Accurate-matching.rar

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基于几何基元的图像匹配方法,可以不受光照的影响,但是只针对少的几何基元。
Accurate-matching.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/622b532015da9b288b92f4c5/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/622b532015da9b288b92f4c5/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">ELSEVIER <span class="_ _0"> </span><span class="ff2 fs1 ls1 ws1">Image <span class="_ _1"> </span><span class="ls2 ws2">and <span class="_"> </span><span class="ls3 ws3">Vision <span class="_ _1"> </span><span class="ls4 ws4">Computing <span class="_ _2"> </span><span class="ls5 ws5">15 <span class="_ _3"></span><span class="ff3 fs2 ls6 ws6">(I <span class="_ _4"></span><span class="ff2 fs1 ls7 ws7">997) <span class="_ _5"> </span><span class="ls5 ws5">889499 </span></span></span></span></span></span></span></span></div><div class="t m0 x2 h3 y2 ff1 fs3 fc0 sc0 ls8 ws8">Accurate <span class="_ _6"> </span><span class="ls9 ws9">matching <span class="_ _6"> </span><span class="lsa wsa">of <span class="_ _5"> </span><span class="lsb wsb">two-dimensional <span class="_ _7"> </span><span class="lsc wsc">shapes <span class="_ _8"> </span><span class="lsd wsd">using <span class="_ _9"> </span><span class="lse wse">the <span class="_"> </span><span class="lsf wsf">minimal </span></span></span></span></span></span></span></div><div class="t m0 x3 h3 y3 ff1 fs3 fc0 sc0 ls10 ws10">tolerance <span class="_ _a"> </span><span class="ls11 ws11">zone <span class="_ _2"> </span><span class="ls12 ws12">error </span></span></div><div class="t m0 x4 h2 y4 ff1 fs0 fc0 sc0 ls13 ws13">Jose <span class="_ _b"> </span><span class="ls14 ws14">A. <span class="_"> </span><span class="ls15 ws15">Ventura*, <span class="_ _c"> </span><span class="ls16 ws16">Wenhua <span class="_ _d"> </span><span class="ls17 ws17">Wan </span></span></span></span></div><div class="t m0 x5 h4 y5 ff4 fs1 fc0 sc0 ls18 ws18">Department <span class="_ _d"> </span><span class="ff3 fs0 ls19 ws19">of <span class="_ _e"></span><span class="fs2 ls1a ws1a">Industrial <span class="_ _f"></span><span class="ff4 fs1 ls5 ws5">and <span class="_ _1"> </span><span class="ls1b ws1b">Manufacturing <span class="_ _10"> </span><span class="ls1c ws1c">Engineering. <span class="_ _c"> </span></span></span>207 <span class="_ _5"> </span><span class="ls1d ws1d">Hummond <span class="_ _9"> </span><span class="ls1e ws1e">Building. <span class="_ _c"> </span><span class="ls1f ws1f">The <span class="_"> </span><span class="ls20 ws20">Pennsylvania <span class="_ _c"> </span><span class="ls21 ws21">State <span class="_ _5"> </span><span class="ls22 ws22">Universiy. <span class="_ _6"> </span>University <span class="_ _d"> </span><span class="ls23 ws23">Park, <span class="_ _5"> </span></span></span>PA <span class="_ _5"> </span><span class="ls24 ws24">16802. <span class="_ _2"> </span><span class="ls25 ws25">USA </span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x6 h5 y6 ff2 fs1 fc0 sc0 ls26 ws26">Received <span class="_ _5"> </span><span class="ls5 ws5">8 <span class="_"> </span><span class="ls27 ws27">December <span class="_ _2"> </span><span class="ls28 ws28">1995: <span class="_"> </span><span class="ff1 fs2 ls29 ws29">revised <span class="_ _4"></span><span class="ls2a ws2a">6 <span class="fs4 ls2b ws2b">May <span class="_ _11"> </span></span><span class="ls2c ws2c">1997; <span class="_ _f"></span><span class="ls2d ws2d">accepted <span class="_ _12"></span><span class="ls2a ws2a">22 <span class="_ _4"></span><span class="fs4 ls2b ws2b">May <span class="_"> </span><span class="fs2 ls2a ws2a">1997 </span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x7 h6 y7 ff5 fs2 fc0 sc0 ls2e ws2e">Abstract </div><div class="t m0 x8 h5 y8 ff1 fs2 fc0 sc0 ls2f ws2f">Automated <span class="_ _b"> </span><span class="ls30 ws30">visual <span class="_"> </span><span class="ls20 ws31">geometric <span class="_ _5"> </span><span class="ls31 ws32">inspection <span class="_ _b"> </span><span class="ls32 ws33">of <span class="_ _3"></span><span class="ls33 ws34">machined <span class="_ _5"> </span><span class="ls34 ws35">parts <span class="_ _11"> </span><span class="ls35 ws36">depends <span class="_ _5"> </span><span class="ls36 ws37">upon <span class="_"> </span><span class="ls2a ws2a">the <span class="_ _3"></span><span class="ls37 ws38">ability <span class="_ _5"> </span><span class="ls38 ws39">to <span class="_ _3"></span><span class="ls39 ws3a">determine <span class="_ _5"> </span></span></span></span>the <span class="_ _11"> </span><span class="ls3a ws3b">underlying <span class="_ _2"> </span><span class="ls3b ws3c">parameters <span class="_ _1"> </span></span></span></span></span></span></span></span>of <span class="_ _3"></span><span class="ls3c ws3d">a <span class="_ _11"> </span><span class="ls3d ws3e">shape </span></span></span></span></span></span></div><div class="t m0 x7 h7 y9 ff1 fs4 fc0 sc0 ls3e ws3f">model <span class="_ _b"> </span><span class="ls3f ws40">that <span class="_ _5"> </span><span class="ls40 ws41">will <span class="_ _1"> </span><span class="ls41 ws42">best <span class="_ _5"> </span><span