cvpr2013-Modeling Mutual Visibility Relationship in Pedestri(5)

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.

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