Software Designs Of Image Processing Tasks With Incremental Refinement Of Computation

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1 IEEE Trasactis Image Prcessig, t appear i 21 1 Sftware Desigs Of Image Prcessig Tasks With Icremetal Refiemet Of Cmputati Davide Aastasia ad Yiais Adrepuls * ABSTRACT Sftware realizatis f cmputatially-demadig image prcessig tasks (eg image trasfrms ad cvluti) d t curretly prvide graceful degradati whe their clck-cycles budgets are reduced, eg whe delay deadlies are impsed i a multi-taskig evirmet t meet thrughput requiremets This is a imprtat bstacle i the quest fr full utilizati f mder prgrammable platfrms capabilities sice wrst-case csideratis must be i place fr reasable quality f results I this paper, we prpse (ad make available lie) platfrm-idepedet sftware desigs perfrmig plae-based cmputati cmbied with a icremetal packig framewrk i rder t realize blck trasfrms, 2D cvluti ad frame-by-frame blck matchig The prpsed framewrk realizes icremetal cmputati: prgressive prcessig f iput-surce icremets imprves the utput quality mtically Cmpariss with the equivalet -icremetal sftware realizati f each algrithm reveal that, fr the same precisi f the result, the prpsed apprach ca lead t cmparable r faster eecuti, while it ca be arrarily termiated ad prvide the result up t the cmputed precisi Applicati eamples with regi-f-iterest based icremetal cmputati, task schedulig per frame, ad eergy-distrti scalability verify that ur prpsal prvides sigificat perfrmace scalability with graceful degradati Ide Terms cmpleity scalable image prcessig, icremetal refiemet f cmputati, prgrammable prcessrs EDICS CODE: ELI-HDW I INTRODUCTION Several ppular applicatis, such as media players, cmputer graphics, image ad vide * Crrespdig authr The authrs are with the Uiversity Cllege Ld, Dept f Electric & Electrical Egieerig, Trrigt Place, WC1E 7JE, Ld, UK; Tel: ; fa: ; daastasia@eeuclacuk (D Aastasia), iadrep@eeuclacuk (Y Adrepuls) The authrs ackwledge the supprt f the EPSRC, grat EP/F215/1

2 IEEE Trasactis Image Prcessig, t appear i 21 2 pst-prcessig, ad mti estimati ad cmpesati, are implemeted tday via sftware slutis i geeral-purpse prcessrs New geeratis f prcessrs are icreasigly pwerful ad eable mre dedicated resurce allcati t real-time multimedia tasks due t multi-cre desigs [1] ad higher levels f parallelism At the same time, state-f-the-art sftware cmpilers w autmatically geerate platfrm-specific ptimized assembly cde [2], thereby eablig platfrm-idepedet C++ slutis t achieve a high degree f utilizati f the prcessr s resurces Hwever, tday there is very little syergy betwee the system layer (sftware desig, prcessr, task maager) ad the multimedia applicati layer (eg image prcessig task, such as filterig) Fr eample, if e is watchig a mvie a prtable vide player (eg [3]) ad this is draiig the system resurces (battery), curret systems d t allw fr seamless tradeffs i visual quality vs battery life (eecuti time per task) I such cases, the user is practically facig the /ff apprach f digital systems, while e wuld strgly pt fr a best-effrt apprach, fte fud i aalg systems, where eergy autmy wuld be icreased with graceful degradati i the decded vide quality Eistig algrithmic-rieted research fcuses cmpleity reducti [4]-[6] r cmpleity scalability fr image prcessig tasks [7]-[9], where cmputatial cmpleity is decreased ad apprimate results are prduced Implemetati-rieted research fcuses multimedia-drive eergy scalig f prcessrs via dyamic vltage scalig [1] [11] i a attempt t prvide cmputatial scalability with apprimate results Overall, fr all eistig appraches: (i) algrithm-specific ad/r system-specific custmizatis are required, which limit the applicability f the prpsed techiques; (ii) ly e peratial pit i the cmpleity-distrti curve [4] [8] ca be btaied, ie e is t able t seamlessly icremet the quality f the utput with icreased cmputati The latter meas that cmple hardware ad sftware recfiguratis are required whe differet thrughput i frames-per-secd (fps) is required Hece, applicati scalability ad rbustess is t btaied istataeusly ad i a atural ad straightfrward maer A ecepti is fud i theretical prpsals fr icremetal cmputati f trasfrms ad saliet pit detecti algrithms [12]-[14], where the mai priciple is: uder a refiemet f the surce descripti, the cmputati f the image prcessig task refies the previusly-cmputed result Hwever, eistig wrk [12]-[14] is ly usig arithmetic cmpleity estimates ad practical realizatis are prpsed

3 IEEE Trasactis Image Prcessig, t appear i 21 3 I this paper we address this aspect by prpsig a uified sftware framewrk fr image prcessig tasks ehiig icremetal refiemet f cmputati Our sftware desigs f trasfrm decmpsitis, tw-dimesial (2D) cvluti ad blck-matchig peratis cmbie icremetal cmputati with a recetly-prpsed packig apprach that eables the calculati f multiple limited dyamic-rage iteger peratis via e 32- r 64- arithmetic perati The prpsed sftware desigs are validated i tw differet systems ad are als prvided lie [15] Our iitial effrts are reprted i [16] I this paper we are prvidig the fllwig additial ctributis: (i) we preset the case f trasfrm decmpsitis; (ii) a ew apprach is prpsed fr icremetal blck matchig usig the sum squared errr criteri; (iii) we preset applicatis f the prpsed apprach with: regi-f-iterest cmputati, parameterized real-time task schedulig with arrary variability, ad vide capturig ad prcessig ehiig pwer-distrti tradeffs Secti II presets ur framewrk Sectis III-V detail the applicati f this apprach fr trasfrm decmpsitis, 2D cvluti ad blck matchig Secti VI presets the eperimetal cmpariss ad Secti VII presets applicatis demstratig the advatages f the prpsed apprach i practical systems Fially, Secti VIII ccludes the paper II IMAGE PROCESSING TASKS REALIZED VIA INCREMENTAL PACKING AND UNPACKING A geeral depicti f the prpsed framewrk fr icremetal cmputati based surce refiemets is give i Figure 1 I the fllwig subsecti we discuss this framewrk i mre detail, while Subsecti B presets the basic tradeffs f the prpsed packig apprach The prpsed framewrk is built uder the ti f prcessig f plaes, startig frm the mst sigificat plae (MSB) f the iput ( = N 1) ad gig dw t the least-sigificat plae (LSB), which is plae = Fr -egative 8- images csidered i this paper, N = 8 Tw useful defiitis f quatities used i the remaider f the paper are give belw Defiiti 1: Fr ay quatity a used i the cmputati f a algrithm, a full, < N, is the cmputed value f a whe the iput csists f plaes N 1 dw t (ad icludig) plae Defiiti 2: Fr ay quatity a used i the cmputati f a algrithm, a, < N, is the cmputed value f a whe ly plae f the iput is used

