Page - 157 - in Document Image Processing

J. Imaging 2018,4, 39 Essentially,both theapproachesapplya functionontheconfidencescore inputs,where therulebased functionsaresimpleroperations likesumrule,maxrule, etc. andclassifiers likek-NNandMLPapply morecomplicatedfunctions. 3.1. RuleBasedCombinationTechniques Rules are applied on the abstract level, rank level andmeasurement level outputs from the classifiers toobtainafinal setofconfidencescores thatcantake intoaccount the insightsprovidedby thepreviousstageofclassification. Elementarycombinationapproaches likemajorityvoting,Borda count, sumrule,product ruleandthemaxrulecomeunder thisapproachofclassifiercombination.DS theoryofevidence isarelativelycomplex technique that isadoptedfor thispurpose,utilising therule ofcombinationfor informationsourceswith thesameframeofdiscernment. 3.1.1.MajorityVoting Astraightforwardvotingtechnique ismajorityvotingoperatingat theabstract level. It considers only thedecisionclassprovidedbyeachclassifierandchooses themost frequentclass labelamong this set. Inorder toreduce thenumberof ties, thenumberofclassifiersusedforvoting isusuallyodd. 3.1.2. BordaCount Bordacount isavoting techniqueonrank level [37]. Foreveryclass,Bordacountadds theranks in then-best listsofeachclassifierso that foreveryoutputclass theranksacross theclassifieroutputs getaccumulated. Theclasswith themost likelyclass label, contributes thehighest ranknumberand the lastentryhas the lowest ranknumber. Thefinaloutput label foragiventestpatternXis theclass withhighestoverall ranksum. Inmathematical terms, this readsas follows: LetNbethenumberof classifiersand rji therankofclass i in then-best listof the j-thclassifier. Theoverall rank riofclass i is thusgivenby ri= N ∑ j=1 rji (1) ThetestpatternXisassignedtheclass iwiththemaximumoverall rankcount ri. Bordacount isverysimple tocomputeandrequiresno training. There isalsoa trainablevariant thatassociates weights to theranksof individualclassifiers. Theoverall rankcount forclass i is thencomputedas givenbelow ri= N ∑ j=1 wjr j i (2) Theweights can be the performance of each individual classifiermeasured on a training or validationset. 3.1.3. ElementaryCombinationApproachesonMeasurementLevel Elementarycombinationschemesonmeasurement levelapplysimplerules forcombination, such assumrule,product ruleandmaxrule. Sumrulesimplyaddsthescoreprovidedbyeachclassifier fromasetofclassifier foreveryclassandassigns theclass labelwith themaximumscore to thegiven inputpattern. Similarly,product rulemultiplies thescore foreveryclassandthenoutputs theclass with themaximumscore. Themaxrulepredicts theoutputbytheselecting theclasscorrespondingto themaximumconfidencevalueamongall theparticipatingclassifiers’outputscores. Interesting theoretical results, includingerrorestimations,havebeenderived for thesesimple combinationschemes.Kittleretal. showedthat sumrule is less sensitive tonoise thanother rules [38]. Despite their simplicity, simple combination schemeshave resulted inhigh recognition rates and showncomparableresults to themorecomplexprocedures. 157