遙感分類精度評價中Kappa系數(shù)的計算方法

遙感分類中，精度評價是一個很重要的環(huán)節(jié)?，F(xiàn)在需要計算一下里邊的Kappa系數(shù)，但是我手頭上沒有書，只能到網(wǎng)上找，但是在中文世界里，要找這樣的東西何其難也。英文的倒是一大批。在一個軟件的使用手冊里我找到了計算方法，說的非常詳細(xì)，連用戶精度，生產(chǎn)者精度，還有我以前沒見過的Hellden以及Short尺度，都說的非常清楚。就是里邊有一點兒小錯誤，不過我已經(jīng)標(biāo)出來了。Evaluatingthtqualityofaclassificationresultiscfhighimportanctinlemcici.sensingjiinct：itJvfevicknerhm,wellrhi：^L：n.cr.]ti：dorU51：dclassifh：「isrupablccxrric-ringthedesiredobjectsfromtheimageComiTionly,asafii5Tevaluation,simplevisualinspectioncanhenxdgevaluartthepLiusibiljtyoftheclassiFicaciimrc^ulo.ichc-lusi.iliisisjustaiuliicctivciiiuiliod；L[]dihushardlytobequimtiHcdur。匕ncipuhkofbci]]^expttSSfidliiCDiiipai'abIcxiilucs.Motedvc]',ith[ItieisatytnubtaiiiiiifoiJiutionahoiirrhec1as>；iFicati^nstabilityandbowcapahluchuclassesarctoextruerriledchiicdititoniiaiioi].Besidedieclasiicjl[iicdiochoficcurjcvassesstiiuiit,ipLcialmc-thochbasfdnpniitiizzycoiicepis±;l口beiisucl.CommonaccuracymeasuresInvtomc^siLri：thequality門FnrhssitiL-1'門ndtc>cornpareandcvalunn-.rl.issitica-tionswithrespectri)rhi：irsnitabiliryfinspecificapplications^jccmacymcjAiircsarellh：c{.Musrlyrlu：y；^ri：derivedonrheqF；iciimpji-iwnofdierla'isifirarioninqui：s-licjiwithanotherclassification.ThisIarterclassificaiionisoften11braincdwithdifKrtiitmethods,c心5byoii-sllc*sundmeasurLEiicms,acidLconsidcicdilILiMlLindtrue,whichi$vdiy備TTii：tim「srluntmground「Tilth"kused,7k：willhiR：\i^cth「n：rm"■leftluna：cla.^ificatii>n，：tuempha^iztcharit很essentiallyalsoaelassi甘匚汨nn,the1tlia-bilitv口「wlikli beassLii-cclaridcaciiioibeLu.kcJigraniucl.SpcciJcatee,.、tobetaltcnifthereferencecla&5)Acatkinisobiahicdwithdatatakenatadiffertntrimerhant,grhedataforrheclass'ificacHinsheevaliiarud.M；)r<iiv<.i,itmu5rht：assuredthatrhereferenceclassificationanddieclaisifieationinquestioncarryeomparatlcinformation.[Illsnkan%llultheyhnvelliesaniuc]：l抬c*oratIullMdissesc:niheassignedtoeachotherVclassesbymergingsandchattheybothhavethesam*苧id,ix.hapcakiJigindigitalterms,thatthepixelshavetheaamelocationandspatialextenton[hi：grumic].In[hi：m：l]llcI'we[;i1yl：;j11tliisft)fgi:iritrc](a^Miiniiiglli^ri\ih：l'cs?(：3rvsorin:piri：-pi-iiccisin<;climsiFinirii-jnandrcfx-ivn^：rl.^'iihcnriiinwaspctk門,乜)z.jissij-mtespeciallythatbothclassificationandreferenceclassificationassignthesameclassesin.]crispwayri.e,,that.]pixelisassignedttiexactlytintcl；iss.Andwe%hdlissunitrhiitrliL：]?ixi：lsuhrbci\：R：ri：nrcckissific；irion；nv；iftuhsetofthott：attheclnssihmrion.Zecajlikctiderive;lso-calledconfusioiLidbkbycuuntingIkwmanyofdiepixcliclassifiedis廣后$<inrhi-L-|；issificnrir?narcijfclass+inthe dassihcnri^Ti.V<?denotcihhnumberby%andwriteitinrowiandcolumn4ofthetable.]hi%tiiblc.st^iiictijnes『匚仁門七&lucanfHsi&nnmtrbcorcnorutiit.yix,containsallihuinfiiiniacrmahcutthereh;ionbetwetnclassificationandrt.fcrtnceclassifjcatuMi.However,itis<ifiuiusufultr.iderivetroEiiitSoelkcliaraclLTislicJilleuIiltswhiclisimplifyihuaccuracyassL^hJiictLLnfthecliissit'LcaiLGE]iKInngalt凸u,]991j.ReferenceclassificationClassificationClass1Class2ClassNClass1a11a12a1N2L外Class2a21a22a2NEL%--?-??-------??ClassNaN1aN2aNNEE2K2L%訃卬AfirstsuchnumberisoverallaccuracyOA.Itistheproportionofallreferencepixelswhichareclassifiedcorrectly(inthesensethattheclassassignmentoftheclassificationandofthereferenceclassificationagree).Itcanbecomputedfromtheconfusiontabicwherenisthenumberofallreferencepixels.SoOAisthesumofthediagonalentriesoftheconfusiontabledividedbythenumberofallreferencepixels.Overallaccuracyisavciycoarsemeasure.Irgivesnoinformationaboutwharclassesarcclassifiedwithgoodaccuracy.Infact,aclassificarionwithpooroverallaccuracymayfindonecertainclasswithhighaccuracy,althoughitconfusesallothers,andthusbeofinterestforcertainapplications.Thereforetochermeasuresareuseful.Onesuchmeasure,prod“cer'$acamicyZM卜Zarsj,estimatestheprobabilitythatapixelwhichisofclassiinthereferenceclassificationiscorrectlyclassified.Itisthusforeachitheproportionofpixelswhereclassificationandreferenceclassificationagreeinclassiandthereferencepixelsarcclassifiedasthisclass.Asthetotalnumberofthepixelsofclassiinthereferenceclassificationisobtainedasthesumofcolumniintheconfusiontable,wehaveProducersaccuracyi$actuallyameasurefortheproducerofaclassification,whichtellshimhowwelltheclassificationagreeswiththereferenceclassification.Itgives,howc*vennoinformationabouthowwelltheclassificationpredictsaclass,i.e.,itgivesnoinformationabouttheprobabilitythatapixelclassifiedasclassiisactuallyofclassi.Thisi$theprimaryinterestofauserofaclassificationandanestimateofthisprobabilityisthuscalledusersaccuracyUA（class^.鄧gestimatethisprobabilitybythepropoitionofpixelswhereclassificationandreferenceclassificationagreeinclass/andthenumberofallreferencepixelsclassifiedasclassibytheclassification.Nowthetotalnumberofpixelswhicharcclassifiedasclassiisobtainedbythesumofrow/oftheconfusiontable,sothatwehaveUA（classJ二UA（classJ二LetusgiveasmallexampletoclarifythedifferencesbetweenPAandUA.Considerthefollowingconfusiontable.ReferenceclassificationClassificationClass1Class2ClassNClass1500050Class24010060200ClassN1004050100100100”300Weobtainhereasproducer'saccuracy&）rclass1PA（classx）=5%恒=0.5,meaningthatonly50%oftheclass1pixelsofthereferenceclarificationarefbundbytheclassification.Ontheotherhand,thevalueUA（class｝）= =L。showsthattheusercanrelycompletelyontheclassificationhere:wheneverapixeli$classifiedtoclass1>thisiscorrect.Thesituationisquitedifferentwhenweconsiderclass2.HerewegetZM（c/as52）= i.c.>theclassificationclassifiesallclass2pixelsofthereferenceclassificationcorrectly.Butthistime,asUA（class2）= =0.5,theusercanbeonly50%surethatapixelclassifiedasclass2isinfactclass2.Suchapixelisinhalfofalleasesconfusedwithotherclasses.Forclass3wefind（clasX）=，%00=°，andUA（class3）= =0?8,Soalthoughagainproducersaccuracyisquitelow,ausercanrelyonapixelclassifiedasclass3to80%.