4 IEEE Trasactis Image Prcessig, t appear i 21 4 The tatial cvetis f Defiiti 1 ad Defiiti 2 are eteded t matrices 1, eg matri ctaiig the cmputed cefficiets f A whe ly plae f the iput image is used A Overall Framewrk A is the As shw i Figure 1, a iput image is iitially partitied it M -verlappig blcks, whse biary (plae-by-plae) represetati is shw i the middle f the figure, frm MSB t the LSB A ttal f N icremet layers are frmed by grupig tgether the th plae f all blcks ( Icremet layer i Figure 1), < N Each icremet layer is als a layer f cmputati We calculate the results f all M blcks f each layer ccurretly usig a icremetal packig apprach, as described i the fllwig First, all M blcks B1,,, B M, f e layer are stacked tgether i e blck D by: m M λtype ( m 1) ρ m= 1 m, (1) D [ i, j] = B [ i, j] 2 m, where B, [ i, j ] is the ( i, j) th value f blck B (1 m M ) that ctais parts f icremet layer belgig t the m th spatial blck, λ type= 1 if 64- flatig-pit represetati is used r λ type= 1 if 32- usiged iteger represetati is used, ad ρ> is the packig cefficiet, whse eplaati ad settig will be discussed i detail i the fllwig subsecti (IIB) The last equati λtype shws that the th plae f the m th blck is scaled by 2 ( m 1) ρ ad is the added t the sum f the previus blcks 1,, m 1 f the same icremet layer This leads t a packed icremet layer havig all M blcks placed e blck D ad usig iteger r flatig-pit represetati The best chice fr the utilized represetati (iteger r flatig-pit) is system depedet, as it will be shw by ur eperimets After the packig apprach, the desired image prcessig task p is applied t < N, eg cvluti with kerel K is perfrmed by: ( ) = p D fr each layer, R D K (2) Depedig the algrithm f iterest, e culd lcalize the calculati f (2) arud areas f iterest based the previusly-cmputed icremet layers (as idicated i Figure 1) This will be used i the 1 Bldface capital letters idicate matrices; the crrespdig italicized letters idicate idividual matri elemets, eg A ad Ai [, j ] ; all idices are itegers; superscripts i matrices r scalars idicate the plae umber ad the frame ide (ecept fr superscript T that idicates traspsiti), the disticti betwee the tw is idetifiable frm the ctet

5 IEEE Trasactis Image Prcessig, t appear i 21 5 blck matchig task ad i ur eperimets with regi-f-iterest based cmputati If a apprpriate cefficiet ρ is chse fr (1), it ca be shw [17] that the results f all the blcks withi icremet layer ca be etracted frm the prcessig kerel K ctais itegers; p is a liear perati 2 R if: This is based the s-called ivaders apprach [17], where ay iteger liear perati ca be perfrmed by packig multiple peratis tgether [see (1)], ad the upackig them by the reverse perati perfrmed recursively fr all values f all blcks Fr flatig-pit represetati ( λ type= 1 ), upackig is perfrmed by [16]: m, 1, 1, R [ i, j] R [ i, j], m= 1 : U1,[ i, j] = R [ i, j] + 5 ( ) ρ m, = m 1, m 1, Um, [ i, j] = Rm,[ i, j] + 5 R [ i, j] 2 R [ i, j] U [ i, j], m {2,, M} : (4) m, where: U is the utput icremet f the result fr blck m, R is the upackig ad a+ 5 the upackig is perfrmed by: where ( a ρ) (3) R matri at the m th perfrms rudig t the earest iteger Fr iteger represetati ( λ type= 1 ), m= 1 : 1, 1, R [ i, j] = R [ i, j], ρ ( 1, ) ( m 1, ρ) ( m 1, ) U [ i, j] = md R [ i, j],2 m, m, R [ i, j] = R [ i, j], m {2,, M} : (6) U [ i, j ] md R [ i, j ρ = ],2 ρ shifts a dw by ρ s ad md( a,2 ) = a a 2 2 ρ ρ (5) is the mdul perati The selecti f the apprpriate packig cefficiet ρ depeds the specific algrithm beig csidered I additi, eve thugh Figure 1 shws all blcks f the iput image beig packed tgether, i practice the value f M depeds the dyamic rage f the result f each icremet layer These aspects are elabrated further i the fllwig sectis As shw i Figure 1, after upackig, the fial stage f the prpsed cmputati icremets the previusly-cmputed results f icremet layers N 1,, + 1 by addig t them the results f the curret layer, U1,,, U M, : 2 I Secti V, we are als csiderig the case where p is a quadratic perati It is shw that such -liear peratis are pssible, but they require careful hadlig withi a packig framewrk

6 IEEE Trasactis Image Prcessig, t appear i 21 6 with U N m,full + 1 m,full m,full m, m {1,, M} : U = U + U (7) This leads t cmputati f the prcessig task with icreased precisi fr icreased umber f icremet layers, as shw i the visual eamples f Figure 1 Due t the utilizati f the packig techique, the results f all M blcks are cmputed ccurretly by (2) Depedig the verhead f packig ad upackig, we epect t save peratis i cmparis t the direct cmputati f each layer Iput image S p a t i a l I m a g e P a r t i t i i g Image blck 1 Image blck M Icremet layer Image blck plaes Packig Results frm layers: N-1,N-2,,+1 Upackig Algrithm cmputati usig layer Results f layer Prcessed iput image up t layer =6 =4 + =2 Figure 1 Icremetal refiemet f cmputati usig packig ad upackig f icremet layers etracted prgressively frm the iput image data The utput result is prgressively refied via the cmputati f mre icremet layers The cmputati f each layer ca als utilize results frm previus layers t reduce cmpleity r fcus the cmputati regis f iterest B Ctrllig Parameters ad Practical Etesis The parameters ctrllig the prpsed apprach f Figure 1 are: the ttal umber f icremet layers (N ), the ttal umber f blcks (M ) ad the packig cefficiet (ρ ) that ctrls the stackig f multiple icremet layers i e perad D [ i, j ] Ideally, we wuld like t maimize the packig capability i rder t perfrm as may peratis simultaeusly as pssible [17] As aalyzed i the rigial ivaders algrithm, the packig capability depeds the dyamic rage f the peratis Furthermre, if packig with iteger represetati is desired, ρ has t be iteger The 5 dyamic rage f the packig btaied with the maimum packig cefficiet cat be smaller tha 2 31 fr 64- flatig-pit represetati [17], ad it cat be larger tha 2 fr 32- usiged iteger represetati, which leads t 5( 1) M λ + type ρ ω type, with ω type= 5 r ω type= 31,

