曲线形态相似性的定义与度量

184200910()JournalofYunnanUniversityofNationalities(NaturalSciencesEdition)Vo.l18No.4Oct.2009:2009-03-30.:(1983~),,.:.江浩褚衍东郭丽峰(,730070).,,,..;;=O211.9;P282=A=1672)8513(2009)04-0316-03DefinitionandMeasurementofShapeSimilarityforCurvesJiangHaoChuYandongGuoLifeng(SchoolofMathematics,PhysicsandSoftwareEngineering,LanzhouJiaotongUniversity,Lanzhou730070,China)Abstract:Theproblemofdefinitionandmeasurementofshapesimilarityforcurvesisstudied.Itintroducesadivisionmethodofcurvesandgetsaratiosample.Basedontheprinciplesofstatistics,thedefinitionandmeasure-mentmethodofshapesimilarityforcurvesisgiven.Andanexamplevalidatesthatthismeasurementmethodisfea-sible.Keywords:curve;similarity;measurement1(GIS),GIS,,,,,,[1-3].1,AB,(s2,PQM),.,.,.,,[4-5].(1),.,,.,,.2A1B1A2B2,316.A1A2B1B2,A2A1O,A1B1A1B1n-2,A1B1A1,P1,P2,,,Pn-2,B1,ny],A1B1P={A1,P1,P2,,,Pn-2,B1}.NA2OB2n-2:A1,A2,,,An-2.NA2OB2,P1,P2,,,Pn-2Ai(i=1,2,,,n-2).A2B2Ai,ki,Qi1,Qi2,,,Qiki(kiIN+),2.,A2B2,Q={A2,Q11,Q12,,,Q1k1,Q21,Q22,,,Q2k2,,,Qn-2,1,Qn-2,kn-2,B2}A2B2.:|OA2||OA1|,1k1Ek1j=1|OQ1j||OP1|,,,1kn-2Ekn-2j=1|OQn-2,j||OPn-2|,|OB2||OB1|,|#|2,2A(xA,yA),B(xB,yB),|AB|=(xA-xB)2+(yA-yB)2.nd1,d2,,,dn,D={d1,d2,,,dn}A1B1A2B2PQ.,,,.,,x=1nEni=1xi[6].,D={d1,d2,,,dn}..D={d1,d2,,,dn}LHPQ,DL,R2.diF(z),diI[L-zR,L+zR],iI{1,2,,,n},zF(z),zF(z)1.1zF(z)z111651196221583F(z)016827019000019500019545019900019973LPiPiHQ,PiQ.kPiIPQ,knLHPQ,SIM(P,Q)=kn.LH,PQLH,LHPQ,LHSIM(L,H)=SIM(P,Q).z=3,/3R0.33,2L1L2,28,1(3174:2).2,D1OL1,D2OL2.DD1D2.z=12.,L=1.7534,R=0.1334,68.27%[1.6200,1.8869],L1L260%.z,2.z=3,[1.3532,2.1537],100%.2D1117088117671117745116978116575115232115095116735118159119679D2312696217969218230310005217951310466217623218071312185313730D119133115828115909117673116864210001118299116774117724117140,z,.:z,.4,,.,;;,,.:[1].[D].:,2004:13-34.[2],.[J]:,2004,29(5):447-465.[3],.[J].,2006,31(2):29-32.[4],,,.[J].,2008,33(6):207-208.[5],,,.[J].,2008,33(6):83-86.[6],.[M].:,2007:94-167.(万志琼)(上接第315页)(1),(2):Y*(Y*X)=(XHY,XHY),X*(X*Y)=(YHX,YHX).:Y*(Y*X)=(X)=(XHY,XHY)=(YHX,YHX)=X*(X*Y),.:YCX=Y*(Y*X)=(XHY,XHY),YCX=XCY,.(7)YCX[X,YPX,YISCR(U).(1)XHYAX,YZXHY[X,Y;(2)XHYAX,YZXHY[X,YYCX[X,Y.X[YZYCX=XYCXX,Y.,,.:[1].[M].,2006.[2].[J].:,2002,11(2):65-67.[3].(Ñ))))Stone[J].:2002,20(2):1-4.[4].MV[J].,2008,22(3):152-155.[5].BCI-[M].:,1987.[6]AHMADB.FuzzyBCI-algebra[J].JFuzzyMath,1993,1(2):445-452.(万志琼)318()18