2015網(wǎng)賽優(yōu)秀第一階段題特等獎(jiǎng)

編號專用頁參賽隊(duì)伍的參賽隊(duì)：（請各個(gè)參賽隊(duì)提前填寫好：1519競賽統(tǒng)一編號（由競賽送至評委團(tuán)前編號競賽評閱編號（由競賽評委團(tuán)評閱前進(jìn)行編號 關(guān)鍵 、運(yùn)用ExcelPhotoshop軟件提取出了圖形的邊界線條，并用Opencv軟件、針對問題一，首先，運(yùn)用Photoshop軟件對圖像進(jìn)行噪點(diǎn)去除；其次，將圖針對問題二，首先，在對模型I修正的基礎(chǔ)上建立了模型II——圖形邊界彩形，并利用軟件將該彩像分離出R,G,B三個(gè)通道的偽灰度圖像邊界線條。采用opencv軟件對邊界線條提取結(jié)果進(jìn)行檢驗(yàn)。（填寫（填寫參賽隊(duì)號 Thispaperisaimedatextractingtheboundarylineofsimplegraphics.weselectblackandwhitepatternasthebreakthroughpoint,and yzethecoordinatespointdataoftheoutlinefeaturecomprehensivly.buildtheBesselgraphicblackandwhiteborderlineextractionmodel,boundarylineextractioncorrectionmodelandsimplegraphicalcolorgraphicboundarylineextractionmodel,byuseofExcel,Photoshop,Matlabsoftwaretoextracttheboundarylineofthegraphics,andOpencvsoftwarefortheinspectionofthelinefitting.Finally,wecombinethemodelresultswithreality.Forthefirstquestion,firstly,usingPhotoshopsoftwaretoremoveimagenoiseinterference?Secondly,cuttheimageintofourparts,doonedimensionalinterpolationtothesmoothpart,dobilinearinterpolationtononsmoothregion?Finally,establishthemodel-graphicalboundarylineextractionmodelbasedonbeziercurve.Forthesecondquestion,firstofall,modelIIisbasedonthemodelOne-graphicboundarylineextractioncorrectionmodel.Secondly,asforthelineararea,weuselengthlimitedpiecewisemethodandCoordinatefine-tuningmethod.Inordertoimprovethegoodness-of-fitoftheimage,weusetheturningpointcuttingprincipletodividetheimageintosixparts,andfittingrespectively,andfinally,useequationtosimulatetheboundarylineofaccuraterepresentation,andusetheultimatealternativemethodforthetestofgoodnessoffit.Forthethirdquestion,webuildamodelⅢ-simplecolorgraphicboundarylineextractionmodel.First,wechoseasimplecolorfigure,whosecolordistributionandshapearesimple,andweusesoftwaretoisolatethethreegrayimagesofR,G,Bchannel.Wetakethemedianfilteringmethodtofilterimageandeliminatenoise.Secondly,wedotheedgedetectionforthethreeimagesandextractthethreeedgelinesofR,G,Bchannel.Finally,takingdifferentmethodsaccordingtodifferentedgedistribution,andwegetthefinalboundarylineofthecolorimage.Lastbutnotleast,weusetheOpencvsoftwaretotesttheresults.Thisarticlealsocarryonthequalitativeysistotheerrors.Andweputforwardtheimprovementdirectionabouttheoptimization,maderationalevaluationtotheproblems.Finally,weputforwardthemodelfromtheblackandwhiteimagestocolorimagesandthentothespacepattern.Thisarticleisclarityandoriginal,andusingavarietyofinterpolationmethods. 問題的重一、背景知識位矢量位圖的處理柵格化及柵格化逆過程（Rasterztin灰度圖像為255，黑色的亮度級別為0位圖的矢量化處理優(yōu)點(diǎn)及應(yīng)用圖矢量化的應(yīng)用：氣象傳真圖、CAXA數(shù)控線切割XP、激光雕刻技術(shù)、電子地圖二、相關(guān)數(shù)據(jù)1]；問題一：對題目中給出的已經(jīng)進(jìn)行柵格化的位圖（見圖一）建立合理的問題二：問題三：簡單彩像的輪廓提取方§2模型的假圖 圖形切割圖圖三彩 與符號說一、二、符號說明123456789t(xi,yi?iXY(tR§5模型的建立與求一、問題一的分析與求解對問題的分析量化。首先，通過對題中已給定的圖形進(jìn)行輪廓特征點(diǎn)提取，得到輪廓問題的求解模型 基于曲線的圖形邊界線條提取模作完成后,還須采取一些必要步驟將它們有效地區(qū)分開。這里我們利用photoshop對進(jìn)行噪點(diǎn)剔除(見參考文獻(xiàn)[1])。②輪廓特征點(diǎn)坐標(biāo)值提取(見程序1)：用分別提取出四組圖；是曲線；2的距離為4( 2xy，構(gòu)造一個(gè)解析函數(shù)，通過這（(3)具體步驟如下：假設(shè)有Q12x1y2Q21x2y1,這兩點(diǎn)由于處在非光滑區(qū)使得這四點(diǎn)成為一個(gè)矩形Q11Q21Q22Q12。如圖：接下來進(jìn)行第一步：X方向的線性插值:f(P1)x2xf(Q11)xx1f(Q),P(x,yx 12f(P)x2xf12