7 IEEE Trasactis Image Prcessig, t appear i 21 7 respectively 3 If the rage f all utputs ( B m, p ) i the iterval { A, A } K (fr every plae ad blck m ) is ctaied ρ lg + 1 ma ma, the, fllwig lse packig thery [17], we have 2 Ama Selectig the miimum value f ρ satisfyig the iequality, we reach ω type M 5 type 1 lg2 Ama + 1 ( λ ) As epected, the umber f packed blcks decreases with the icrease f the utput s dyamic rage The utput dyamic rage f each layer depeds the algrithm f iterest ad it will be discussed separately i the fllwig sectis I rder t esure there is umerical errr i the calculati whe packig with flatig-pit arithmetic, the magitude f the maimum pssible errr [17] must allw fr crrect rudig by (3) ad (4), ie: (8) 2 ω ma ( 1) ρ type A 2 M < 5 (9) I ur desigs, M is iitially derived by (8) ad the decreased (if eeded) s that (9) hlds Fr tatial simplicity, this paper discusses wise iputs ad N = 8 icremet layers fr 8- images; hwever, e ca cmbie a umber r plaes it e layer i rder t reduce the icremets required t btai the full-precisi result This is eabled by the implemetati f the prpsed apprach [15] ad it is utilized i the eperimetal secti f the paper i rder t make the eecuti time f the prpsed apprach cmparable t the equivalet -icremetal desig f each algrithm f iterest Fially, eve thugh Figure 1 idicates that all image blcks are packed tgether (ie the algrithm splits the image it M blcks), there are practical cases where the desired umber f blcks is larger tha the value f M calculated by (8) ad (9), eg i a 4 4 blck trasfrm decmpsiti f a piel image Fr thse cases, after packig Q grups f M blcks (where Q M gives the ttal umber f image blcks), the prcessig, upackig ad result-icremetig prcesses are iterleaved This is shw i the schematic f Figure 2 Oce the first icremet is cmputed fr all grups, the iterleavig allws fr arrary termiati f the algrithm eve i-betwee icremet layers: this is a feature that allws fr virtually seamless quality imprvemet with icreased cmputati withi each icremet layer 3 The term M 5( λ 1) + presets the fact that whe λ type= 1 (flatig pit), there is a type additial packig at the matissa which is t icluded withi ω type= 5 ; whe λ type= 1 (iteger represetati), the etire packig is achieved withi ω type= 31

8 IEEE Trasactis Image Prcessig, t appear i 21 8 Image blck 1 Image blck Q M Icremet layer Packig it Q grups f M blcks grup 1 grup q grup Q Prcessig ad upackig f M blcks Prcessig ad upackig f M blcks Prcessig ad upackig f M blcks Results f layer +1 f grup 1 1st grup f layer Results f layer +1 f grup q qth grup f layer Results f layer +1 f grup Q Q th grup f layer Results f layer f all Q grups Figure 2 Packig, prcessig, upackig ad icremetig the result with Q grups f M blcks III INCREMENTAL TRANSFORM DECOMPOSITION The iput f this case is Q grups f M blcks f C C iput piels, B m,full, 1 m M, with C= {4, 8,16} fr typical cases f blck trasfrms fud i the literature [18]-[2] The trasfrm matri is give by a C C iteger kerel T fr, eg the H trasfrm [18] Trasfrms kerels with -iteger cefficiets ca be apprimated by a fied-pit (FXP) represetati with the apprpriate umber f fractial s [21] Hece, they ca be cmputed with a iteger kerel fllwed by iverse scalig after the termiati f the calculati ad ca be accmmdated by ur framewrk The fllwig describe the prpsed icremetal cmputati fr all M blcks f each grup f blcks q, 1 q Q Uder a iteger trasfrm kerel, the decmpsiti f the m th blck is perfrmed by: T m,full Tfr Bm,fullTfr m {1,, M} : U = (1) Whe plaes f the iput are used fr the trasfrm decmpsiti, the prcess ca be perfrmed fr each plae (frm = N 1 dw t = ) f the m th blck by: T m, Tfr Bm,Tfr m {1,, M} : U = (11) ad the results are added t the previusly-cmputed results by (7) The abve prcess was already prpsed withi trasfrm-specific frmulatis fr icremetal cmputati f the discrete Furier trasfrm [12] ad the liftig-based discrete wavelet trasfrm [13] Here, we csider packig the results i rder t accelerate the icremetal cmputati i sftware We frm D by (1) ad it is used t cmpute the packed result f all M blcks by:

9 IEEE Trasactis Image Prcessig, t appear i 21 9 The results are upacked frm T = fr fr R T D T (12) R usig (3) ad (4) [r (5) ad (6) if iteger packig is perfrmed] ad the fial results per plae are derived by (7) Ntice that ly e trasfrm decmpsiti with blck D is perfrmed by (12) istead f M blck decmpsitis perfrmed by (11) This is epected t save peratis by cmbiig blcks tgether via the icremetal packig apprach As shw by (8) ad (9), the ttal umber f blcks cmbied (packig capability), M, depeds the wrst-case dyamic rage A ma f (11) This rage ca be fud by assumig the wrst-case blck: s 1, if ( 1) Tfr[ i, j] > Bs[ i, j] = fr i, j< C, s {,1} (13) s, if ( 1) Tfr[ i, j] p C 1 1 ( 2 1) ma{ ma { C [ ] [, ] } ma { [ ] [, ] i= s j= s }} (14) A = T i j B i j T i j B i j ma fr fr s j i where p is the umber f plaes packed i each icremet layer, eg p= 1 whe we pack a sigle biplae i each icremet layer Ccerig the trasfrm recstructi (sythesis) prcess, the same apprach ca be fllwed, where the sythesis is give by 1 fr T m,full iv m,full iv m {1,, M} : B =T R T, (15) with T = T I this case the maimum plae f the iput is chaged depedig the dyamic iv rage epasi f the frward trasfrm Whe usig packig with iteger represetati, the icremetal apprach as preseted s far ly cvers the use f trasfrm kerels with -egative cefficiets because the sig ifrmati is t preserved via iteger packig I rder t cver the geeral case f arrary trasfrm kerels, we eed t cvert all trasfrm cefficiets t -egative umbers by: with P= mi { fr } i, j T fr+ = T fr+ P, (16) T [ i, j ] 1 C C ad 1 C C a C C matri f es After the icremetally-cmputed decmpsiti is perfrmed fr each iput blck D usig T fr+, we eed cmpesate fr the added cmpet f the kerel f (16) durig the derivati f the fial results per plae Hwever, simple liear algebra shws that several multiplicatis ad additis are eeded i rder t derive the crrect result sice the decmpsiti with the trasfrm kerel f (16) derives: T T T T + fr fr+ fr+ fr + R =T D T PD T T D P PD P (17) T ut f which ly the term TfrDT fr is the desired icremet Hece, we d t ivestigate this pti i

10 IEEE Trasactis Image Prcessig, t appear i 21 1 this paper ad restrict ur apprach t flatig-pit represetati fr the trasfrm decmpsiti case IV INCREMENTAL TWO-DIMENSIONAL CONVOLUTION Fr a image csistig f Ri Ci piels, the blck partitiig f this case separates the image it M partially verlappig hriztal stripes, each f which is the csidered t be the iput blck f samples, B m (1 m M ), havig C i clums The umber f rws i each blck is ctrlled by the iput image rws ad the packig capability (ie the value f M ) The cvluti filter is give by a V C kerel kerel -cefficiet kerel cv T ad cvluti f the m th blck is perfrmed by:,full B,full Tcv m {1,, M} : Um = m (18) I rder t prduce the crrect result with the blck-based calculati f (18), csecutive blcks share a cmm subset f rws Vverlap= Vkerel 2, ie the first blck ( stripe ) is verlappig with the secd blck vertically by V verlap rws, all subsequet blcks verlap with their previus ad et blcks by V verlap rws (abve ad belw the blck), ad the last blck verlaps with its previus blck by V verlap rws Whe plaes f the iput are used, the prcess ca be perfrmed fr each plae f the m th blck by: m, m, cv m {1,, M} : U =B T, (19) ad the results are added t the previusly-cmputed utputs by (7) If we csider packig the results i rder t accelerate the icremetal cmputati, the frmed by (1) ad it is used t cmpute the packed result f all M blcks by: The results are upacked frm = cv D is R D T, (2) R usig (3) ad (4) [r (5) ad (6) if iteger packig is perfrmed] ad the fial results per plae are derived by (7) Visual eamples f Gaussia filterig whe {6,4,2} are give i Figure 1; similar eamples with {5,2,} are give i Figure 8 As i Secti III, the packig capability depeds the wrst-case dyamic rage, which is calculated usig T cv i (13) ad the: ma ( 2 p 1 kerel kerel ) ma V { 1 C 1 [, ] s cv [, ] i= j= } A = B i j T i j s (21) I additi, similarly t the trasfrm decmpsiti case, kerels with -iteger cefficiets ca be apprimated by a FXP represetati Whe usig packig with iteger represetati ad the

