Modelng acgound fom Compessed Vdeo Weqang Wang Daong Chen Wen Gao Je Yang School of Compue Scence Canege Mellon Unvesy Psbugh 53 USA Insue of Compung echnology &Gaduae School Chnese Academy of Scences ejng 8 Chna {wqwang wgao}@jdl.ac.cn {daong je.yang}@cs.cmu.edu Absac acgound models have been wdely used fo vdeo suvellance and ohe applcaons. Mehods fo consucng bacgound models and assocaed applcaon algohms ae manly suded n he spaal doman (pxel level. Many vdeo souces howeve ae n a compessed foma befoe pocessng. In hs pape we popose an appoach o consuc bacgound models decly fom compessed vdeo. he poposed appoach ulzes he nfomaon fom DC coeffcens a bloc level o consuc accuae bacgound models a pxel level. We mplemened hee epesenave algohms of bacgound models n he compessed doman and heoecally exploed he popees and he elaonshp wh he counepas n he spaal doman. We also pesen some geneal echncal mpovemens o mae hem moe capable fo a wde ange of applcaons. he poposed mehod can acheve he same accuacy as he mehods ha consuc bacgound models fom he spaal doman wh much lowe compuaonal cos (5% on aveage and moe compac soages.. Inoducon he explosve gowh of vdeo souces has ceaed new challenges fo daa ansmsson soage and analyss. Vaous daa compesson echnologes have been wdely used o solve poblems of vdeo ansmsson and soage. We ae now able o connuously ecod mulple vdeo seams fom vdeo cameas ono a compue had ds usng hadwae compesson devces. Howeve how o pocess hese vdeo daa s sll an open poblem. adonal compue vson algohms may no be effcen enough o pocess huge vdeo daa because mos compue vson algohms ae desgned fo uncompessed mages n he spaal doman. Suppose we ecod vdeo a 3 fames pe second. Fo only one camea we would have 59 fames pe day. I s clea ha we need moe effcen ways o pocess hese vdeo daa. Vdeo suvellance s a majo souce ha can geneae huge vdeo daa. Vsual suvellance sysems use vdeo cameas o mono he acves of ages n a scene such as human acvy n ndoo envonmens and vehcles n pang los. I s vey dffcul howeve fo a human opeao o eman ale fo moe han a few hous. Auomac acng echnologes have been suded fo decades o eplace o educe human effos. A fundamenal echnology used n he exsng acng sysems s bacgound subacon whch segmens movng egons n an mage sequence capued fom a sac camea by compang each new fame wh a bacgound model. A cucal sep of hs echnque s o oban a sable and accuae bacgound model fom a vdeo sequence. Much eseach has been deced o buldng bacgound models. acgound models have been esmaed fom pxel values a each locaon n a vdeo sequence. Pxel values can be gay o colo. asc mehods ae he aveage mehod [] he unnng aveage mehod he medan mehod [] and he selecve aveage mehod. Advanced mehods ae mosly based on sascal modelng echnques such as he sngle Gaussan esmao (pfnde [3] he mxue of Gaussan esmao [4] he enel densy esmao [5] he sequenal enel densy esmao [6] he mean-shf esmao [6] he egen bacgound [7] and he obus PCA bacgound [8]. Some mehods also ae he coelaons of pxels wh he neghbohood no accoun [9]. All he above mehods eque a vdeo sequence n uncompessed foma. On he ohe hand eseaches n mulmeda pocessng aeas have also poposed some mehods fo buldng bacgound models n he compessed doman [][][][3]. hey wee developed fo segmenng movng objecs o fo encodng puposes. Mos algohms use only Dscee Cosne ansfomaon (DC DC coeffcens and wo on bloc level. Fo example he algohm n [] exacs objecs a a sze of 8 by 8 blocs and can no oban accuae objec conou. Fuhemoe hese algohms ae dsconneced