class="ls42 ws43">fit <span class="_ _11"> </span><span class="ls43 ws13">the <span class="_ _1"> </span><span class="ls44 ws44">reference <span class="_ _13"> </span><span class="ls45 ws45">shape <span class="_ _5"> </span></span></span></span></span></span>to <span class="_"> </span><span class="ls43 ws13">the <span class="_ _1"> </span><span class="ls46 ws46">real <span class="_ _5"> </span><span class="ls45 ws45">shape <span class="_ _5"> </span><span class="ls47 ws47">captured. <span class="_ _9"> </span><span class="ls48 ws48">This <span class="_ _5"> </span><span class="ls49 ws49">paper <span class="_ _b"> </span><span class="ls4a ws4a">presents <span class="_ _9"> </span><span class="ls4b ws4b">a <span class="_ _3"></span><span class="ls4c ws4c">parametric <span class="_ _13"> </span><span class="ls4d ws4d">approach <span class="_ _9"> </span><span class="ls4e ws4e">for <span class="_ _1"> </span></span></span></span></span></span></span></span></span></span></span>the <span class="_ _1"> </span><span class="ls4f ws4f">matching <span class="_ _8"> </span><span class="ls50 ws50">of <span class="_"> </span><span class="ls51 ws51">two- </span></span></span></span></span></span></div><div class="t m0 x7 h7 ya ff1 fs4 fc0 sc0 ls52 ws52">dimensional <span class="_ _c"> </span><span class="ls53 ws2c">profiles, <span class="_ _2"> </span><span class="ls54 ws53">which <span class="_ _b"> </span><span class="ls55 ws54">are <span class="_"> </span><span class="ls56 ws55">composed <span class="_ _13"> </span><span class="ls50 ws50">of <span class="_"> </span><span class="ls57 ws56">straight-line <span class="_ _d"> </span><span class="ls58 ws57">segments <span class="_ _8"> </span><span class="ls59 ws58">and <span class="_"> </span><span class="ls11 ws2">circular <span class="_ _2"> </span><span class="ls5a ws59">arcs, <span class="_ _5"> </span><span class="ls45 ws45">based <span class="_ _5"> </span><span class="ls3e ws3f">on <span class="_"> </span><span class="ls43 ws13">the <span class="_ _1"> </span><span class="ls5b ws5a">tolerancing <span class="_ _13"> </span><span class="ls5c ws5b">requirements <span class="_ _c"> </span><span class="ls5d ws5c">defined <span class="_ _b"> </span></span></span></span></span>by <span class="_"> </span><span class="ls43 ws13">the </span></span></span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x7 h7 yb ff1 fs4 fc0 sc0 ls5e ws5d">AINSI <span class="_ _5"> </span><span class="ls5f ws5e">standards. <span class="_ _9"> </span><span class="ls60 ws5f">The <span class="_"> </span><span class="ls45 ws45">shape <span class="_ _5"> </span><span class="ls4f ws4f">matching <span class="_ _9"> </span><span class="ls61 ws60">problem <span class="_ _2"> </span><span class="ls62 ws61">is <span class="_ _3"></span><span class="ls63 ws62">formulated <span class="_ _13"> </span><span class="ls64 ws3e">as <span class="_ _3"></span><span class="ls4b ws4b">a <span class="_ _3"></span><span class="ls65 ws63">minimax <span class="_ _2"> </span><span class="ls66 ws64">optimization <span class="_ _13"> </span><span class="ls3e ws3f">model <span class="_ _b"> </span><span class="ls59 ws58">and <span class="_"> </span></span></span></span></span>a <span class="ls67 ws65">procedure <span class="_ _8"> </span><span class="ls4e ws4e">for <span class="_"> </span><span class="ls68 ws66">solving <span class="_ _b"> </span><span class="ls69 ws67">this <span class="_ _1"> </span><span class="ls66 ws64">optimization </span></span></span></span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x9 h7 yc ff1 fs4 fc0 sc0 ls3e ws3f">model <span class="_ _5"> </span><span class="ls62 ws61">is <span class="_ _3"></span><span class="ls6a ws68">developed. <span class="_ _13"> </span><span class="ls6b ws69">Experimental <span class="_ _d"> </span><span class="ls6c ws6a">results <span class="_ _b"> </span><span class="ls67 ws65">have <span class="_"> </span><span class="ls6d ws6b">shown <span class="_ _b"> </span><span class="ls43 ws13">the <span class="_ _11"> </span><span class="ls6e ws6c">proposed <span class="_ _9"> </span><span class="ls6f ws6d">algorithm <span class="_ _2"> </span><span class="ls40 ws41">to <span class="_ _3"></span><span class="ls70 ws6e">be <span class="_ _11"> </span><span class="ls71 ws6f">consistently <span class="_ _d"> </span><span class="ls72 ws70">accurate <span class="_ _b"> </span><span class="ls59 ws58">and <span class="_"> </span><span class="ls73 ws71">extremely <span class="_ _8"> </span><span class="ls74 ws72">fast. <span class="_ _1"> </span><span class="ls75 ws73">0 <span class="_ _b"> </span>1997 <span class="_ _14"></span><span class="ls76 ws74">Elsevier </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x9 h7 yd ff1 fs4 fc0 sc0 ls77 ws75">Science <span class="_ _9"> </span><span class="ls78 ws76">B.V. </span></div><div class="t m0 x7 h7 ye ff4 fs1 fc0 sc0 ls79 ws77">Keywords: <span class="_ _15"> </span><span class="ff1 fs4 ls7a ws78">Automated <span class="_ _13"> </span><span class="ls7b ws79">visual <span class="_ _b"> </span><span class="ls7c ws7a">inspection; <span class="_ _d"> </span><span class="ls7d ws2d">Minimal <span class="_ _2"> </span><span class="ls7e ws7b">tolerance <span class="_ _13"> </span><span class="ls70 ws6e">zone <span class="_ _5"> </span><span class="ls7f ws7c">error: <span class="_ _b"> </span><span class="ls80 ws7d">Minimax; <span class="_ _9"> </span><span class="ls81 ws7e">Optimization <span class="_ _16"> </span><span class="ls42 ws43">model; <span class="_ _2"> </span><span class="ls82 ws7f">Profile <span class="_ _b"> </span><span class="ls83 ws80">tolerance; <span class="_ _13"> </span><span class="ls84 ws81">Shape <span class="_ _5"> </span><span class="ls4f ws4f">matching </span></span></span></span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x9 h6 yf ff5 fs2 fc0 sc0 ls2a ws2a">1. <span class="_ _11"> </span><span class="ls85 ws82">Introduction </span></div><div class="t m0 xa h5 y10 ff1 fs2 fc0 sc0 ls86 ws83">Significant <span class="_ _10"> </span><span class="ls87 ws84">advances <span class="_ _a"> </span><span class="ls88 ws85">in <span class="_ _2"> </span><span class="ls89 ws86">computer <span class="_ _a"> </span><span class="ls8a ws87">technology, <span class="_ _10"> </span><span class="ls8b ws88">sensing </span></span></span></span></span></div><div class="t m0 x7 h5 y11 ff1 fs2 fc0 sc0 ls8c ws89">devices, <span class="_ _6"> </span><span class="ls35 ws36">pattern <span class="_ _c"> </span><span class="ls8d ws8a">recognition <span class="_ _17"> </span><span class="ls8e ws8b">and <span class="_ _8"> </span><span class="ls8f ws8c">image <span class="_ _c"> </span><span class="ls90 ws8d">processing <span class="_ _a"> </span><span class="ls91 ws8e">tech- </span></span></span></span></span></span></div><div class="t m0 x9 h5 y12 ff1 fs2 fc0 sc0 ls92 ws8f">niques <span class="_ _2"> </span><span class="ls93 ws90">have <span class="_ _b"> </span><span class="ls94 ws91">made <span class="_ _5"> </span><span class="ls95 ws92">automated <span class="_ _d"> </span><span class="ls30 ws30">visual <span class="_ _2"> </span><span class="ls31 ws32">inspection <span class="_ _16"> </span><span class="ls96 ws93">an <span class="_"> </span><span class="ls97 ws94">important </span></span></span></span></span></span></span></div><div class="t m0 x7 h5 y13 ff1 fs2 fc0 sc0 ls98 ws95">component <span class="_ _17"> </span><span class="ls32 ws33">of <span class="_ _2"> </span><span class="ls99 ws96">many <span class="_ _c"> </span><span class="ls89 ws86">computer <span class="_ _a"> </span><span class="ls9a ws97">integrated <span class="_ _18"> </span><span class="ls9b ws98">manufacturing </span></span></span></span></span></div><div class="t m0 x9 h5 y14 ff1 fs2 fc0 sc0 ls1b ws99">systems <span class="_ _8"> </span><span class="ff3 ls9c ws9a">[l-3]. <span class="_ _a"> </span></span><span class="ls9d ws9b">Fig. <span class="_ _b"> </span><span class="ls2a ws2a">1 </span>is <span class="_"> </span><span class="ls96 ws93">an <span class="_"> </span><span class="ls9e ws9c">overview <span class="_ _13"> </span><span class="ls32 ws33">of <span class="_ _11"> </span><span class="ls3c ws3d">a <span class="_ _3"></span><span class="ls9f ws9d">typical <span class="_ _8"> </span><span class="ls95 ws92">automated </span></span></span></span></span></span></span></div><div class="t m0 x9 h5 y15 ff1 fs2 fc0 sc0 ls30 ws30">visual <span class="_ _8"> </span><span class="ls31 ws32">inspection <span class="_ _a"> </span><span class="lsa0 ws9e">system. <span class="_ _13"> </span><span class="ls96 ws93">A <span class="_"> </span><span class="lsa1 ws9f">camera <span class="_ _13"> </span><span class="lsa2 wsa0">takes <span class="_ _2"> </span></span></span>an <span class="_ _5"> </span><span class="ls8f ws8c">image <span class="_ _9"> </span><span class="ls32 ws33">of <span class="_ _5"> </span><span class="ls2a ws2a">the </span></span></span></span></span></span></div><div class="t m0 x9 h5 y16 ff1 fs2 fc0 sc0 lsa3 wsa1">manufactured <span class="_ _a"> </span><span class="lsa4 wsa2">part <span class="_ _1"> </span><span class="lsa2 wsa0">whose <span class="_ _b"> </span><span class="lsa5 wsa3">precise <span class="_ _9"> </span><span class="lsa6 wsa4">location <span class="_ _13"> </span><span class="ls8e ws8b">and <span class="_"> </span><span class="lsa7 wsa5">orientation <span class="_ _6"> </span><span class="ls9d ws9b">is </span></span></span></span></span></span></span></div><div class="t m0 x9 h5 y17 ff1 fs2 fc0 sc0 lsa8 wsa6">unknown. <span class="_ _c"> </span><span class="lsa9 wsa7">The <span class="_ _5"> </span><span class="ls8f ws8c">image <span class="_ _2"> </span><span class="ls9d ws9b">is <span class="_ _3"></span><span class="ls6 wsa8">then <span class="_ _b"> </span><span class="ls32 ws33">processed <span class="_ _8"> </span><span class="ls38 ws39">to <span class="_ _11"> </span><span class="lsaa wsa9">yield <span class="_ _2"> </span><span class="lsab wsaa">higher <span class="_ _2"> </span><span class="lsac wsab">level </span></span></span></span></span></span></span></span></span></div><div class="t m0 x9 h5 y18 ff1 fs2 fc0 sc0 ls20 ws31">geometric <span class="_ _d"> </span><span class="lsad wsac">descriptions, <span class="_ _a"> </span><span class="ls1c