11 IEEE Trasactis Image Prcessig, t appear i cvluti kerel ctais egative cefficiets, we apply (16) usig T cv ad the, after upackig, we icremet the result by: V 1C 1 m,full m,full m, cv m, i, j i= j= { } kerel kerel + 1 U = U + U + m {1,, M} : mi T [ i, j] B [ i, j] (22) i rder t cmpesate fr the added elemet P= mi { cv } i, j T [ i, j ] 1 C C Fially, i rder t permit icremetal cmputati eve withi a icremet layer, the calculati f (2) ad the upackig ad icremetati f results are iterleaved fr each utput cefficiet R [ i, j ] This permits virtually seamless quality imprvemet with icreased cmputati withi each icremet layer V INCREMENTAL BLOCK MATCHING The prblem f blck matchig betwee tw successive images I ad I (f Ri Ci piels) ca be abstracted as fllws Give the q th -verlappig blck, t 1 full, t q,full, t full B f C ( 1 q Q, assumig Q blcks i ttal) ad a crrespdig search area, t 1 full verlappig blcks i I, fid the C C piels i, t 1 q,full I, t full S f 2W 2W C blck i the search area that is clsest t the q th blck Cvetial search algrithms use -liear distace criteria, such as the sum squared errr (SSE) r the sum f abslute differeces (SAD) [6] I this paper, we prpse a apprach t perfrm icremetal blck matchig usig the SSE criteri Hwever, sice the framewrk f (1)-(7) wrks with liear prcessig, careful hadlig f the packig, prcessig ad upackig is required The first prblem t be addressed is the packig itself There are several ways e ca csider usig icremetal prcessig with packig i the blck matchig case The first, mst straightfrward, apprach is t csider tw csecutive image blcks i frame I ad pack icremets f these blcks tgether t cmpute a sigle distace criteri fr bth blcks, ie fllwig the geeric verview f Figure 1 Hwever, due t the fact that the psitis f the best match withi the search rages i frame I will be differet, this has tw imprtat detrimets: it makes early termiati difficult t apply fr blck matchig 4 ad, fr icremets beyd the first e, it cmplicates the lcalizati f the calculati arud the previusly-established match, t full Ather way t csider icremetal prcessig fr this case is t pack tw sets f samples f a sigle, t 1 full 4 Early termiati stps the calculati f the distace fr a cadidate match ce the distace value has eceeded the e f the already-fud best match [6] This becmes cumbersme fr ccurret prcessig f tw (r mre) blcks as they have differet matches with differet miimum distaces

12 IEEE Trasactis Image Prcessig, t appear i blck tgether i rder t cmpute the distace criteri bth sets ccurretly The search area ca als be packed i the same way i rder t allw fr cmpariss betwee packed icremetal represetatis This is detailed i the fllwig subsecti Subsecti B eplais hw the (-liear) SSE criteri ca be calculated usig the packed represetatis The verall blck matchig algrithm is summarized i Subsecti C A Packig f Icremetal Blck ad Search-area Samples usig the Quicu Lattice We split the blck ad search-area samples it tw -verlappig sets usig the quicu lattice, whse samples [ i, j ] ad [ i, j ] are shw i Figure 3 fr a eample 4 4 blck ad its crrespdig 8 8 search area Fr each ew icremet f the blck ad search area, the packig withi each blck, t q,full B is de by 5 ( i< C,, t, t j C 2 < ):,,, q,full q,full q,full B [ i, j] = [ i, j] + [ i, j] 2 (23), t with q,full [, ], q,full [, ] the samples f B q,full up t (ad icludig) the th plae ad fllwig the quicu lattice f Figure 3(a) ad ρ the packig cefficiet, whse settig is discussed i Subsecti B, t 1 q,full Fr the crrespdig search area S, we frm fur packigs by ( i< 2W, j< W ): with, t 1 q, t 1, 1, 1,full [,,,] t,full [, ] t ρ q i j = q i j + q,full [ i, j] 2 S (24), t 1, 1, 1,full [,,1,] t,full [, ] t ρ q i j = q i j + q,full [ i, j] 2 S (25), t 1, 1, 1,full [,,,1] t,full [, ] t ρ q i j = q i j + q,full [ i, j+ 1] 2 S (26), t 1, 1, 1,full [,,1,1] t,full [, ] t ρ q i j = q i j + q,full [ i, j+ 1] 2 S (27),full [, ], t 1, q,full [, ], t 1 the samples f S q,full up t (ad icludig) the th plae ad fllwig the quicu lattice f Figure 3(b) Ntice that the packig rules f (23)-(27) crrespd t the case f M= 2 f (1) but, istead f usig tw blcks, we use the tw lattice sample sets The eed fr the fur separate packigs give by (24)-(27) becmes evidet ce we eamie the samples that will be cmpared i the packed represetati fr every pssible cmbiati f search psitis I particular, the packigs f (24) ad (25) are used whe the blck is cmpared t blcks lcated at (eve,eve) ad (dd,eve) psitis i the search grid, respectively The packigs f (26) ad (27) are used whe the blck is cmpared t blcks lcated at (eve,dd) ad (dd,dd) psitis i the search grid, respectively ρ 5 Fr epsiti simplicity we fcus the case f flatig-pit packig, ie λ type= 1

13 IEEE Trasactis Image Prcessig, t appear i Eamples fr all fur cases are give i Figure 3(b) Hece, fr each search lcati S, t 1 q,full is js (, ) we use S, t 1 q,full [ is, js 2, g, z] with g= md( i s,2) ad z= md( js,2) T keep the required memry ftprit fr (23)-(27) small, the packig ad blck matchig is perfrmed separately fr each blck ad its search area I this way, eve fr blcks with ± 16 piels search rage, less tha 2Kb is required per blck match, ie a amut f memry that ca easily fit i the level-e cache f all mder prcessrs I the fllwig subsecti, we eamie the apprach we fllw t calculate the packed SSE Search lcati (i s, j s ) (eve,eve) (eve,dd) (,) (2,7) (dd,eve) (dd,dd) (5,2) (7,7) (a) (b) Figure 3; (a) Eample f quicu lattice fr a 4 4 blck; (b) Eample f quicu lattice f a 8 8 search area with idicative search psitis highlighted Ay subblck f the search area withi the crdiates {(,), (7,7)} ca be selected as a match B SSE Calculati usig Packed Represetatis The blck SSE calculati with packed represetatis usig M= 2 is perfrmed as fllws Assume the packed blck samples, t q B,full [ i, j ] ad a cadidate blck i the packed search area S, t 1 q,full [ is+ i, js 2 + j, g, z], which crrespds t search lcati, t 1 ( i s, j s ) i S q,full We calculate the packed SSE by: C 1C 2 1, t, t 1 2 SSE = ( q,full [ i, j] q,full [ is+ i, js 2 + j, g, z]) i= j= D B S (28) Per blck psiti ( i, j ), (28) perfrms the squared differece betwee the packig f (23) ad e f the packigs f (24)-(27) I the remaider f this subsecti, we aalyze the case whe (23) ad (24) are used i (28), ie g= ad z=, sice all ther cases f ( g, z ) are eamied i the same maer By replacig the packed represetatis usig (23) ad (24), ad epadig the square we have:

14 IEEE Trasactis Image Prcessig, t appear i D C 1C 2 1 2, t, t 1, t, t 1 ρ SSE = ( q,full [ i, j] q,full [ is+ i, js 2 + j] ) + ( q,full [ i, j] q,full [ is+ i, js 2 + j] ) 2 i= j= C 1C 2 1 C 1C , t, t 1, t ( q,full [ i, j] q,full [ is+ i, js 2, t 1 2ρ = + j] ) + q,full[ i (, j] q,full [ is+ i, js 2 + j] ) 2 i= j= i= j= C 1C 2 1, t, t 1, t, t 1 ρ + 2 ( q,full [ i, j] q,full [ is+ i, js 2 + j] )( q,full [ i, j] q,full [ is+ i, js 2 + j] ) 2 i= j= The three terms f (29) shw that we ca upack the SSE f each samplig grid ad discard the uwated crss-prduct term (which is scaled by 2 ρ ) This is de fllwig the upackig prcess f (3) ad (4): D, D ρ =2 ( D U ), U = D +5, U ρ ( D U ) U1= SSE+5 SSE,1 SSE 1 2 SSE,1 3 SSE,1 2 (29) = The ttal SSE f bth grids is D SSE,grid= U1 + U3 ad U 2 is the upacked crss-prduct term Hece, the packed SSE f (28) carries withi it the result f bth icremetal grids Ntice that, eve thugh we packed tw iputs, we eed t perfrm three upackigs because f the uwated crss-prduct term Settig f packig cefficiet ρ : As eplaied i Subsecti IIB, ρ ca be set based the wrst-case dyamic rage ( A ma ) f the cmputed results withi the packed represetati The wrst case 2 fr (29) ccurs i the crss-prduct term, where we have ( 2 N A C ) 2 ma = Whe we have large blcks (eg whe C= 16 ) r whe we reach the least sigificat s ( = ) this rage may be prhiively large t permit M= 3 crrect upackigs Hwever, durig the calculati f (28) we check at the ed f every dd-umbered rw fr early termiati (ie whether the SSE eceeds the previusly-fud best e) Hece, we ca als set a wrst-case dyamic rage early A ma which, if eceeded, we efrce early termiati because this will mst-likely t crrespd t a gd match Usig (8) ad (9) with M = 3, we fid that lse packig ca accmmdate A ma= Based eperimets with umerus real-wrld vide sequeces, we set A early A ma 2 ma = as the threshld fr early termiati C Overall Blck Matchig Algrithm The basic algrithm perfrmed fr each icremet is give i Figure 4 I particular, each icremet layer applies the search algrithm with a rw-by-rw sca patter usig early termiati The search area grid t be used is selected via step 5, which is perfrmed befre the lp that calculates the packed SSE This simplifies the ideig f the sftware implemetati This algrithm ca be readily eteded t csider iterplati grids, ad multi-frame mti estimati

15 IEEE Trasactis Image Prcessig, t appear i ma = 2 2 N early Set ρ= lg2 A ma + 1 // set packig cefficiet t be used,, Set ( i, j ) = ( W 1, W 1) // crdiates f best match are set t the ceter f the search area Setup: Set A early C ( ) 2 s, q s, q Basic Algrithm: Icremetal Blck Matchig usig SSE fr each iput blck B ad search area S Fr each icremet, = N 1,, {, t q,full, t q,full, t 1 q,full, t 1 q,full 1 Etract B ad S 2 Calculate B ad S usig (23)-(27) Set D SSE= // the miimum distace will g i D SSE, 3 Fr each search rw i s, i s =,,2W 1 { 4 Fr each search clum j s, js=,,2w 1{ 5 Set: g= md( is,2), z= md( js,2), D SSE= 6 Fr each blck rw i, i=,, C 1{ 7 Fr each blck clum j, j=,, C 2 1 {,, D t t SSE D SSE + ( B q,full [ i, j] S q,full [ is+ i, js 2 + j, g, z]) // a b assigs b t a } 9 If md( i,2) = 1 { 1 U1= SSE+5 D, D ρ SSE,1=2 ( D SSE- U1), U2= SSE,1+5 D, U ( ) 3= ρ 2 SSE,1-U2 + 5 D Set D SSE,grid= U1 + U3 // upack the D SSE values f bth grids ad add them early 11 If ( DSSE,grid > D SSE r D SSE,grid> Ama ) The G t Step 12 // early termiati } },,, t q,full 12 If DSSE,grid < D SSE The { Set DSSE = D SSE,grid Set ( i s, q, j s, q ) = ( i s, j s ) } } },, s, q s, q s s 13 Stre crdiates f best match fr icremet f blck q :( i, j ) = ( i, j ) } Figure 4 Pseudcde f icremetal blck matchig usig sum squared errr, t 1 q,full Icremetal blck matchig ca beefit frm the kwledge f the best match fud fr each blck durig the previus icremet layers N 1,, + 1 i rder t speed up the eecuti This is perfrmed as fllws Fr the first icremet layer = N 1, we perfrm a fast search usig the lgarithmic-step search fllwed by a spiral search patter arud the lcati f the best match [6] Fr subsequet icremets f each blck q, we ly search i the eighbrhd f the previusly-fud best match fr this blck This is perfrmed by perfrmig a spiral search withi a fied distace limit f W piels hriztally ad vertically (see [15] fr full details the implemetati) The use f lg-search ad the lcalizati f the search arud the previusly-fud best match will prduce apprimate results per icremet layer Cmpariss agaist the cvetial (-icremetal) full search algrithm i terms f predicti quality vs eecuti time are give i the et secti spiral