fom he spaal doman whee many compue vson and mage pocessng echnologes have been developed. In hs pape we popose an appoach o model bacgound decly fom a compessed vdeo usng DC coeffcens. he poposed appoach can no only effcenly consuc bacgound models fom compessed vdeo bu also acheve accuacy as good as ha of algohms n he spaal doman. hs can lead o a moe effcen famewo o pocess compessed vdeo daa fom boh compessed domans and spaal domans. Fuhemoe he poposed appoach can ae advanage of he sucue and avalable nfomaon n he compessed vdeo n mplemenng saeof-he-a bacgound modelng algohms. Fo example when we use a mxue of Gaussan (MoG o model he bacgound fom compessed vdeo he model has less nonzeo paamees because DC coeffcens ae ohogonal. he es of he pape s oganzed as follows. In Secon we noduce modelng a bacgound n he spaal doman and some bascs fo compessed vdeo. We descbe hee
common bacgound models: unnng aveage medan and MoG used n he spaal doman. In secon 3 we pesen he poposed mehod. We dscuss mplemenaons of unnng aveage medan and MoG n he compessed doman. he poposed hee algohms can acheve he same o compaable accuacy n he compessed doman as n he spaal doman bu wh much less compuaonal cos. hs means ha hose models obaned fom he compessed doman can be decly used n he spaal doman whch bdges wo domans ogehe. In Secon 4 we show he expemenal esuls. In Secon 5 we conclude he pape.. Poblem Descpon he goal of bacgound modelng s o auomacally oban a sac mage ha conans only bacgound fom a sequence of vdeo capued by a fxed camea. Inuvely we consde he man challenge of he bacgound modelng s he occlusons of foegound objecs. In pacce hee ae many ohe challenges fom he moons of bacgound objecs and llumnaon changes of he envonmen fo example he hgh-fequency bacgound objec moon (wae waves ee banches and CR dspla camea oscllaons long-em sac foegound objec (e.g. a paed ca gadual lghng changes fom sunshne sudden lghng changes fom clouds and egula lghng changes fom ndoo lghs ec... acgound Modelng n he Spaal Doman Many bacgound modelng mehods have been poposed n he spaal doman. Hee we ovevew hee ypcal algohms n deals. Lo e al. [] poposed a fas algohm ha consucs he bacgound mage as he aveage of he pevous n fames. he algohm eques pleny of memoy o soe he pevous n fames. A alenave mehod s called unnng aveage whch esmaes he bacgound + fom only he cuen fame F and he pevous bacgound : ( α + = αf + ( whee he leanng ae α s ypcally se as.5. he dawbac of hese aveage mehods s ha he foegound objecs can leave some ghoss n he bacgound mages. Cucchaa e al. [] poposed o use a medan funcon o oban he bacgound. In hs algohm each locaon ( x y n he bacgound mage ( xy a me s compued by he followng equaon: n =... n j = j ( xy = ag mn D ( xy ( j c= { g b j whee D ( xy = max F ( xyc. F ( xyc. (3 and he F ( x. c ae he R G values of he pxel a (x n he fame fo me. We can also use selecve algohm o emove esdues fom foegound objecs. Each pxel n he cuen fame s fs classfed as ehe foegound o bacgound. hose foegound pxels ae no used n consucng he bacgound model. he dffculy of he selecve mehod s how o choose he classfcaon heshold. Wen e al. [3] poposed o f one Gaussan dsbuon o he hsogam of he pxel values n pevous n fames. hs gves he bacgound PDF wh vaances ahe han sngle means (aveage values. Sauffe e al. [4] exended hs dea no MoG ( xy ~ N( µ σ w. Each pxel has a MoG whch s fsly nalzed by -means and updaed by evey new fame. he algohm fs compues he machng models fo each pxel (x : F( x µ.5σ M = <. (4 ohewse he weghs