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1、CORRESPONDENCE875more,asweconsiderthedichotomiesgeneratedfrom{[(I)I(RRiVJ(Yi+k-Yi)l(x;+k-xi)forsomek>1,ratherthansimplyusingthefirsti=1,2,.*.,2m,itisclearthatfori>2mn-i,m>0,(RRi)willdifference(i.e.,k=1);butitisnotclearhowtochoosethesmoothinggenerateco
2、mbinationsthathavealreadybeengeneratedby(Ri)forfactork.i<2m-1since(R)=R!/i!(R-i)!.ItisforthisreasonthatC(R)isThepurposeofthiscorrespondenceistodescribeaprocedureforhalfofthecombinationsgeneratedin(1).Nowwehavetodetermineadefiningsignificantcurvaturema
3、xima(andpossiblyalsopointsofdistinctsetofstateassignmentcolumns,{Cd}fromthedichotomiesinflection)onadigitalcurve,usingavariabledegreeofsmoothing.generatedaspreviouslydescribed.ThisisdonebyassigninganR-tupleThisprocedureisexactlyanalogoustoanedge-detec
4、tiontechnique,of{0,1}toeachofthedichotomiesinthesetofdichotomies:describedin[4],[5],whichdetectssignificantmaximaintherateofchangeofaveragegraylevel,usingavariabledegreeofaveraging.ItisaRRi=1,2,2-m>0(A2)"parallel"procedure,inthesensethattheresultsatea
5、chpointdonot1i1R-i'''A2'dependonresultspreviouslyobtainedatotherpoints.Theprocedureisasfollows(allintegersaremodulon).Wedefinethewhereallcomponentsofonesideofthedichotomyareassignedthek-vectorsatpiassamevalue0(or1)and1(or0)totheothersideofthedichoto
6、my.Withoutlossofgeneralitywecanassign0tothesideofthedichotomyaik=(xi-Xi+k,Yi-Yi+k)thathasrow1asanelement.Wehavealreadyestablishedin(6)thatCLR)=2R-1-1.Furthermore,itisclearthatthereexistsexactlybik=(xi-Xi-k,Yi-Yi-k)2-1R-tupleswiththerow1elementequalto0
7、.HerewehavegeneratedallofthesecombinationsexceptC0,whichisnotacceptableandthek-cosineatPiasasaCdelement.Hence,withtheassignmentof{0,1}asshown,wehavegeneratedthesetC1,C2,**,C2R1_,and(Al)isproved.Cik=(elk*bik)/IaikIIbik'REFERENCESThisCikisthecosineofthe
8、anglebetweenaikandbik.Thus-16[IIJ.R.Story,H.J.Harrison,andE.A.Reinhard,"OptimumstateCik<1,wherecikiscloseto1ifaikandbikmakeananglenear00assignmentforsynchronoussequentialcircuits,"IEEETrans.andCikiscloseto-1ifaikandbikmakeananglenear1800;inoth