Theoverallaccuracyinthisexample,

givesnoinformationtotheproducerOA(50+100+40)/ 063Theoverallaccuracyinthisexample,

givesnoinformationtotheproducerOA(50+100+40)/ 063brafhcrjowIt/DWoruseroftheclassificationastowhichclassesarewelldetected,althoughsomeofthemcanbeofinterestincertainapplications(eg,class1canbeofinterestinthedesignofaclassifierandclasses2and3canbeofinterestintheuseoftheclassification).Inordertocompensateforthedifferentinterestsofusersandproducersofaclassifi-cation,certaincombinationsofproducersandusersaccuracyarcused.AfirstsuchchoiceistheproductPA..UA(class)=PA(class^UA{class^orthejniniHuoriPAaUA(class^=min(P\(classi),UA(classi))ofthetwo.Theygivevaluesclosetooneifbothaccuraciesarchighandareclosetozeroifanyofthetwoislow.Intheexampleabovewegeeforclasses1,2and3respectivelythevaluesfc)rPA?(ZA050.5and0.32,andfbrPAAUAwefind0.5,().5and04OtherpossibilitiesarcthemeasureofHclldcn[3,4]orthemeasureofShort[4,5]HA(class^=F—&whichisthebarmomcmeanHA(cLass)= 1 HA(class^=F—&whichisthebarmomcmeanHA(cLass)= 1 + IPA[classt)UA(class^ofPA(classandUA(class^ic,B4)—叫)?LZA(c/a叫SA(class^=fForShortsmeasurewefina、SA(class^)= PA(c如,)+UA(clasSt)1

(曲叫)?tZA(c/o叫) PA[class+UAfclass^-Ri(class^UA(class^Theinterpretationofthisaccuracymeasureisnotsoeasy.Letusonlymentionthatitisthequotientofthepioductt-norm=a?。andtheassociatedt-conornis(d,/3)=1-f(l-aj-/?)fora=PA(class^and=UA(class).SA(c如s)PA叫)SA(c如s)PA叫)^PAkUA(class)mHA^class-)whichsaysthatinacertainsense,Shortsaccuracymeasureortheproductofproducer'sandusersaccuraciesisthemostpessimistic,andHelldensaccuracymeasureisthemostoptimistic.Theuseofproducersaccuracyorusersaccuracyaloneshouldbetreatedwithcaution,asbothanswercompletelydifferentquestions.Thereisanotheraccuracymeasurewhichhasattainedwiderinterestintheclassificationcommunity,namelyCohen'skappacoefficient[1>4].Itfollows,however,adifferentidea.Whereasoverallaccuracy,OA,checkshowmanyofallpixelsarcclassifiedcorrect-ly>assumingthatthereferenceclassificationistrue,hereitisassumedthatbothclassificationandreferenceclassificationareindependentclassassignmentsofequalreliability;howwelltheyagreeiswhatismeasured.Thebigadvantageofthekappacoefficientoveroverallaccuracyi$thatkappatakeschanceagreementintoaccountandcorrectsforit.Chanceagreementmeansheretheprobabi