ae hen updaed as: ( β β w = w + M (5 whee β s a consan elaed o he speed of he dsbuon change. he unmached models eman he same and he mached model s updaed as: ( ( µ = ρ µ + ρ F ( x and σ = ρ σ + ρ ( F ( x µ ( F ( x µ (6 ( ( β F x y µ whee ρ = exp(. π σ σ We wll mplemen he counepas of hese hee algohms n he compessed doman n Secon 3.. Compessed Vdeo and DC o ansm and soe vdeo daa effcenly vdeo compesson echnques ae employed o educe he sze of an mage sequence by emovng spaal and empoal edundancy. Accodng o he popula nenaonal sandads of vdeo compesson such as MPEG- 4 and H.6X a compessed vdeo consss of I P fames whee P and fames can only be econsuced by usng adjacen I fames. Each I fame s fs paoned no 8 by 8 pxel blocs n he spaal doman and hen each pxel bloc s encoded as a se of Dscee Cosne ansfomaon (DC coeffcens. he Dscee Cosne ansfomaon s defned as follows: 7 7 Cuv ( = I ( jb ( uv uv =...7 (7 = j= j whee I ( j s a pxel value a he locaon ( j n pxel blocs Cuv ( s a DC coeffcen max whch chaacezes he powe dsbuon of sgnals wh dffeen fequences ( uv. he bass max s defned by π(+ u π( j+ v b j( u v = α( u α( vcos( cos( (8 6 6
whee α ( s = f s = α ( s = ohewse. If we concaenae evey column of he max Cuv ( ogehe no a 64-dmensonal column veco c and fom anohe column veco p usng all he pxels of I( j n he same way DC can be ewen no a compac max mulplcaon as c = Kp (9 h whee K s a 64 by 64 max and s m column s jus he veco fom of he max b j( u v m = + 8j. ecause DC s an ohogonal ansfomaon K = K. hus nvese DC (IDC can be defned by Equaon ( p = K c ( whee K denoes he anspose of he max K. he IDC s he mos expensve pa of vdeo decodng. An algohm opeang n he compesson doman geneally means IDC compuaon s no nvolved n he algohm. 3. acgound Consucon n DC Doman In ou famewo we use a se of DC coeffcens as he daa sucue o epesen a bacgound.e. D = { d =... L} whee d s a 64-dmensonal veco chaacezng an 8 by 8 egon coespondng o he h pxel bloc L s he numbe of blocs n a fame of he analyzed vdeo sequence. hough evewng hose sae-ofhe-a bacgound subacon echnques we found many popula algohms explo a sequence of lnea evaluaons o consuc he bacgound models. Hee we wll mahemacally pove ha f a bacgound consucon algohm only nvolves a sequence of lnea evaluaons he poposed bacgound epesenaon wll have a counepa n he DC doman whch has much lowe me complexy bu does no lose any accuacy fo a geneaed bacgound. L We use he max F = [ f f... f... f ] o denoe he fame n a vdeo sequence and use a 64-dmensonal column veco f o denoe he ansfomaon of he max whee bloc d D L D d... d Kf h bloc. hus he DC F can be compued by = KF ( = and he DC coeffcens of each =. So he IDC can be compued hough: F = K D. ( Suppose a spaal doman bacgound s modeled usng lnea combnaon of ecen fames N = ω F (3 = whee ω ( =... ae weghs specfed by bacgound modelng algohms. Le he max and F have he same sucue as hose defned n Equaon (.e. each column veco coesponds o a bloc n a fame and le boh sdes of Equaon (3 be mulpled by he DC enel N max K we oban K = ω( KF = Le D = K D = KF we have D N ωd = =. (4 Appaenly D s a max made up of DC coeffcens. hus Equaon (4 gves an equvalen bacgound compuaon model n he DC doman hough whch bacgound can be consuced wh he same accuacy as s counepa does n he spaal doman bu fully decomposng a vdeo sequence s no equed. 