ws6c">such <span class="_ _5"> </span><span class="ls32 ws33">as <span class="_ _3"></span><span class="lsae wsad">edge <span class="_ _5"> </span><span class="lsaf wsae">points, <span class="_ _9"> </span></span>edge <span class="_ _5"> </span><span class="lsb0 wsaf">types <span class="_ _b"> </span><span class="ls8e ws8b">and </span></span></span></span></span></span></div><div class="t m0 x9 h5 y19 ff1 fs2 fc0 sc0 lsb1 wsb0">dimension <span class="_ _a"> </span><span class="ls32 ws33">of <span class="_"> </span><span class="lsb2 wsb1">each <span class="_ _b"> </span><span class="lsb3 wsb2">segment, <span class="_ _d"> </span><span class="ls2a ws2a">the <span class="_ _1"> </span><span class="lsb4 wsb3">relationship <span class="_ _a"> </span><span class="lsb5 wsb4">between <span class="_ _d"> </span><span class="lsae wsad">edge </span></span></span></span></span></span></span></div><div class="t m0 x9 h5 y1a ff1 fs2 fc0 sc0 lsb6 wsb5">segments, <span class="_ _13"> </span><span class="lsa4 wsa2">etc., <span class="_ _1"> </span><span class="lsb7 wsb6">which <span class="_ _b"> </span><span class="lsb8 wsb7">are <span class="_"> </span><span class="lsb9 wsb8">more <span class="_ _5"> </span><span class="lsba wsb9">useful <span class="_ _2"> </span><span class="ls88 ws85">in <span class="_ _11"> </span><span class="ls2a ws2a">the <span class="_"> </span><span class="ls8d ws8a">recognition <span class="_ _6"> </span><span class="ls8e ws8b">and </span></span></span></span></span></span></span></span></span></div><div class="t m0 x9 h5 y1b ff1 fs2 fc0 sc0 lsa6 wsa4">matching <span class="_ _d"> </span><span class="ls2a ws2a">stages. <span class="_ _b"> </span><span class="lsa9 wsa7">The <span class="_ _5"> </span><span class="lsbb wsba">vision <span class="_ _9"> </span><span class="lsbc wsbb">system <span class="_ _2"> </span><span class="lsbd wsbc">recognizes <span class="_ _c"> </span><span class="ls8e ws8b">and <span class="_ _1"> </span><span class="lsbe wsbd">inspects </span></span></span></span></span></span></span></div><div class="t m0 x9 h5 y1c ff1 fs2 fc0 sc0 ls3c ws3d">a <span class="_"> </span><span class="lsa4 wsa2">part <span class="_ _b"> </span><span class="lsbf wsbe">based <span class="_ _9"> </span><span class="lsc0 wsbf">on <span class="_ _b"> </span><span class="ls2a ws2a">the <span class="_ _b"> </span><span class="ls20 ws31">geometric <span class="_ _c"> </span><span class="ls8a ws87">description <span class="_ _a"> </span><span class="ls6 wsa8">obtained <span class="_ _c"> </span><span class="ls88 ws85">in <span class="_ _b"> </span></span></span></span></span>the </span></span></span></span></div><div class="t m0 x9 h5 y1d ff1 fs2 fc0 sc0 ls8f ws8c">image <span class="_ _13"> </span><span class="ls90 ws8d">processing <span class="_ _a"> </span><span class="lsa2 wsa0">stage <span class="_ _9"> </span><span class="ls8e ws8b">and <span class="_ _2"> </span><span class="ls2a ws2a">the <span class="_ _2"> </span>stored <span class="_ _8"> </span><span class="ls20 ws31">geometric <span class="_ _6"> </span><span class="ls78 wsc0">models </span></span></span></span></span></span></div><div class="t m0 x9 h5 y1e ff1 fs2 fc0 sc0 lsb7 wsb6">which <span class="_ _d"> </span><span class="lsb8 wsb7">are <span class="_ _2"> </span><span class="ls63 ws53">derived <span class="_ _16"> </span><span class="lsc1 wsc1">from <span class="_ _13"> </span><span class="ls2a ws2a">the <span class="_ _2"> </span><span class="lsc2 wsc2">CAD <span class="_ _13"> </span><span class="lsc3 wsc3">model <span class="_ _c"> </span><span class="lsc4 wsc4">database. <span class="_ _6"> </span><span class="lsa9 wsa7">The </span></span></span></span></span></span></span></span></div><div class="t m0 x9 h5 y1f ff1 fs2 fc0 sc0 ls8d ws8a">recognition <span class="_ _6"> </span><span class="lsc5 wsc5">ensures <span class="_ _13"> </span><span class="ls2a ws2a">that <span class="_ _1"> </span>the <span class="_ _5"> </span><span class="ls2d ws2d">correct <span class="_ _2"> </span><span class="lsc6 wsc6">object <span class="_ _2"> </span><span class="ls9d ws9b">is <span class="_"> </span><span class="lsc7 wsc7">being <span class="_ _9"> </span><span class="ls29 ws29">viewed, </span></span></span></span></span></span></span></div><div class="t m0 x9 h5 y20 ff1 fs2 fc0 sc0 ls8e ws8b">and <span class="_"> </span><span class="ls2a ws2a">the <span class="_"> </span><span class="lsa6 wsa4">matching <span class="_ _13"> </span><span class="lsc8 wsc8">gives <span class="_ _b"> </span><span class="lsc9 wsc9">information <span class="_ _6"> </span><span class="lsc0 wsbf">on <span class="_"> </span></span></span></span></span>the <span class="_"> </span><span class="lsca wsca">position, <span class="_ _8"> </span><span class="lscb wscb">orienta- </span></span></span></div><div class="t m0 x9 h5 y21 ff1 fs2 fc0 sc0 lscc wscc">tion <span class="_ _b"> </span><span class="ls8e ws8b">and <span class="_ _5"> </span><span class="ls3a ws3b">underlying <span class="_ _6"> </span><span class="ls20 ws31">geometric <span class="_ _c"> </span><span class="ls3b ws3c">parameters <span class="_ _d"> </span><span