0 xf h7 y60 ff1 fs4 fc0 sc0 ls34 ws0">can<span class="_ _6"> </span>be<span class="_ _6"> </span>written<span class="_ _6"> </span>[4]<span class="_ _6"> </span>as</div><div class="t m0 x15 h7 y61 ff1 fs4 fc0 sc0 ls19 ws0">(2)</div><div class="t m0 xc h7 y62 ff1 fs4 fc0 sc0 ls1a ws0">where</div><div class="t m0 x16 h7 y63 ff1 fs4 fc0 sc0 ls43 ws0">denotes<span class="_ _1"> </span>the<span class="_ _1"> </span>speed<span class="_ _1"> </span>of<span class="_ _c"> </span>the<span class="_ _1"> </span>e<span class="_ _2"></span>volution<span class="_ _c"> </span>and<span class="_ _19"> </span><span class="ls4a">is<span class="_ _1"> </span>the<span class="_ _1"> </span>gradient</span></div><div class="t m0 xc h7 y64 ff1 fs4 fc0 sc0 ls34 ws0">operator.<span class="_ _b"> </span>Caselles<span class="_ _5"> </span><span class="ff2 ls1e">et<span class="_ _b"> </span>al.<span class="_ _b"> </span></span><span class="ls4b">propo<span class="_"> </span>sed<span class="_ _b"> </span>a<span class="_ _b"> </span>model<span class="_ _b"> </span>for<span class="_ _b"> </span>active<span class="_ _5"> </span>contours</span></div><div class="t m0 xc h7 y65 ff1 fs4 fc0 sc0 ls24 ws0">based<span class="_ _c"> </span>on<span class="_ _c"> </span>a<span class="_ _c"> </span>geometric<span class="_ _c"> </span>partial<span class="_ _1"> </span>diff<span class="ls35">erential<span class="_ _c"> </span>equatio<span class="ls22">n<span class="_ _c"> </span>[5]<span class="_ _c"> </span>that<span class="_ _c"> </span>is<span class="_ _1"> </span>also</span></span></div><div class="t m0 xc h7 y66 ff1 fs4 fc0 sc0 ls22 ws0">used<span class="_ _6"> </span>in<span class="_ _6"> </span>the<span class="_ _6"> </span>geodesic<span class="_ _6"> </span>activ<span class="_ _d"></span>e<span class="_ _6"> </span>contour<span class="_ _6"> </span>[6]:</div><div class="t m0 x15 h7 y67 ff1 fs4 fc0 sc0 ls19 ws0">(3)</div><div class="t m0 x17 h9 y68 ff1 fs5 fc0 sc0 ls2e ws0">1070-9908<span class="_ _c"> </span>&#169;<span class="_ _c"> </span>201<span class="_ _f"></span>5<span class="_ _c"> </span>IEEE.<span class="_ _c"> </span>Personal<span class="_ _c"> </span>use<span class="_ _c"> </span>is<span class="_ _c"> </span>pe<span class="_"> </span>rm<span class="_ _f"></span>itted,<span class="_ _c"> </span>but<span class="_ _1"> </span>r<span class="_"> </span>ep<span class="_ _f"></span>ublication/redistribution<span class="_ _c"> </span>requi<span class="_ _f"></span>res<span class="_ _c"> </span>IEEE<span class="_ _c"> </span>permission.</div><div class="t m0 x18 h9 y69 ff1 fs5 fc0 sc0 ls27 ws0">See<span class="_ _c"> </span>http://www.ieee.org/publications_standards/pub<span class="ls4c">lications/rights/index.html<span class="_ _c"> </span>for<span class="_ _c"> </span>mor<span class="_"> </span>e<span class="_ _c"> </span>inform<span class="_"> </span>ation.</span></div></div><div class="pi" data-data='{"ctm":[1.621622,0.000000,0.000000,1.621622,0.000000,0.000000]}'></div></div> </body> </html>
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