Page - 77 - in Document Image Processing

J. Imaging 2018,4, 37 each cut portion is of length d. Similarly, divide the query Xq into samenumber p of fixed lengthportions. (ii) Foreachclass, compute theglobalprincipalalignments foreachcutportionseparately. Theseare the cut specific principal alignments for the class. For ith class and jth cut portion the cut specific principal alignments are computed from {xji1, . . .x j i|ci|} and these are denoted as G j i. Thesealignmentsarecomputedforall thecutportions foreachclass. (iii) Thefinalstepcomputes thecutspecificprincipalalignments for thegivenqueryXq as follows. ForeachcutportionofXq,wecomputetheDTWdistance(Euclideandistanceover thecutspecific principal alignments)with the corresponding cut portions of all the classmeans using their correspondingcutspecificprincipalalignments. Thedistancebetweenthe jthcutportionofXq i.e.,Xjq andthe jthcutportionof the ithclassmeani.e.,μ j i isdenotedas Disji= ∑ π∈Gji Euclidπ(X j q,μ j i) (4) ForeachcutportionofXq,wecompute theminimumdistancemeancutportionoverall theclass meanvectors. Thecorrespondingcutspecificprincipalalignmentsof theclosestmatchingmean cutportionsaretakenasthecutspecificprincipalalignmentsof thequerycutportion. Inaddition, thecorrespondingclassmeancutportion is takenas thematchingcutportionforconstructing thequerymean. Let the jthcutportionof thequeryhavethebestmatchwith the jthcut-portion of theclasswith index c. c= argmin i Disji (5) Here theminimumdistance iscomputedoverall the frequentclasses.Wethushave GjXq ←−G j c and μ j q←−μjc (6) HereGjXq is thecutspecificprincipalalignments for the jthcutportionofXq. Together, all thesequerymeancutportionsgive thequeryclassmean. Thequeryclassmean μq isgivenasμq=(μ1q,μ2q, . . . ,μ p q). Thisqueryclassmeanμq is thenusedas inEquation (2) to compute theLDAweightwq (queryclassifierweight). Thequeryspecific (QS)DTWdistancebetween thequeryXq andasampleX fromthedata is givenas dtw qs (Xq,X)= p ∑ i=1 dtwGiXq (Xiq,X i) (7) where p is thenumberofcutportions. Figure3showsall theprocessingstagesof thenearestneighborDQC. Tosummarize,wegenerate query specificprincipal alignments on theflyby selecting and concatenating the global principal alignmentscorrespondingtothesmallerngrams (cutportions).Ourstrategy is tobuildcut-specific principal alignments for themost frequent classes; these are theword classes thatwill bequeried more frequently. Thesecut-specificprincipalalignmentsare thenusedtosynthesize thequeryspecific principalalignments (seeFigure4). Theresultsdemonstrate thatourstrategygivesgoodperformance forqueries fromboththe frequentwordclassesandrarewordclasses. 77