发表在CVPR13上的行人检测方法
Figure4.Themutualvisibilitydeepmodelforpretraining.
wehaveL=3.Wl,gl
cllearned.Wlmodelsthei,andi
aretheparameterstobe
correlationbetweenhlandhl+1,wli, istheithrowofWl,gliistheweightforsli,andclisthebiasterm.Theelementwl
i
i,jofWlin(8)issetto
zeroifthereisnoconnectionbetweenunitshll+1
inFig.2(b).Sincesisobtainedfromthepart-basediandhmodelj
atboththetrainingandthetestingstages,weconsiderthemastheobservedinputvariablesandneednotmodelp(s).Thisdeepmodelisadiscriminativemodel.
Similartotheapproachin[16],theparametersin(8)aretrainedlayerbylayerandtwoadjacentlayersareconsid-eredasaRestrictedBoltzmannMachine(RBM)thathasthefollowingdistributions:p(hl, hl+1|x)∝ehlT
Wlhl+1+(cl+gl sl)Thl+(cl+1+gl+1 sl+1)Thl+1
,
p(hli
=1|h
l+1
,x)=
σ(wli, hl+1+cli+glTisl
i),
(9)
p(hlj
+1
=1|hl,x)=σ(hlTwl ,j+clj+1+glj
+1Tslj+1),wherewli, istheithrowofWlandwl
,jisthejthcolumnofWl.Thegradientofthelog-likelihoodforthisRBMiscomputedasfollows:
L(hl) wl∝(<hll+1>datal+1
i,j
ihj <hlihj>model), L(hl) cl∝(<hl(10)
ii>data <hli>model), L(hl) gl∝(<hlisli>data <hlli
isi>model),wherewl
i,jisthe(i,j)thelementinmatricesWl,<·>denotestheexpectationwithrespecttothedistributiondatap(hl+1|hl)p(hl)datawithp(hl)datasampledfromtrainingdata,and<·>modeldenotesexpectationwithrespecttothedistributionp(hl+1,hl)de nedin(9).Thecontrastivedivergencein[15]isusedasthefastalgorithmforlearningtheparametersin(9).
Toobtainthep(y1|y2=0,x1)in(2)forisolatedpedes-trian,GMMisnotusedandonlyonedeepmodelistrained.Thisdeepmodelcanbeobtainedbyremovingnodesrelatedtothepedestrian2inFig.2andFig.4,andthenreplacingywithy1inFig.2.Thetrainingandinferenceofdeep
Figure5.Examplesofcorrelationbetweenh2andh1learnedfromthedeepmodel.
modelforisolatedpedestrianissimilartothetrainingandinferenceofthemutualvisibilitydeepmodel.
4.3.Analysisonthedeepmodel
Inthismodel,thevisibilityofpartsforonepedes-trianin uencesthevisibilityofpartsforanotherpedestrian
throughtheWlin(8).Whentheweightbetweenhl1+1
,iandhl2,jispositive,theithpartforpedestrian1atlayerl+1andthejthpartforpedestrian2atlayerlareconsideredbythedeepmodelascompatible.Ontheotherhand,ifbetweenhl1+1theweight
,iandhl
2,jisnegative,theyareincompatible.
Fig.5showsexamplesoftheweightbetweenh31andh2
learnedfromthedeepmodel.Thetopexampleisfrommix-2ture5andthebottomexampleisfrommixture4.DenotetheleftpedestrianbyPedPedLanddenotetherightpedestrianbyR.Forthetopexample,thehead-shoulderpartofPedRiscompatiblewithhead-shoulderpartofPedwiththeright-halfpartofPedLbutincompatibletomexample,theleft-head-torsopartofPedL.Forthebot-iblewiththeleft-halfpartofPedRiscompat-.
Lbutincompatiblewiththeright-halfpartofPedLAsthepartdetectionscoresforwndprovidedbythepart-basedmodels,1andwndtheextra2areal-readycom-putationsrequiredbyourapproacharestep2andstep3inTable1.Inordertosavecomputation,weenforcep(y1=1|x1,x2)=0ifthedetectionscoreofthepart-basemodelforwindowwnd1islowerthanathreshold.Simi-larly,weenforceφp(y=1;x)=0ifthedetectionscoreofthepart-basemodelforwindowwndthreshold.Therefore,φ(y;x)andφ2islowerthanap(y;x)arecomputedforsparsewindowpositions.Withpartdetectionscoresprovided,thestep2andstep3inTable1takelessthan5%theexecutiontimeofthewholedetectionprocessona2.27GHzCPUwithmulti-threadturnedoffontheCaltechtrainingdataset.