16 IEEE Trasactis Image Prcessig, t appear i VI EXPERIMENTAL RESULTS FOR BITPLANE-DRIVEN INCREMENTAL COMPUTATION Fr ur eperimets, we used the -laptp f the OLPC fudati (detailed specificati ca be fud i [22]) ruig its ative Liu peratig system (deted as lw-ed prfile) ad a Dell Latitude D63 maistream laptp with a Itel Cre 2 Du prcessr (clcked at 25GHz with 2Gb RAM) ruig Micrsft Widws XP (deted as maistream prfile) All prgrams were writte i C++ ad cmpiled with the gcc412 cmpiler i Liu ad with the Micrsft Visual Studi 28 cmpiler i Widws, with all default ptimizatis f -2 (maimize speed) mde i bth cases T achieve stable eecuti-time measuremets with high precisi i bth platfrms, we used the Widws QueryPerfrmaceCuter() fucti ad the Liu gettimefday() fucti ad ru all prgrams i highest pririty Oly the eecuti time required fr the cmputati was measured fr the results f this secti (ad cverted t millisecds based system-specific timig measuremet) All I/O time frm/t the disk was ecluded, sice it prduced the same verhead fr bth the cvetial ad the icremetal appraches We utilized the Cmm Iterchage Frmat (CIF) vide sequeces Castguard, Frema Mbile, Silet ad Stefa as iput vide frames at 3fps The sequeces csist f 3 frames each ad prvide a 15-frame vide with diverse ctet Fr the lw-ed prfile, we dwsampled the sequeces t quarter-cif (QCIF) frmat at 1fps i rder t achieve real-time (r ear real-time) prcessig with the -laptp The sigal-t-ise rati (SNR) r the peak-sigal-t-ise rati (PSNR) measuremets preseted i the results utilize ly the Y (lumiace) chael SNR was measured fr all trasfrm ad cvluti eperimets usig as referece (ise-free) the result whe prcessig up t the LSBs f each frame (full precisi, = ) PSNR was measured fr the blck matchig eperimet by usig the predicti errr f frame-by-frame mti cmpesati (usig the rigial frames) with the mti vectr f each blck prduced frm the lcati f the best match fud withi the search area A Icremetal Trasfrm Decmpsiti ad 2D Cvluti Eperimets We preset results with the 4 4 H264/AVC blck trasfrm [18] ad with the fidelity-rage etesi (FREt) blck trasfrm kerel [19] i rder t cver tw differet trasfrm sizes that are used i practice Fr the 2D cvluti case, we preset results with ad 6 6 Gaussia kerels with their cefficiets apprimated by FXP represetati with fractial part set t 8 s ad 6 s, respectively, with the fial results ruded t 8- itegers fr display purpses The selecti f the

17 IEEE Trasactis Image Prcessig, t appear i umber f s fr the fractial part f the FXP represetati esured that SNR abve 58dB was btaied fr all ur filterig eperimets i cmparis t the results btaied with the flatig-pit represetati f the filter kerels The small kerel is applied the QCIF ctet i the lw-ed prfile ad the large e the CIF ctet i the maistream prfile We als perfrmed a eperimet f blck crss-crrelati usig radm image blcks f 8 8 piels as kerel T cv fr the tw prfiles The results are shw i Figure 5-Figure 7, where we als reprt the umber f packed blcks (M ) achieved by the icremetal apprach fllwig (8) ad (9) The crrespdig average SNR results are give i Table 1 Visual eamples f utputs f the Gaussia filterig at differet precisis are give i Figure 8 Results epsiti: Fr the results f the icremetal apprach, istead f isertig each plae separately i the icremetal cmputati, we iserted grups f plaes tgether fllwig the patter {3,3,2}, ie the three mst sigificat plaes, fllwed by the 3 itermediate plaes, fllwed by the tw least-sigificat plaes Per vide frame, this prvides fr three quality-drive termiati pits fr the algrithm s eecuti, which are idicated by the termiatig plaes f the figures Cversely, the cvetial (-icremetal) apprach was eecuted three times, each time usig the surce precisi idicated by the termiatig plaes i the figures Eve thugh the prpsed icremetal apprach ca als termiate at arrary pits i-betwee icremet layers, we d t demstrate this i the results f Figure 5-Figure 7 sice the cvetial apprach cat prvide fr arrary termiati Istead, this feature is eplred i detail i Secti VII Cmpariss perfrmed: I rder t eamie the impact f the utilized umerical represetati, Figure 5-Figure 7 shw eecuti time results fr bth cvetial ad icremetal appraches whe usig flatig-pit ad iteger represetati The ly ecepti is i Figure 5 (trasfrm decmpsiti), where Secti III demstrated [via (17)] that iteger represetatis are impractical whe the prcessig kerel has egative cefficiets I additi, i rder t demstrate the impact f usig packed prcessig, Figure 5-Figure 7 iclude the eecuti time required fr packig ad upackig (withut prcessig) This time is icluded withi the reprted results fr the icremetal appraches We als preset the perfrmace f the icremetal apprach whe packig is t used, ie each icremet f each blck is cmputed separately

18 IEEE Trasactis Image Prcessig, t appear i Eecuti Time (ms) blck trasfrm (Maistream, M=5) Cvetial (it) Cvetial (flat) Icremetal (flat) Packig/Upackig Icremetal, packig Eecuti Time (ms) trasfrm (Lw-ed, M=5) Cvetial (it) Cvetial (flat) Icremetal (flat) Packig/Upackig Icremetal, packig 5 1 Eecuti Time (ms) Termiatig Bitplae 1616 blck trasfrm (Maistream, M=2) Cvetial (it) Cvetial (flat) Icremetal (flat) Packig/Upackig Icremetal, packig (a) Eecuti Time (ms) Termiatig Bitplae 1616 trasfrm (Lw-ed, M=2) Cvetial (it) Icremetal (flat) Cvetial (flat) Packig/Upackig Icremetal, packig 5 2 Termiatig Bitplae 5 2 Termiatig Bitplae (b) Figure 5 Trasfrm decmpsiti results; (a) 4 4 AVC trasfrm ; (b) FREt kerel Eecuti Time (ms) [Maistream,M={3 (it), 5 (flat)}] Cvetial (it) Icremetal (it) Cvetial (flat) Icremetal (flat) Packig/Upackig Icremetal, packig Eecuti Time (ms) [Lw-ed, M={3(it), 5(flat)}] Cvetial (it) Icremetal (it) Cvetial (flat) Icremetal (flat) Packig/Upackig Icremetal, packig Termiatig Bitplae 5 2 Termiatig Bitplae Figure 6 2D cvluti results with (maistream prfile) ad 6 6 (lw-ed prfile) Gaussia kerels apprimated with fied-pit represetati

19 IEEE Trasactis Image Prcessig, t appear i Eecuti Time (ms) blck [Maistream,M={2(it),4(flat)}] Cvetial (it) Icremetal (it) Cvetial (flat) Icremetal (flat) Packig/Upackig Icremetal, packig Eecuti Time (ms) blck [Lw-ed, M={2(it),4(flat)}] Cvetial (it) Icremetal (it) Cvetial (flat) Icremetal (flat) Packig/Upackig Icremetal, packig Termiatig Bitplae Figure 7 Blck crss-crrelati results 5 2 Termiatig Bitplae Termiatig Trasfrm Decmpsiti SNR (db) 2D Filterig SNR (db) Bitplae Gaussia 8 8crss-crrelati = = Table 1 Average sigal-t-ise rati fr the termiatig plaes f the maistream-prfile eperimets f Figure 5-Figure 7 SNR was ifiity fr all cases whe = Bth cvetial ad icremetal algrithms achieved idetical SNR fr each termiatig plae Figure 8 Represetative utput frame fr termiatig the cmputati at = {5, 2, } plaes (shw frm left t right) fr the Gaussia filterig Aalysis f eecuti efficiecy: The eperimets summarized i Figure 5-Figure 7 demstrate that the 32- iteger represetati eecutes faster tha duble-precisi flatig-pit i the lw-ed prfile The maistream prfile ehis the reverse behavir The tw prfiles aalyzed lead t the fllwig geeric rules fr the prpsed apprach: (i) Represetatis with larger width are advatageus fr the prpsed apprach because they icrease the packig capability, as shw i the results f Figure 6 ad Figure 7 (ii) Use f packig is always beeficial fr the prpsed apprach; icremetal prcessig withut packig is csistetly fud t ru slwer i all eperimets (iii) Whe the packig capability (M ) is lwer r equal t the umber f termiatig plaes, the