3. Runnng Aveage Algohm n DC doman In he unnng aveage algohm only lnea evaluaons ae nvolved so we can oban s equvalen veson n DC doman. If we nalze he bacgound by = F and le Equaon ( be eavely exended we wll have + = α + ( α = ( α( α + ( α = F F F. (5 Followng he same pocedue fom Equaon (3 o (4 we deve he mplemenaon of he unnng aveage algohm n he compesson doman as: D+ = αd + ( α D (6 whee D = K and D = KF. Each eny n he max D can be decly obaned wh vey small decodng cos fo an MPEG vdeo decode. Appaenly an algohm opeang on F wll geneally be fa less effcen han he counepa opeang on D because he fome needs o fequenly use Equaon ( o oban F whle he lae does no. Moeove he lae can oban an esmaon of bacgound as accuae as ha geneaed by he fome algohm by applyng IDC o D + usng Equaon ( when equed. 3. Medan Algohm n DC doman he medan algohm n he pxel doman has been acceped as a smple and effecve mehod hough expemenal evaluaons. In hs subsecon we fs analyze mahemacally and explan he aonaly of he algohm; hen a heoecal pncple wll be deved fo he poposed medan algohm n DC doman hough fuhe analyss;
fnally we pesen he deals of ou medan algohm and dscuss some advanages compaed wh he medan algohm n pxel doman. In a hsoy wndow a he locaon ( x y all he pxels can be paoned no wo ses and we le FO ( x and O ( x denoe he se of pxel values coespondng o a foegound objec and he se fo bacgound especvely. I s easy o mahemacally pove ha f max{ O ( x } < mn{ FO ( x } (7 o max{ FO ( x } < mn{ O( x } (8 holds he medan of he se FO( x O( x wll belong o he se ha conans moe elemens. Geneally Equaon (7 o Equaon (8 holds and O ( x conans moe elemens n a hsoy wndow so he medan wll come fom O ( x and coesponds o he bacgound a he locaon ( x y. ha s why he medan algohm n spaal doman can wo well. Now we consde a pxel bloc Μ ha les a he locaon n he fame a me n a hsoy wndow. he aveage of all he pxel values n Μ s a ( = ( p ( x + p ( x 64 ( xy FO( ( xy O( whee FO ( and O ( especvely denoe he se of foegound pxels and bacgound pxels n Μ p ( x y s he value of a pxel ha les a he locaon ( x y n he fame. A bnay value funcon s defned: f FO ( s a empy se ϒΦ ( = else ϒΦ ( = o chec f he bloc Φ s compleely coveed by bacgound. he funcon ( ϒΦ paoned all he blocs Φ = s s... s L n he hsoy wndow no wo ses. Coespondngly we use A ( and A F ( o denoe he se of aveages of hose blocs ha belong he wo ses especvely.e.: A ( = { ν v= a ( ϒ( Φ = = s s... s L} A ( = { ν v= a ( ϒ( Φ = = s s... s L} F If a pxel a ( x belongs o bacgound p ( x y geneally changes n a vey small ange n a sho hsoy wndow.e. mn{ O( x } max{ O( x }. Hee we assume ha p ( x y aes he same value n he wndow when he pxel a me s coveed by bacgound and ha fo each locaon n a bloc ehe Equaon (7 always holds o Equaon (8 always holds f boh FO ( x and O ( x ae no empy. hen we can easly deve ha fo any membe b A( f AF( ehe b < f always holds n he hsoy wndow o f < b always holds. Moeove Snce A ( geneally conans moe elemens n a hsoy wndow he medan of A ( AF ( wll belong o A (. ased on he above analyss we now ha fo he pxel blocs Φ ( = s s... s L n a hsoy wndow f he aveage of a bloc Μ % s jus he medan of he aveages of all he pxel blocs n ha hsoy wndow and ou assumpons hold hen all he pxels n Μ % ae coveed by bacgound. hus we can use he medan of { a ( = s s... s L } o denfy he bloc ha can epesen he bacgound a he coespondng locaon. If we le u = v = n Equaon (7 we oban 7 7 C( = I( j. (9 8 = j = hus he C ( eflecs he aveage of he pxels n a bloc and s called DC coeffcen n he leaues. We use he followng noaon o descbe ou algohm: he subscp c s used n he followng defnons o dsngush dffeen componens n colo space YCbC. mdl c ( : a 64-dmensonal DC coeffcen veco fo he pxel bloc n he bacgound mage a me. Gc = { mdlc ( = K } s a epesenaon of he bacgound mage usng DC coeffcens. dc c ( : a 64-dmensonal DC coeffcen veco of he pxel bloc n he fame a me. n Wc ( = { dcc ( dcc ( K dcc ( } denoes a ecen hsoy wndow whee dc c ( s a DC coeffcen fo he pxel bloc a me. md (v : he funcon o evaluae he medan of he se v Ou bacgound model updae pocedue s shown as follows: Fo each npu fame a me { dc c ( c = Y Cb C =...