class="ls32 ws33">of <span class="_"> </span><span class="ls2a ws2a">the <span class="_ _1"> </span><span class="lsa4 wsa2">part <span class="_ _5"> </span><span class="lsc7 wsc7">being </span></span></span></span></span></span></span></span></div><div class="t m0 x9 h5 y22 ff1 fs2 fc0 sc0 ls84 wscd">inspected <span class="_ _c"> </span><span class="ls32 ws33">[4]. </span></div><div class="t m0 xa h5 y23 ff1 fs2 fc0 sc0 lscd wsce">In <span class="_ _2"> </span><span class="ls2a ws2a">the <span class="_ _2"> </span>past <span class="_ _8"> </span><span class="ls2d ws2d">decade, <span class="_ _d"> </span></span>the <span class="_ _9"> </span><span class="lsce wscf">study <span class="_ _13"> </span><span class="ls32 ws33">of <span class="_ _2"> </span><span class="ls3d ws3e">shape <span class="_ _8"> </span><span class="lsa6 wsa4">matching <span class="_ _a"> </span><span class="ls8e ws8b">and </span></span></span></span></span></span></div><div class="t m0 x9 h5 y24 ff1 fs2 fc0 sc0 lscf wsd0">dimensional <span class="_ _19"> </span><span class="lsd0 wsd1">parameter <span class="_ _1a"> </span><span class="lsd1 wsd2">estimation <span class="_ _17"> </span><span class="lsa2 wsa0">has <span class="_ _13"> </span><span class="lsd2 wsd3">received <span class="_ _a"> </span><span class="ls3c ws3d">a <span class="_ _2"> </span><span class="lsd3 wsd4">great </span></span></span></span></span></span></div><div class="t m0 x9 h5 y25 ff1 fs2 fc0 sc0 ls94 ws91">deal <span class="_ _1"> </span><span class="ls32 ws33">of <span class="_ _11"> </span><span class="lsd4 wsd5">attention <span class="_ _d"> </span><span class="lsd5 wsd6">[5- <span class="_ _5"> </span><span class="ls2a ws2a">101. <span class="_ _4"></span><span class="lsa9 wsa7">The <span class="_ _1"> </span><span class="ls69 wsd7">general <span class="_ _9"> </span><span class="lsd6 wsd8">approach <span class="_ _9"> </span><span class="lsb0 wsaf">first <span class="_"> </span><span class="lsd7 wsd9">analyzes </span></span></span></span></span></span></span></span></span></div><div class="t m0 x9 h5 y26 ff1 fs2 fc0 sc0 ls2a ws2a">the <span class="_ _5"> </span><span class="lsd8 wsda">reference <span class="_ _c"> </span><span class="lsc6 wsc6">object <span class="_ _13"> </span><span class="ls8e ws8b">and <span class="_ _b"> </span><span class="lsd9 wsdb">develops <span class="_ _c"> </span><span class="ls3c ws3d">a <span class="_"> </span><span class="ls3d ws3e">shape <span class="_ _2"> </span><span class="lsc3 wsc3">model <span class="_ _8"> </span><span class="lsda wsdc">off-line. </span></span></span></span></span></span></span></span></div><div class="t m0 xb h5 y27 ff1 fs2 fc0 sc0 ls2a ws2a">* <span class="_ _4"></span><span class="lsdb wsdd">Corresponding <span class="_ _1b"></span><span class="lsdc wsde">author. <span class="_ _f"></span><span class="lsdd wsdf">Tel: <span class="lsa4 wsa2">(804) <span class="_ _1c"></span><span class="ls2a ws2a">865 <span class="_ _12"></span><span class="ls2c ws2c">3841; <span class="_ _1c"></span><span class="lsb9 wsb8">fax: <span class="_ _12"></span><span class="lsa4 wsa2">(814) <span class="_ _12"></span><span class="ls2a ws2a">863 <span class="_ _1c"></span><span class="ls2c ws2c">4745; <span class="_ _12"></span><span class="lsde wse0">e-mail: </span></span></span></span></span></span></span></span></span></span></span></div><div class="t m0 x7 h5 y28 ff1 fs2 fc0 sc0 ls36 ws37">javl <span class="_ _14"></span><span class="lsdf wse1">@email.psu.edu </span></div><div class="t m0 x9 h5 y29 ff1 fs2 fc0 sc0 lse0 wse2">0262-8856/97/$17.00 <span class="ls2a ws2a">0 <span class="_ _b"> </span>1997 <span class="_ _4"></span><span class="fs4 ls76 ws74">Elsevier <span class="_ _5"> </span><span class="ls77 ws75">Science <span class="_ _b"> </span><span class="ls78 ws76">B.V. <span class="_"> </span><span class="lse1 wse3">All <span class="_ _11"> </span><span class="lse2 wse4">rights <span class="_ _1"> </span><span class="lse3 wse5">reserved </span></span></span></span></span></span></span></div><div class="t m0 x9 h7 y2a ff4 fs1 fc0 sc0 lse4 wse6">P/I <span class="_ _13"> </span><span class="ff1 fs4 lse5 wse7">SO262-8856(97)00038-3 </span></div><div class="t m0 xc h5 y2b ff1 fs2 fc0 sc0 lsa9 wsa7">The <span class="_ _9"> </span><span class="lsa6 wsa4">matching <span class="_ _a"> </span><span class="lse6 wse8">problem <span class="_ _16"> </span><span class="ls9d ws9b">is <span class="_ _b"> </span><span class="lse7 wse9">formulated <span class="_ _1a"> </span><span class="ls32 ws33">as <span class="_ _b"> </span><span class="ls96 ws93">an <span class="_ _2"> </span><span class="lsd1 wsd2">optimization </span></span></span></span></span></span></span></div><div class="t m0 xc h5 y2c ff1 fs2 fc0 sc0 lsc3 wsc3">model <span class="_ _9"> </span><span class="lsbf wsbe">based <span class="_ _2"> </span><span class="lsc0 wsbf">on <span class="_ _5"> </span><span class="ls3c ws3d">a <span class="_"> </span><span class="lse8 wsea">particular <span class="_ _c"> </span><span class="lse9 wseb">fitting <span class="_ _2"> </span><span class="ls8f ws8c">criterion. <span class="_ _c"> </span><span