20 IEEE Trasactis Image Prcessig, t appear i 21 2 prpsed apprach teds t be iefficiet This is particularly evidet i the lw-ed prfile results f Figure 5(b) Cversely, if M is high, the prpsed apprach becmes very efficiet, uless if it uses a represetati that is t fast i the implemetati hardware (eg lw-ed prfile f Figure 6 with flatig-pit represetati) (iv) Whe the packig/upackig cst requires mre tha 3% f the eecuti time f the cvetial (-icremetal) apprach, the prpsed apprach becmes iefficiet [eg lw-ed prfile f Figure 5(a)] The ecepti t this rule is whe high packig capability is achieved usig a fast umerical represetati i the utilized hardware, as see i the maistream prfile f Figure 5(a) (v) The average eecuti time f the prpsed apprach is icreasig liearly whe the surce is prcessed with icreased precisi (lwer termiatig plaes) This ctrasts with the cvetial apprach that requires cstat eecuti time regardless f the iput precisi Oce tw icremets have bee prcessed, this feature ca be used t establish the average eecuti time f subsequet icremets f the prpsed apprach These five rules ecapsulate all ur eperimetal bservatis They als frm useful guidelies fr decidig if ad hw t deply the prpsed apprach: which umerical represetati t use, hw may termiatig plaes are pssible withut sigificat lss i efficiecy, whether the algrithm is t cmple eugh t utweigh the cst f packig ad upackig, are all factrs that affect the deplymet f the prpsed apprach Aalysis f visual quality: Idetical SNR results were btaied fr bth cvetial ad icremetal algrithms i all cases (Table 1) Imprtatly, SNR per frame is mtically icreased whe prcessig mre icremets (lwer termiatig plaes) A eample is give i Figure 9(a) by ivertig the results f the 4 4 trasfrm decmpsiti back t the image dmai ad cmparig with the rigial vide frames (sice the trasfrm is lssless at full precisi) Sice SNR cmpariss may t reflect the visual distrtis caused by termiatig the prcessig t higher plaes, we have als perfrmed tests with the structural similarity ide measure (SSIM) f Wag et al [23] usig the related Matlab surce cde 6 with the suggested parameter settigs We used the Y-frames f each sequece fr this purpse ad prvide a eample i Figure 9(b) fr the trasfrm decmpsiti Ideed, the cmparis betwee Figure 9 (a) ad 6 available lie at

21 IEEE Trasactis Image Prcessig, t appear i (b) shws that eve thugh a sigificat drp ccurs i SNR, the utput results are visually meaigful sice the mea SSIM remais arud 8 Frema (CIF) 4 1 Frema (CIF) SNR (db) Termiatig plae =5 Termiatig plae =2 Mea SSIM Termiatig plae =5 Termiatig plae = Frame (a) Frame Figure 9 Frame-by-frame cmparis fr the recstructi f the icremetally-cmputed 4 4 trasfrm decmpsiti f Figure 5(a); (a) SNR cmparis; (b) MSSIM cmparis Oly the first 1 frames are shw Fr termiatig plae = SNR is ifiite ad the MSSIM is e As a fial remark, it is imprtat t emphasize that the icremetal apprach prduces all eecuti-time vs distrti measuremets via e sigle eecuti I ther wrds, if, fr ay frame, the cmputati is termiated arrarily at a give pit by a task scheduler, the results based the already cmputed plaes f that frame are readily available i the prgram s allcated memry B Icremetal Blck Matchig Eperimets The average eecuti times btaied fr the blck matchig algrithms are shw i Figure 1 The crrespdig PSNR results are shw i Table 2 We preset the case f C= W = 16 fr bth prfiles The cvetial apprach is usig SAD-based matchig i rder t crrespd t the cmm full-search algrithm fud i the literature We als iclude the prpsed icremetal blck matchig scheme withut the use f packig fr cmparis purpses Similar t the previus case, istead f always isertig idividual plaes, we iserted the iput-image plaes fllwig the patter {3,3,2} (as idicated by the termiatig plaes f Figure 1) The PSNR results f Table 2 demstrate that the lg-search perfrmed fr the first termiatig biplae ( = 5 ) prvides sigificatly iferir predicti result fr the icremetal methd as cmpared t the cvetial apprach that perfrms full search (apprimately 6dB lss i perfrmace) Hwever, the predicti quality f the icremetal algrithm appraches the cvetial apprach ce mre plaes are prcessed ad the spiral search refies the best match lcati fud per blck I particular, ver the (b)

22 IEEE Trasactis Image Prcessig, t appear i larger rage f vide ctet tested (15 frames frm 5 sequeces), icremetal blck matchig leads t ly 2dB lss f predicti efficiecy at full precisi ( = ) We used W spiral= 9 i the maistream prfile ad W spiral= 8 i the lw-ed prfile I additi, sice the perfrmace seems t saturate whe < 2, the prpsed apprach ca termiate the cmputati earlier ad achieve ear real-time perfrmace, smethig that the cvetial apprach cat take advatage f, sice its eecuti time des t scale dw with decreased precisi Althugh the results f Figure 1 ca be viewed as a fast blck matchig algrithm icurrig sme lss i predicti perfrmace, this is t the velty f ur prpsal; istead, ur apprach presets successively-refied precisi f blck matchig with additial cmputati as mre plaes are prcessed, withut the eed t re-cmpute the result fr each ew icremet This eables the arrary termiati f blck matchig per frame whe delay cstraits are met (r whe resurces suddely becme uavailable) ad retaiig the vectrs f all blcks with the already-cmputed precisi blck matchig (Maistream) blck matchig (Lw ed) Eecuti Time (ms) Termiatig Bitplae Cvetial Icremetal Icremetal, packig Eecuti Time (ms) Termiatig Bitplae Cvetial Icremetal Icremetal, packig Figure 1 Blck matchig results Termiatig Maistream prfile PSNR (db) Lw-ed prfile PSNR (db) Bitplae Icremetal Cvetial Icremetal Cvetial = = = Table 2 Average peak-sigal-t-ise rati fr the termiatig plaes f the eperimets f Figure 1 VII APPLICATIONS: REGION-OF-INTEREST COMPUTATION, SCHEDULING AND ENERGY-DISTORTION TRADEOFFS I this secti, we eplit the icremetal ad scalable ature f the prpsed icremetal cmputati i rder t shw its usefuless i applicatis We first preset a simple eample f hw e ca use the