} { Fo each componen c {Y Cb C} Fo each bloc wh he componen c { d( = ag md({ dc ( =...} c ( = d ( mdl dcc ( } If needed oupu { G c c = Y Cb C } } Snce medan evaluaon s a nd of nonlnea evaluaon he poposed algohm s no equvalen o he medan algohm n spaal doman n heoy. In compason wh he lae he poposed algohm n DC doman has wo advanages. Fs he algohm has much lowe compuaonal cos snce IDC s no equed. Fuhemoe medan evaluaon s pefomed only one me fo each pxel c
bloc whle he counepa n pxel doman pefoms 64 mes medan evaluaon. Second he poposed bloc-based algohm wll no neglec he coelaon of pxels n he same bloc. Ou algohm can guaanee each bloc n a bacgound mage compleely comes fom he same fame whle he medan algohm n pxel doman opeaes each pxel ndependenly and canno povde such guaanee. 3.3 MoG algohm n DC doman he MoG algohm n spaal doman models each pxel as a mxue of Gaussans. In hs subsecon we popose an algohm ha models DC coeffcens of each bloc n DC doman as a mxue of Gaussans. We fs pesen a bloc-based Gaussan bacgound model n DC doman. We assume DC coeffcens n a bloc sasfy a mulvaable Gaussan dsbuon.e. pd ( Λ Σ = exp( ( d Λ Σ ( d Λ M 3 M = ( π Σ whee d s a 64-dmensonal DC coeffcens veco fo he bloc ( Λ Σ ae he mean veco and covaance max. Hee he dffeen componens of d ae ndependen of each ohe snce hey ae evaluaed hough pojecng a pxel veco ono a se of ohogonal bass usng Equaon (9. MPEG Vdeo compesson sandads have exploed hs ohogonal popey of he DC o emove spaal coelaon of pxels n a bloc. heefoe we can use a vaance veco = σ =...64 o epesen he covaance max ( Σ = I. We can epesen ( 64 unvaable Gaussans.e. pd ( Λ Σ = pd ( Λ σ = pd Λ Σ as a poduc of 64. hus we can equvalenly assume each DC coeffcen s a Gaussan andom vaable and esmae s paamees ndependenly. Equaon ( shows ha each pxel n a bloc can be evaluaed hough a lnea combnaon of 64 DC coeffcens. Pobably heoy n mahemacs ells us ha a lnea combnaon of a sequence of ndependen Gaussan andom vaables s also a Gaussan andom vaable and s paamees can be deved fom he paamees of hose ndependen Gaussans. In ohe wods Gaussans modelng pxels n spaal doman can be decly deved fom 64 Gaussans fo DC coeffcens. heefoe modelng bacgounds usng Gaussans n DC doman s conssen wh dong n pxel doman. So we can easonably mplemen Gaussan based bacgound consucon algohms n DC doman. Fo example we can use Equaon ( o esmae he paamees of a sngle Gaussan bacgound model. Λ = ( ρ Λ + ρd ( σ = ( ρ σ + ρ( d Λ ( d Λ he MoG algohm n DC doman can be fuhe mplemened. We model each pxel bloc as a mxue of 64-demensonal Gaussans and assume each dmenson of a Gaussan has he same sandad vaance. he MoG algohm pocesses each pxel bloc jus as he algohm n [4] does on each pxel. he Eucldean dsance s chosen as he machng funcon. A heshold s assocaed wh o deemne f he cuen bloc maches a Gaussan and he heshold wll be updaed n he smla way ha s counepa deals wh vaances. A good popey of he poposed algohms s ha a pxel bloc s epesened wh a vey compac fom. Geneally DC can lead o many zeo DC coeffcens whch eflecs sgnals wh some specfc fequences ae no conaned by he pxel bloc. So a Gaussan n DC doman can be dscaded f s paamee Λ s vey small. ha means we can use fewe paamees o epesen a bacgound han he Gaussan model n pxel doman. Snce he esmaon of vaances s no lnea evaluaon he poposed algohms ae no equvalen o he counepas n pxel doman n heoy. he poposed MoG algohm models a pxel bloc as a mxue of Gaussan nsead of 64 mxues so much less model paamees ae esmaed n he model adapaon whch esuls n hgh effcency n compuaon. 