class="lsa9 wsa7">The <span class="_ _b"> </span></span></span></span></span></span></span></span>model <span class="_ _8"> </span><span class="ls9d ws9b">is </span></div><div class="t m0 xc h5 y10 ff1 fs2 fc0 sc0 ls6 wsa8">then <span class="_ _b"> </span><span class="lsb6 wsb5">solved <span class="_ _b"> </span><span class="lsea wsec">with <span class="_ _5"> </span><span class="ls96 ws93">an <span class="_ _1"> </span><span class="lseb wsed">input <span class="_ _2"> </span><span class="lsec wsee">shape, <span class="_ _5"> </span><span class="lsb7 wsb6">which <span class="_ _2"> </span><span class="ls9d ws9b">is <span class="_ _3"></span><span class="lsed wsef">represented <span class="_ _c"> </span><span class="lsc0 wsbf">by <span class="_"> </span><span class="lsee wsf0">all </span></span></span></span></span></span></span></span></span></span></div><div class="t m0 xc h5 y11 ff1 fs2 fc0 sc0 ls2a ws2a">the <span class="_"> </span><span class="lsef wsf1">sampled <span class="_ _9"> </span><span class="lsaf wsae">points, <span class="_ _9"> </span><span class="ls88 ws85">in <span class="_"> </span></span></span></span>the <span class="_"> </span><span class="lsf0 wsf2">on-line <span class="_ _13"> </span><span class="ls34 ws35">stage. <span class="_ _5"> </span><span class="lsa9 wsa7">The <span class="_ _5"> </span><span class="lsf1 wsf3">solution <span class="_ _9"> </span><span class="ls32 ws33">of <span class="_ _11"> </span><span class="lsf2 wsf4">this </span></span></span></span></span></span></div><div class="t m0 xc h5 y12 ff1 fs2 fc0 sc0 lsc3 wsc3">model <span class="_ _9"> </span><span class="lsf3 wsf5">can <span class="_ _b"> </span><span class="lsf4 wsf6">be <span class="_ _5"> </span><span class="ls1c ws6c">used <span class="_ _b"> </span><span class="ls38 ws39">to <span class="_"> </span><span class="ls39 ws3a">determine <span class="_ _16"> </span><span class="ls2a ws2a">the <span class="_ _5"> </span>pose <span class="_ _b"> </span><span class="ls8e ws8b">and <span class="_ _5"> </span><span class="lscf wsd0">dimensional </span></span></span></span></span></span></span></span></div><div class="t m0 xc h5 y13 ff1 fs2 fc0 sc0 ls3b ws3c">parameters <span class="_ _c"> </span><span class="ls32 ws33">of <span class="_ _1"> </span><span class="ls2a ws2a">the <span class="_ _5"> </span><span class="lsc6 wsc6">object <span class="_ _9"> </span><span class="ls88 ws85">in <span class="_ _5"> </span></span></span>the <span class="_ _5"> </span><span class="ls67 ws6e">scene, <span class="_ _9"> </span><span class="ls8e ws8b">and <span class="_ _b"> </span><span class="ls23 wsf7">perform <span class="_ _13"> </span><span class="lsf5 wsf8">out-of- </span></span></span></span></span></span></div><div class="t m0 xc h5 y14 ff1 fs2 fc0 sc0 lsf6 wsf9">profile <span class="_ _13"> </span><span class="lsf7 wsfa">inspection. <span class="_ _a"> </span><span class="lsf8 wsfb">Least-squares <span class="_ _10"> </span><span class="ls9d ws9b">is <span class="_ _5"> </span><span class="ls2a ws2a">the <span class="_ _b"> </span><span class="lsf2 wsf4">most <span class="_ _9"> </span><span class="lsf9 wsfc">widely <span class="_ _d"> </span><span class="ls1c ws6c">used </span></span></span></span></span></span></span></div><div class="t m0 xc h5 y2d ff1 fs2 fc0 sc0 lse9 wseb">fitting <span class="_ _8"> </span><span class="ls73 wsfd">criterion <span class="_ _16"> </span><span class="lsae wsad">for <span class="_ _b"> </span><span class="ls3d ws3e">shape <span class="_ _2"> </span><span class="lsa6 wsa4">matching <span class="_ _a"> </span><span class="ls7b wsfe">[9-121. <span class="_ _d"> </span><span class="lsbc wsbb">For <span class="_ _b"> </span><span class="lsc1 wsc1">example, </span></span></span></span></span></span></span></div><div class="t m0 xc h5 y2e ff1 fs2 fc0 sc0 ls8f ws8c">Ponce <span class="_ _13"> </span><span class="lsa2 wsa0">et <span class="_ _5"> </span><span class="lsc6 wsc6">al. <span class="_ _2"> </span><span class="ls6a wsff">[I <span class="_ _11"> </span><span class="ls2a ws2a">11 <span class="_ _14"></span><span class="lsfa ws100">applied <span class="_ _d"> </span><span class="lsfb ws101">elimination <span class="_ _17"> </span><span class="lsab wsaa">theory <span class="_ _13"> </span><span class="ls38 ws39">to <span class="_ _5"> </span></span></span></span></span></span></span>construct </span></span></div><div class="t m0 xc h5 y17 ff1 fs2 fc0 sc0 ls96 ws93">an <span class="_"> </span><span class="lsfc ws102">implicit <span class="_ _8"> </span><span class="ls6 wsa8">equation <span class="_ _8"> </span><span class="ls2a ws2a">that <span class="_ _1"> </span><span class="lsfd ws103">relates <span class="_ _2"> </span></span>the <span class="_ _11"> </span><span class="lsb9 wsb8">observed <span class="_ _13"> </span><span class="lseb wsed">input <span class="_ _b"> </span><span class="lsfe ws104">informa- </span></span></span></span></span></span></div><div class="t m0 xc h5 y18 ff1 fs2 fc0 sc0 lscc wscc">tion <span class="_ _5"> </span><span class="ls38 ws39">to <span class="_ _11"> </span><span class="ls2a ws2a">the <span class="_"> </span><span