x )xx1f(Q),P(x,yx2

x2

YP1P2R1R2P1f(P)y2yf(P)yy1f(P),P(x,y1y2

y2

這樣對每兩個(gè)點(diǎn)都做如上處理，用編程輔助，可以對邊緣的非光滑區(qū)為時(shí)，分成四段的曲線，可以小于千分之一的最大半徑誤差近似于圓線性曲線給定點(diǎn)P0,P1，B(t)代表經(jīng)過t時(shí)間的坐標(biāo)軸位置，線性條B(tP0P1P0t1tP0tP1t[0,1]二次方曲線二次方曲線的路徑由給定點(diǎn)P0,P1,P2的函數(shù)B(t)B(t1t2P2t(1t)Pt2Pt 則n階曲線可如下推斷。給定點(diǎn)P1,P2,...,Pn，其曲線即曲線

n

n1

0

i(1 0P0(1t) 1P1(1 nPn(1t)t ①使用軟件檢驗(yàn)：Flash、Ai、Coreldraw、AutoCAD對問題的分析首先I進(jìn)行四部分切割之后發(fā)現(xiàn)原圖與擬合后的的矢量曲線不能很粗略連線應(yīng)該是一條光滑的圓弧，再利用曲線進(jìn)行擬合。問題的求解模型Ⅱ圖形邊界線條提取修正模型①直線區(qū)域與曲線區(qū)域的檢測:當(dāng)相鄰3點(diǎn)的斜率相等(直線,斜線)。其余情況當(dāng)相鄰3點(diǎn)的斜率相等(即為直線,斜線)時(shí)候，我們采取以下兩種方法：i便需要對插值點(diǎn)的選取做一定微調(diào)，我們采?。▁i0且0y）對于（xiy）做修改后帶入，再進(jìn)行spline插值擬合。i折點(diǎn)重新切割成線段AB,BC,AC三種情況，如圖：圖十圖像輪廓切割圖 nn n0 n11 0 i(1