3.4. Idenfyng and Segmenng Foegound Objecs o denfy movng objecs he bacgound subacon echnque subacs an obseved mage fom he esmaed bacgound mage and hose pxels n he dffeence mage ha have a lage value han a pedefned heshold wll be ncluded n a foegound objec. In ou famewo we fs denfy hose blocs fom an obseved mage ha have a lage dffeence fom hose a he same locaon n he bacgound mage. Le f =... L denoe a column veco made up of pxel values n a bloc of he obseved mage and d = Kf s he coespondng DC d coeffcens veco. Fo he bacgound mage f and ae used o denoe a coespondng pxel veco and s DC coeffcens veco especvely. We use he Eucldean dsance beween d and d n Equaon ( o measue he exen o whch he bacgound n he bloc s coveed by a foegound objec. Ω = d d ( he Sum of Squaed Dffeences (SSD s commonly exploed by vdeo encodes o measue he exen o whch a bloc maches anohe bloc so a lage value fo f f epesens he bloc s beng coveed by a movng objec. I s noed ha
f f = ( f = ( d = ( d d = ( K d = f d d ( f d ( d f KK ( d d K d ( K d d K d hus Ω s a easonable measue. If Ω > τ whee τ s a heshold he bloc wll be labeled as a foegound bloc. Appaenly based on he measue we can selec hose ha ae no labeled as foegound blocs o esmae a bacgound whch can mae he esmaon of he bacgound model moe accuae. Fo example he unnng aveage algohm n he compesson doman can be mpoved as d ( f Ω > τ d ( + = αd ( + ( α d ( ohewse whee d( d( denoe he h column veco of he max D and D especvely a me. In some applcaons he accuae shape nfomaon of a movng objec s pefeed. In ou famewo gven a bacgound D = { d( =...} and an obseved mage D = { d( =...} a funcon S: D s defned o accuaely segmen a foegound objec whee = {( b =...} denoes a bnay mage. A bacgound pxel s epesened by he value whle a foegound pxel by. If he bloc s no a foegound bloc b ( = s a zeo veco; ohewse le b ( = K ( d( d ( and b ( s he h componen of b ( f he absolue value b ( > η η s a heshold b ( = ; else b ( =. If we dese he exue and colo of movng objecs o be ep n he esulan mage and epesens a bacgound pxel jus le b ( = K ( d ( d ( + Kd ( when b ( > η. 4. Fuhe Dscusson of DC-based acgound Consucon In hs secon we wll dscuss some mplemenaon ssues of he poposed appoaches fo dffeen applcaons. 4. Usage of P Fames and Fames P fames and fames (see n Secon. can also be exploed fo updang a bacgound model o exacng movng objecs. A bloc n P fames o fames s called as an na-coded bloc f can be encoded ndependenly. DC coeffcens of an na-coded bloc can be easly obaned. An ne-coded bloc eques nfomaon fom ohe blocs n encodng. I s usually encoded hough moon compensaon.e. a moon veco mang a efeence bloc n efeence mages plus compensaon eos.e. d ( = d + d( e ( whee d ( d d ( denoe DC coeffcens vecos e fo he cuen ne-coded bloc s efeence bloc and pedcon eos. If a bloc n P fames s a pa of bacgound and s ne-coded s efeence bloc should nuvely be a he same locaon n a efeence fame. Due o hgh-fequency bacgound objecs such as ee banches and noses f he moon veco mv( s smalle han a vey small heshold µ.e. mv ( < µ we can appoxmae as a zeo veco ( whch means d can be esmaed by he bloc a he same locaon n he efeence fame hus d = d(. d ( can be decly obaned. If e d ( s avalable d( can be evaluaed hough d ( = d( + d( and hen e d( can be used fo bacgound consucon o foegound exacon. If d ( s no avalable.e. mv ( > µ he bloc wll be gnoed. Fo fames he smla pocess can be used o fnd hose blocs whose DC coeffcens can be decly o ndecly obaned pecsely so ha hey can be used by he famewo n he same way as blocs n I fames. 