class="lsff ws105">three-dimensional <span class="_ _19"> </span><span class="ls100 ws106">position <span class="_ _13"> </span><span class="ls8e ws8b">and <span class="_"> </span><span class="lsa7 wsa5">orientation <span class="_ _16"> </span><span class="ls32 ws33">of <span class="_ _11"> </span></span></span></span></span></span>the </span></span></div><div class="t m0 xc h5 y19 ff1 fs2 fc0 sc0 lsfa ws100">object. <span class="_ _13"> </span><span class="lscb wscb">They <span class="_ _9"> </span><span class="ls6 wsa8">then <span class="_ _9"> </span><span class="lsb6 wsb5">solved <span class="_ _13"> </span><span class="ls2a ws2a">the <span class="_ _b"> </span><span class="ls3d ws3e">shape <span class="_ _2"> </span><span class="lsa6 wsa4">matching <span class="_ _16"> </span><span class="lse6 wse8">problem <span class="_ _c"> </span><span class="lsc0 wsbf">by </span></span></span></span></span></span></span></span></div><div class="t m0 xc h5 y1a ff1 fs2 fc0 sc0 ls101 ws107">minimizing <span class="_ _18"> </span><span class="ls2a ws2a">the <span class="_ _b"> </span><span class="ls102 ws108">sum <span class="_ _b"> </span><span class="ls32 ws33">of <span class="_ _5"> </span><span class="ls103 ws109">squares <span class="_ _8"> </span></span>of <span class="_ _5"> </span></span></span>the <span class="_ _5"> </span><span class="lsae wsad">errors <span class="_ _2"> </span><span class="ls94 ws91">measured <span class="_ _c"> </span><span class="lsc0 wsbf">by </span></span></span></span></div><div class="t m0 xc h5 y2f ff1 fs2 fc0 sc0 ls2a ws2a">the <span class="_ _9"> </span><span class="lsa9 wsa7">algebraic <span class="_ _a"> </span><span class="ls104 ws10a">distance <span class="_ _16"> </span><span class="lsb5 wsb4">between <span class="_ _6"> </span><span class="lsb2 wsb1">each <span class="_ _8"> </span><span class="ls32 ws33">data <span class="_ _8"> </span><span class="ls58 ws10b">point <span class="_ _d"> </span><span class="ls8e ws8b">and <span class="_ _9"> </span></span></span></span></span></span></span></span>the </div><div class="t m0 xc h5 y1c ff1 fs2 fc0 sc0 ls105 ws10c">developed <span class="_ _6"> </span><span class="ls106 ws10d">equation. <span class="_ _6"> </span><span class="lsa6 wsa4">Chen <span class="_ _13"> </span><span class="ls8e ws8b">and <span class="_ _2"> </span><span class="ls107 ws10e">Ventura <span class="_ _c"> </span><span class="ff3 ls108 ws2a">[ <span class="_ _4"></span><span class="ff1 ls2a">121 <span class="_ _11"> </span><span class="ls105 ws10c">developed <span class="_ _a"> </span><span class="ls3c ws3d">a </span></span></span></span></span></span></span></span></div><div class="t m0 xd h5 y1d ff1 fs2 fc0 sc0 ls3d ws3e">shape <span class="_ _2"> </span><span class="lsc3 wsc3">model <span class="_ _8"> </span><span class="lsea wsec">with <span class="_ _2"> </span><span class="ls94 ws91">four <span class="_ _2"> </span><span class="ls3b ws3c">parameters <span class="_ _16"> </span><span class="ls109 ws10f">(one <span class="_ _2"> </span><span class="lsae wsad">for <span class="_ _b"> </span><span class="ls10a ws110">scale, <span class="_ _2"> </span><span class="ls8e ws8b">one <span class="_ _2"> </span></span></span>for </span></span></span></span></span></span></div><div class="t m0 xc h5 y1e ff1 fs2 fc0 sc0 lsa7 wsa5">orientation <span class="_ _16"> </span><span class="ls8e ws8b">and <span class="_"> </span><span class="ls2a ws2a">two <span class="_ _1"> </span><span class="lsae wsad">for <span class="_"> </span><span class="ls10b ws111">position) <span class="_ _8"> </span></span>for <span class="_"> </span><span class="ls10c ws112">planar <span class="_ _b"> </span><span class="lsfa ws100">complex <span class="_ _13"> </span><span class="ls34 ws35">shapes. </span></span></span></span></span></span></div><div class="t m0 xc h5 y1f ff1 fs2 fc0 sc0 lsa9 wsa7">The <span class="_ _2"> </span><span class="lsae wsad">errors <span class="_ _2"> </span><span class="lsb5 wsb4">between <span class="_ _c"> </span><span class="ls2a ws2a">the <span class="_ _5"> </span><span class="ls10d ws113">boundary <span class="_ _6"> </span><span class="ls100 ws106">points <span class="_ _13"> </span><span class="ls8e ws8b">and <span class="_ _b"> </span><span class="ls10e ws114">fitted <span class="_ _2"> </span></span></span></span></span></span></span></span>curves </div><div class="t m0 xc h5 y20 ff1 fs2 fc0 sc0 ls10f ws115">were <span class="_ _b"> </span><span class="ls94 ws91">measured <span class="_ _13"> </span><span class="lsc0 wsbf">by <span class="_"> </span><span class="ls2a ws2a">the <span class="_ _1"> </span><span class="lsb9 wsb8">true <span class="_ _5"> </span><span class="lsda wsdc">Euclidean <span class="_ _c"> </span><span class="ls110 ws116">distances. <span class="_ _d"> </span><span class="lsa9 wsa7">The <span class="_ _b"> </span><span class="ls111 ws117">shape- </span></span></span></span></span></span></span></span></div><div class="t m0 xd h5 y21 ff1 fs2 fc0 sc0 lsa6 wsa4">matching <span class="_ _13"> </span><span class="lse6 wse8">problem <span class="_ _8"> </span><span class="ls112 ws4d">was <span