0P0(1t) 1P1(1 nPn(1t)t 切割，切割成AB,BC,CD,DE,EF,AF六段，切割情況如下：進(jìn)行擬合（見程序2）并求解方程結(jié)果如下：X(t)24-27t2.22106t19-1.69107t205.65107t21-1.09108t1.32108t23-1.03108t245.03107t25-1.41107t261.74106t27Y(t).3103t.7104t4.105t5.106t6.107t.2107t82.67108t9-1.09109t103.92109t11-1.201010t123.111010t13-6.781010t141.251011t15-1.941011t162.561011-2.841011t182.631011t19-2.021011t201.261011t21-6.291010t2.451010t23-7.14109t241.47109t25-1.90108t261.16107tX(t)527t-3.51102t25.85103t3-5.27104t43.23105t5-1.48106t65.33106t7-1.55107t83.75107t9-7.59107t101.30108t111.91108t122.41108t13-2.61108t142.43108t15-1.96108t161.35108t17-7.971074.00107t19-1.69107t20-2.61108t142.43108t151.96108t161.35108-7.97107t184.00107t191.69107t20-2.61108t142.43108t15-1.961081.35108t17-7.97107t184.00107t19-1.69107t205.92106t21-1.70106t3.86105t23-6.73104t248.42103t25-6.75102t262.610tY(t)285.40102t1.05103t21.76104t31.76105t41.21106-6.22106t62.49107t7-7.99107t82.06108t9-3.88108t102.61108t111.70109t12-9.45109t132.971010t14-6.9110101.271011t16-1.911011t172.361011t18-2.401011t192.001011t-1.361011t217.321010t22-3.061010t239.47109t24-2.04109t2.70108t26-1.65107tX(t)3130t-1.31106t27-6.13105t291.27106t286.85105t-1.42105t251.18105tY(t)418.01108t9-5.93105t6-3.78109t10-1.22108t81.22107t-1.461012t19-5.29109t27-4.68108t292.06109t281.141010t-3.721010t251.411011t248.801011t22-1.381012t211.641012t9.421011t18-3.681011t17-1.521010t161.571011t15-1.4510118.691010t13-3.901010t121.371010t11-4.141011t234.56107tX(t)3332t-2.80107t23289109t28-1.85109t29-9.28108t257.64108t-3.01109t271.96107t32-1.84108t312.42108t24+2.08109tY(t)7-9.10106t61.21106t5-1.08105t44.96103t3-1.751013t215.05107t-4.941010t126.991012t204.551012t17-2.21108t8-4.941010t126.991012t4.551012t17-2.21108t8-6.061011t148.13108t9-3.041012t16-4.501012t1.531012t15-3.011013t231.861012t28-2.90109t101.161010t11-5.031011t2.651013t22-1.941013t259.621010t30-5.191012t271.911011t136.80108t-1.161010t312.691013t249.331011t191.121013tX(t)=24+200t7-50t8-308t6+224t5-70tY(t)=88AB段X(t)20-3.63104t101.20104t726t4.07104t9-2.83104t8-3.43103t61.28103t5-7.15102t42.86102t3-78t27.93102t13-6.019103t121.9734104Y(t)7.72103t10-3.26104t7-2.50104t93.73104t81.71104t6-5.14103t57.15102t44.62102t13-1.84103t121.24103程：X(t),Y(t),(0t1)表示曲線。但參數(shù)方程本身無法利用nR21(

ny? (

y)i

iX(t),Y(t)有相應(yīng)的值x?1?2,x?n，y?1?2,y?nx1y1x2y2xmym，任取原始數(shù)x0x?1x?2,x?n中必存在一點(diǎn)0.001，?i圖十三y?0值的模糊取值A(chǔ)E段擬合曲線R2=0.9431,擬合效果很好；EF段擬合曲線R2=0.9946擬合DFR2=0.9921，CD段擬合曲線R2=0.9796，擬合效果非常好；BC段擬合曲R2=0.7572擬合效果較好；AB段三、問題三的分析與求解對問題的分析 彩像的轉(zhuǎn)換為R,G,B三個(gè)灰度圖像使用編程實(shí)現(xiàn)，由于問題的求解模型 簡單彩形邊界線條提取模對圖一 像進(jìn)行分離，得到R，G，B三個(gè)偽灰度圖像，結(jié)果如圖十五-1R偽灰度圖 圖十五-2G偽灰度圖圖十五3B②對分離的圖像分別進(jìn)行中值濾波處理之R,G,B三個(gè)圖像的邊緣線 圖十六1R邊緣線條 G邊緣線條圖十六3BR邊緣線條圖上點(diǎn)坐標(biāo)為(XR,YR),G邊緣線條圖上點(diǎn)坐標(biāo)為XGYG,B邊緣線條圖上點(diǎn)坐標(biāo)為XBYB)三幅圖融合成的曲線的坐標(biāo)為(X0,Y0)?？紤]到三條曲線輪廓特征點(diǎn)的分布情況，采取如下方法進(jìn)行坐標(biāo)點(diǎn)的剔(XX)2(YY)2 (XRXG)2(YRYG)2 ①邊緣輪廓特征點(diǎn)并點(diǎn)法：如果上面式成立，則說明該兩點(diǎn)在R圖和G圖明該兩點(diǎn)在R圖和G圖上分布位置不同，都要保留。nn

B(t)

i nP(1t)nt0nP(1t)n1t1nP(1t)0tn,t 對處理后的坐標(biāo)值用畫出來，結(jié)果如下圖十七彩像邊界線條§6模型的誤差分形輪廓便會(huì)產(chǎn)生一定的散亂點(diǎn)，雖然