23 IEEE Trasactis Image Prcessig, t appear i prpsed framewrk fr regi-f-iterest cmputati Subsecti B presets results with a real-time schedulig framewrk, while Subsecti C presets idicative results fr the eergy-distrti tradeffs eabled by the prpsed sftware-based icremetal cmputati f image prcessig the ultra lw-pwer -laptp Sice the last tw applicati eamples use multi-prcess eecuti, the reprted timig measuremets therei iclude bth the cmputati time as well as all I/O time frm/t the disk A Regi-f-Iterest based Icremetal Cmputati f Image Prcessig Tasks The prpsed apprach ca selectively refie parts f the cmputati fr a give iput vide depedig a preselected regi-f-iterest (ROI) mask T demstrate this, we selected the Silet sequece that ivlves a sig-laguage preseter at a static lcati i each frame ad defied the arrary ROI mask shw i Figure 11 that fcuses the preseters face ad hads regi The 44 AVC blck trasfrm decmpsiti was used as a idicative prcessig algrithm (ruig the maistream prfile) The decmpsiti ccurred prgressively fr each termiatig plae {5,2,} withi the ROI Hwever, the decmpsiti utside f the ROI termiated at = 5 (first icremet ly) The average eecuti times per frame were: 5ms fr = 5, 6ms fr = 2 ad 7ms fr = Icremetal cmputati withut the ROI required 5ms, 1ms ad 16ms, respectively Cvetial ( icremetal) cmputati required 15ms fr all cases sice the eecuti time des t scale dw with decreased precisi Idicative visual results f this prcess are shw i Figure 11 by recstructig the vide frm each calculated decmpsiti Figure 11 ROI-based icremetal trasfrm decmpsiti A eample frame with termiatig plaes 5, 2, is shw (frm left t right)

24 IEEE Trasactis Image Prcessig, t appear i B Time-drive Cmputati f Image Prcessig Tasks Cvetial real-time sftware fr image prcessig tasks perates uder wrst-case assumptis, eg see [5] Here, we wat t ivestigate what happes whe schedulig deadlies d t cmply with the wrst case T this ed, we csider the sceari where, fr each vide frame, the image prcessig task f iterest is ctrlled by a scheduler (timer), which termiates the task after the scheduled time per vide frame elapses Whe the termiati sigal is received, the task immediately prvides the already cmputed results fr the iput frame, befre prceedig t the et vide frame We illustrate this apprach i Figure 12 I rder t implemet this desig, we have used the crss-platfrm OpeMP framewrk [24] where tw idepedet threads (timer ad mai thread) are ccurretly eecuted The tw threads share the cmm memry elemet flag_it t realize the sigalig: whe flag_it is set t true by the timer thread, the applicati thread termiates the prcessig f the curret frame ad resets flag_it t false Scheduler Timer Thread Thread Cvetial Thread Icremetal Thread Set Time Read Frame Read Frame Start Timer stp sigal Prcessig Read Bitplae Packig flag_it = true stp sigal restart sigal Write Frame Restart Timer stp sigal Prcessig & Upackig & Icremetig Waitfr restart sigal restart sigal yes flag_it Set flat_it = false Write Frame yes Last Bitplae? restart sigal Restart Timer Set flat_it = false Figure 12 Time-drive cmputati f image prcessig tasks The timer thread seds the stp sigal t the applicati thread i rder t termiate their eecuti fr each frame The applicati thread iitiates the timer thread by the restart sigal The sigalig is achieved via checkig ad settig/resettig flag_it

25 IEEE Trasactis Image Prcessig, t appear i I ur first eperimet, the termiati sigal is geerated by the timer thread usig a average value A with D% f variability arud the average value Tw cases are csidered: (i) regular-variability schedulig, where A=1% f the average frame cmpleti time fr each task ad D=3% f A, ad (ii) aggressive-variability schedulig, where A=8% f the average frame cmpleti time fr each task ad D=5% f A I rder t reprt results fr bth cvetial ad icremetal versis f the algrithms, we measure tw aspects: (i) the percetage f ucvered frames; these are frames with areas withi them that have t bee prcessed (cvered) at all (ie areas with decmpsiti r filterig, r blck matchig fr sme blcks); (ii) the percetage f fully-cmpleted frames; these are fully-cvered frames ad with the result cmputed at full precisi Naturally, fr ptimal perfrmace, the first percetage shuld be as clse t zer as pssible, while the secd shuld be as clse t 1% as pssible The results are give i Table 3 Schedulig Type Trasfrm Decmpsiti Regular-variability (A=1% f each methd, D=3%) Aggressive-variability (A=8% f each methd, D=5%) Measuremet Ucvered Fully-cmpleted Ucvered Fully-cmpleted Cvetial 339% 661% 4299% 571% Icremetal 19% 916% 561% 8186% 2D Filterig Measuremet Ucvered Fully-cmpleted Ucvered Fully-cmpleted Cvetial 441% 9559% 631% 9369% Icremetal 6% 9987% 56% 9759% Blck Matchig Measuremet Ucvered Fully-cmpleted Ucvered Fully-cmpleted Cvetial 7524% 2476% 799% 291% Icremetal 1% 7685% 188% 6758% Table 3 Percetage f ucvered ad fully-cmpleted frames fr 4 4 ad iteger blck trasfrms (tp part), 8 8 crss-crrelati ad cvluti (middle part), 8 8 ad blck matchig (bttm) The prpsed apprach als has a itermediate case, which is cvered frames but t fully-cmpleted, ie t all icremets have bee cmputed Represetative visual eamples f the artifacts bserved are give i Figure 13 Pst-prcessig with errr ccealmet culd ptetially reduce the distrti caused by ucvered areas i bth cvetial ad icremetal prcessig at the cst f additial cmpleity Hwever, the results f Table 3 shw that the prpsed icremetal apprach rarely requires this, sice the

26 IEEE Trasactis Image Prcessig, t appear i percetage f ucvered frames remais well belw 1% i all but tw eperimets This is a rder f magitude differece with the cvetial apprach that typically leaves mre tha 1% f the frames with ucvered areas whe peratig uder schedulig This demstrates that, ulike the cvetial implemetatis, the prpsed apprach btais reasable quality eve whe the scheduler des t prvide fr the wrst-case It is iterestig t bserve that, apart frm this advatage, the prpsed methd als prvides sigificatly-higher percetage f fully-cmpleted frames uder bth schedulig prvisis We bserved that the eecuti time f the prpsed icremetal apprach fluctuates less acrss differet frames i cmparis t the cvetial apprach This allws fr successful cmpleti f mre frames fr this methd whe the schedulig time fluctuates arud the mea eecuti time Figure 13 Visual eample f vide frame; frm left t right: fully-cmpleted frame, ucvered frame, cvered frame but t fully cmpleted (ie the result is t cmputed t full precisi) I a secd schedulig eperimet, we wat t eplre the thrughput/quality tradeffs eabled by the prpsed apprach via eecuti with fied deadlie per frame Figure 14(a) shws typical SNR versus thrughput results (i terms f fps) btaied with the icremetal 2D cvluti with the Gaussia mask (maistream prfile) We gradually decreased the schedulig deadlie (withut variability) frm A=31ms t A=19ms per frame 7, which leads t icreased thrughput, frm 323fps t 526fps respectively, with a crrespdig drp i SNR frm ifiity (full precisi) t 1936dB Represetative visual results are shw i Figure 8: frm left t right the displayed frames represet typical utputs frm highest fps t lwest fps, ie frm stppig at icremet layer = 5 t stppig at =, respectively It is imprtat t remark that, fr all results reprted i Figure 14, ucvered frames were prduced, ie there were sudde blaks i the filtered vide apart frm the gradual quality reducti This 7 Ntice that the schedulig deadlie icludes I/O time, therefre the schedulig deadlies are higher tha the timig measuremets f Figure 6 that are reprtig ly the average cmputati time per frame

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