class="_"> </span><span class="lse7 wse9">formulated <span class="_ _c"> </span><span class="ls32 ws33">as <span class="_ _3"></span><span class="ls96 ws93">an <span class="_"> </span><span class="ls113 ws118">unconstrained <span class="_ _1a"> </span><span class="ls114 ws119">opti- </span></span></span></span></span></span></span></div><div class="t m0 xd h5 y22 ff1 fs2 fc0 sc0 ls115 ws11a">mization <span class="_ _d"> </span><span class="lsc3 wsc3">model <span class="_ _9"> </span><span class="lsbf wsbe">based <span class="_ _b"> </span><span class="lsc0 wsbf">on <span class="_ _5"> </span><span class="ls2a ws2a">the <span class="_ _1"> </span><span class="ls116 ws11b">least-squares <span class="_ _6"> </span><span class="ls8f ws8c">criterion. </span></span></span></span></span></span></div><div class="t m0 xe h5 y23 ff1 fs2 fc0 sc0 lsa9 wsa7">The <span class="_ _5"> </span><span class="ls6e ws1a">ANSI <span class="_ _5"> </span><span class="lsae wsad">Y <span class="ls117 ws11c">14.5M- <span class="_"> </span><span class="ls2a ws2a">1982 <span class="_ _11"> </span><span class="ls118 ws11d">protocol <span class="_ _8"> </span></span><span class="ff3 ls108">[ <span class="_ _4"></span><span class="ff1 ls2a">131, <span class="lsb7 wsb6">which <span class="_ _5"> </span><span class="ls119 ws11e">establishes </span></span></span></span></span></span></span></span></div><div class="t m0 xc h5 y24 ff1 fs2 fc0 sc0 ls2a ws2a">the <span class="_"> </span><span class="ls11a ws11f">standards <span class="_ _9"> </span><span class="lsae wsad">for <span class="_"> </span><span class="ls11b ws120">stating <span class="_ _b"> </span><span class="ls8e ws8b">and <span class="_ _1"> </span><span class="ls6 wsa8">interpreting <span class="_ _16"> </span></span></span></span></span></span>the <span class="_ _11"> </span><span class="ls11c ws121">requirements <span class="_ _6"> </span><span class="ls32 ws33">of </span></span></div><div class="t m0 xd h5 y30 ff1 fs2 fc0 sc0 ls11d ws122">tolerancing <span class="_ _a"> </span><span class="ls32 ws33">of <span class="_ _5"> </span><span class="ls11e ws123">location, <span class="_ _c"> </span><span class="lsb7 wsb6">form, <span class="_ _2"> </span><span class="ls1c ws6c">profile, <span class="_ _8"> </span><span class="lsa7 wsa5">orientation <span class="_ _a"> </span><span class="ls8e ws8b">and <span class="_ _b"> </span><span class="ls11f ws124">run- </span></span></span></span></span></span></span></div><div class="t m0 xd h5 y26 ff1 fs2 fc0 sc0 lsea wsec">out, <span class="_ _2"> </span><span class="lsa2 wsa0">has <span class="_ _b"> </span><span class="ls120 ws125">been <span class="_ _13"> </span><span class="lsf9 wsfc">widely <span class="_ _d"> </span><span class="ls1c ws6c">used <span class="_ _9"> </span><span class="ls88 ws85">in <span class="_ _2"> </span><span class="ls121 ws126">industry. <span class="_ _16"> </span><span class="ls122 ws127">Profile <span class="_ _13"> </span><span class="ls7a ws128">tolerances </span></span></span></span></span></span></span></span></div><div class="t m0 xd h5 y31 ff1 fs2 fc0 sc0 lsb7 wsb6">which <span class="_ _2"> </span><span class="lse6 wse8">control <span class="_ _13"> </span><span class="ls2a ws2a">the <span class="_ _b"> </span><span class="ls123 ws129">outline <span class="_ _13"> </span><span class="ls32 ws33">of <span class="_ _1"> </span><span class="ls96 ws93">an <span class="_ _5"> </span><span class="lsc6 wsc6">object <span class="_ _8"> </span><span class="ls88 ws85">in <span class="_ _5"> </span><span class="ls3c ws3d">a <span class="_"> </span><span class="lsc7 wsc7">given <span class="_ _8"> </span><span class="ls124 ws12a">plane <span class="_ _9"> </span></span></span></span></span></span></span>as </span></span></span></span></div><div class="t m0 xc h5 y32 ff1 fs2 fc0 sc0 lsc5 wsc5">defined <span class="_ _2"> </span><span class="lsc0 wsbf">by <span class="_ _1"> </span><span class="ls2a ws2a">the <span class="_"> </span><span class="ls6e ws1a">ANSI <span class="_ _2"> </span><span class="ls125 ws12b">standards, <span class="_ _13"> </span><span class="ls29 ws29">specify <span class="_ _2"> </span><span class="ls3c ws3d">a <span class="_ _3"></span><span class="ls126 ws12c">uniform <span class="_ _13"> </span><span class="ls10d ws113">boundary </span></span></span></span></span></span></span></span></div><div class="t m0 xd h5 y28 ff1 fs2 fc0 sc0 lsf4 wsf6">zone <span class="_ _b"> </span><span class="ls127 ws12d">along <span class="_ _b"> </span><span class="ls2a ws2a">the <span class="_"> </span><span class="lsb9 wsb8">true <span class="_ _1"> </span><span class="lsf6 wsf9">profile <span class="_ _2"> </span><span class="ls128 ws12e">within <span class="_ _2"> </span><span class="lsb7 wsb6">which <span class="_ _b"> </span></span></span></span></span>the <span class="_ _1"> </span><span class="lsba wsb9">elements <span class="_ _d"> </span><span class="ls32 ws33">of <span class="_ _3"></span></span></span>the </span></span></div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,-1.568627]}'></div></div> </body> </html>
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