4. Fles and Pepocessng In a genec bacgound subacon algohm opeang n he spaal doman fles especally lnea fles ae usually used n he pepocessng sep. Fo example smple empoal and/o spaal smoohng fles can be used as a pepocessng sep o educe noses. Hee we wll pesen a scheme o show how lnea fles can be mplemened and appled n DC doman. Le a 64-dmensonal veco f ( denoe a bloc n he spaal doman and he coespondng veco n he DC doman s d ( so f ( = K d(. A lnea fle opeang on a bloc n he spaal doman can be chaacezed by a 64 by 64 max F. ecause he enel max fo DC s an ohogonal max we can deve Ff ( = FK d( = ( K K FK d(. (3 = K [( KFK d( ] Equaon (3 ells us ha f a lnea fle F s appled ono a bloc n he spaal doman a coespondng fle KFK can be found n he DC doman and he esuls obaned afe applyng wo fles o he DC pa of a sngle bloc also fom a DC pa. hus fo a spaal lnea fle F we can consuc a fle KFK o mplemen he
same funcon n he compessed doman fo a sngle bloc. Compaed wh he spaal fles opeang n pxel doman he poposed scheme n he DC doman opeaes n a specal way. I fles a fame hough fleng each bloc n he fame so bloc effecs may exs due o he same eason as magn effecs may exs fo a fle opeang n pxel doman. he lmaon s nheen due o he echnques adoped by he popula vdeo compesson sandads Fo a empoal lnea fle can be epesened by a veco [ w w... w n ]. Le f ( = +... + n denoe pxel values veco n he bloc a me and d ( = Kf ( = +... + n. Applyng he fle o he bloc along he empoal axs we have n n wf = = = n = K = ( w[ K d( ]. (4 wd ( Equaon (4 shows ha n ou famewo we can decly apply a empoal lnea fle o a bloc s DC coeffcens o mplemen he same funcon. Dffeen fom he poposed spaal lnea fle he poposed empoal lnea fle s compleely equvalen o s counepa n pxel doman. 5. Expemens We have evaluaed he poposed algohms usng he USF/NIS mage sequences whch s publcly avalable fo bacgound subacon and ga analyss [4]. We chose 6 oudoo sequences and some epesenave fames ae shown n Fgue capued a wo locaons wh walng humans fom he USF/NIS daabase. One locaon has concee floo and he ohe has meadow. hee sequences fo he same locaon ae capued unde dffeen lghng condons. hee ae many bacgound vaaons n hese sequences such as sudden lghng changes small moon of ee banches small moon of bushes and shadow dsoons by he walng people. compessed vdeo seams. Fgue shows he bacgound mages geneaed by he poposed unnng aveage medan and he MoG algohms n he DC doman n compason wh hose geneaed by he coespondng algohms n he spaal doman. he leanng ae α n he unnng aveage algohms and β n he MoG algohms ae.5. he lengh of he hsoy wndow s 9 n he medan algohm. he vaance n he MoG algohm s nalzed as. All hese confguaons eep he same fo he algohms n boh spaal and DC domans. Runnng aveage Medan MoG Sequence 463CAL Sequence 35CAL Sequence 3693CAR Fgue he Fames exaced fom he esng mage sequences o smulae he vdeo compesson effecs we compessed each sequence no he MPEG- foma. In ou expemens he bacgound models ae consuced only usng I fames whch exs evey ohe 9 fames n ou Sequence 353GAL
Sequence 3653GAL Sequence 3678GR Fgue acgound geneaed by ou algohms and he counepas n spaal doman Fgue gves all he bacgound mages geneaed fo sx vdeo sequences. Fo each sequence he mages n he fs ow ae geneaed by ou algohms and he second ow by he counepas n he spaal doman. Ou eyes can no peceve evden dffeence n vsual qualy beween hem. he compuaon speed of he poposed mehods s aveagely. mes fase han he counepas n he spaal doman plus decodng cos. he dealed speed ao of each algohm s shown n he followng able. able. Compuaon speed aos beween he poposed algohms and counepas n pxel doman Aveage Medan Gaussan MoG Speed.37.5. 3.3 hese expemenal esuls ae conssen wh ou heoecal analyss. 6. Conclusons We have poposed some algohms o consuc bacgound models decly fom compessed vdeo daa. In he poposed mehods a bacgound model s epesened hough a se of DC coeffcens epesenng he powe of dffeen fequences and compued based on each 8 by 8 pxel bloc nsead of pe pxel. We have mahemacally poved ha f a bacgound consucon algohm n he spaal doman only nvolves a sequence of lnea evaluaons hee mus be a counepa n he DC doman whch has much lowe compuaonal complexy bu he same accuacy. o demonsae he valdy of he famewo we have poposed hee epesenave algohms wh dffeen syles whn he famewo.e. unnng aveage medan Gaussan and fuhe pesened some geneal possble echncal mpovemens o mae hem moe capable fo a wde ange of applcaons. Fo each poposed algohm we all gve some heoecal devaon and analyss o exploe he popees and he elaonshp wh he counepas n he spaal doman. he expemenal esuls on sandad evaluaon vdeo sequences ae conssen wh ou heoecal dscusson. Snce ou appoach has he aacve vsual accuacy fo geneaed bacgound mages much lowe compuaonal cos compac model soage as well as easonable heoecal explanaon has many poenal applcaons n pocessng compessed vdeo. Refeences [].P.L. Lo and S.A. Velasn Auomac congeson deecon sysem fo undegound plafoms Poc. of In. Symp. on Inell. Mulmeda Vdeo and Speech Pocessng pp. 58-6. [] R. Cucchaa C. Gana M. Pccad and A. Pa. Deecng movng objecs ghoss and shadows n vdeo seams. IEEE ans. on PAMI 5(:337-34 3. [3] C. Wen A. Azabayejan. Daell and A. Penland Pfnde:Real-me acng of he Human ody IEEE ans. on PAMI 9(7:78-785 997. [4] C. Sauffe W.E.L. Gmson Adapve bacgound mxue models fo eal-me acng Poceedngs of CVPR Vol. pp. 46-5 999. [5] M. Elgammal D. Hawood L. S. Davs Non-paamec Model fo acgound Subacon Poceedngs of he 6 h ECCV pp. 75 767. [6]. Han D. Comancu and L. Davs Sequenal enel densy appoxmaon hough mode popagaon: applcaons o bacgound modelng Poc. ACCV 4. [7] N. M. Olve. Rosao and A. P. Penland A ayesan Compue Vson Sysem fo Modelng Human Ineacons IEEE ans. on PAMI (8: 83-843. [8] F. De la oe M. J. lac A famewo fo obus subspace leanng Inenaonal Jounal of Compue Vson 54(-3: 7-4 3. [9] M. Se. Wada H. Fujwaa K. Sum acgound deecon based on he cooccuence of mage vaaons Poc. of CVPR 3 vol. pp. 65-7 [] R.S. Aygun A. Zhang Saonay bacgound geneaon n mpeg compessed vdeo sequences IEEE ICME pp. 7-74. [] X. Yu L. Duan Q. an Robus movng vdeo objec segmenaon n he MPEG compessed doman Poc. ICIP vol. pp. 933-936 3. [] W. Zeng W. Gao D. Zhao Auomac movng objec exacon n mpeg vdeo Poc. of ISCAS'3 vol. pp. 54-57 3. [3]. Ugu öeyn A. Ens Çen Anl Asay M. lgay Ahan. Movng Regon Deecon n Compessed Vdeo. ISCIS pp.38-39 4. [4] J. Phllps S. Saa I. Robledo P. Gohe and K. owye. aselne esuls fo he challenge poblem of human d usng ga analyss. Poceedngs of Face and Gesue Recognon