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WO2025054297A1 - Adaptive loop filter for video coding - Google Patents

Adaptive loop filter for video coding Download PDF

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Publication number
WO2025054297A1
WO2025054297A1 PCT/US2024/045348 US2024045348W WO2025054297A1 WO 2025054297 A1 WO2025054297 A1 WO 2025054297A1 US 2024045348 W US2024045348 W US 2024045348W WO 2025054297 A1 WO2025054297 A1 WO 2025054297A1
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WIPO (PCT)
Prior art keywords
rane
aeas
ane
zeroer
veo
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Application number
PCT/US2024/045348
Other languages
French (fr)
Inventor
Che-Wei Kuo
Xiaoyu XIU
Wei Chen
Hong-Jheng Jhu
Ning Yan
Changyue MA
Xianglin Wang
Qi Huang
Bing Yu
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Dajia Internet Information Technology Co Ltd
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Beijing Dajia Internet Information Technology Co Ltd
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Publication of WO2025054297A1 publication Critical patent/WO2025054297A1/en
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Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/80—Details of filtering operations specially adapted for video compression, e.g. for pixel interpolation
    • H04N19/82—Details of filtering operations specially adapted for video compression, e.g. for pixel interpolation involving filtering within a prediction loop
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
    • H04N19/117—Filters, e.g. for pre-processing or post-processing
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
    • H04N19/17—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object
    • H04N19/176—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object the region being a block, e.g. a macroblock
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
    • H04N19/186—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being a colour or a chrominance component
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/70—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals characterised by syntax aspects related to video coding, e.g. related to compression standards
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/90—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using coding techniques not provided for in groups H04N19/10-H04N19/85, e.g. fractals
    • H04N19/98—Adaptive-dynamic-range coding [ADRC]

Definitions

  • veoocsn accorance w somememnen aano exnesm oare sresseenmosr encon anecon .s aocaramusran an exemar veocosure.
  • somememenaons oe encoern accorance w somememen.as aocraesreanmsucsorsaurne.
  • escron, c saomus oeeusrreaseenascoseuree,rm asn “rse,” ac “csoemconan,”n anee usene snus oecs, an no useoescre an secc orer rawns are useo unersooaeaa usens wa maenercane une or seuence.
  • econ veoocsnaraen accorance w somear ssem or encon an scosure.s sownn.,e shimcues a smemenaons oeresen encoes veoaaoeecoe a aaerme a ourceevce aeneraes an aneesnaonevce ma comrse a esnaonevce.e sourceevce cou servers, server c n o a we vare o eecroncevces,ncunooxes, aeeovmsuonesr,s, caemseroas, orsaao coevmceuse,rs,aae m ceomauears,e srms,a sunnyoneasm, se- consoes, veo sreamnevce, oree.n somememen
  • eevvccee m maanecu accee asnse o a vaerees onasonruevece oroc vaa an accnesusenearaa sceo.e sorae as aarrve,u-rascs, aersaess s,omacscea-rane mea suc - s,as memor, voae or non-voae memor, or an oer su emores meaor sorne encoe veoaa.n aurer exame,e soraea sorae corresono ae server or anoernermeae soraeev aeevce ma aaenerae e sourceevce.eesnaonevcecea maoe encoe veo rome soraeevce va sreamn orownoa ma accesse sore veoa
  • croamnsmr see or.ne oer m enocroe seam vee aorraasa, moa comrse a seuence ocures, eac o wc ma croman r or oom r exame,uma onor monocromeuma anwo or convenence an orreen,ue, an ren asonown as oman.
  • vronmens currennown oreveoene w somem.emse aocaramusran an exemar veo encoern accorance erormn naonsescreneresen acaon.
  • soschreibra usen aonoeeocner resen acaons nomeoe emomensescreeaore ecnue,e mae aeo a suaon were an oses s eren, annsea,e acaon croma comonenswc ma eeceor an o auma comonen anwo oman or, an n reroemseann,or c aonrn roman, anon o acaon asescre aove a nvenence o noaon anermnoons comonenso mo sa an ccocmoronneno aanse o oner oe seeecumea o cosme.onuern aenr, seowuo c asroomae ornee.: .
  • curosmraae comao anenrss co am seocnoenn m coemnoonneene mreenn monae an oeuma comonen anewo comonen anewo croma comonens, eeren mae an oer oeuma remann one oeuma comone an ar comonen menoneeren mae aooers mae o n anewo croma comonens.n some exames,en- oe .me vee,o an encoeerecoe veooc maerecrove e summer un or maeve amon one maaeeorm o axe orrorammaearware e veoaa memo or more oeusraexe orrorammaearware uns.
  • vesoarocosn,n maareronnss accornoreene sn srucures suc as aua or oer srucure assocae w e veoaa.e veorames or mae reare-ree mensona arra or marx o sames w same vaues. same as awo- reerreo as axe or ae.
  • numer o samesnorzona an maurerearro anxees oe veoocene a sze oe veooc.e veooc ocs,or ex no one or moreocarons or su-ocswc maorm aan ree aroanmne, orerave usn aronn,nar-ree aronn orre- “veooc” as useere ann m caomen aaoornone,reno.arc suoaur a reeca nnoeuarasuaeree orrm no “n-o scu”ar oer ornee.: .
  • voreoon,o oc a mraamee o orr a corrcesuroen.o a reoerennce,reeor enxame,,o a, a anrecon,neoc o or aransormn anor mae or corresono a corresonnoc, e.. a r oc , aonoc , areconoc o onree a su-oc.
  • mo ocess oeneran moon vecors sacemen o a veooc wn a curren on vecor,or exame, mancaee wn a reerencerame rea veorame orcure reaveo arecveoc reeermneaern maveoe currenocen coe wne currenrame.enra un maeermnees vencaoers v, e.eo.,raomces vencores, seoruennrcae as coranmesn o ar manrnaemre ssm.aer ornee.: .
  • vareo veceooerecoenrcn accorance memor
  • an enroecon un areconrocessn u ues a veoaa un, annverseransormrocessn n, annverseuanzaon rocessn un urerncues a mo un, a summer, an a .erecon annra un.e veoe on comensaon un, annrarecon un, anoe enconr coer maerorm aeconrocessenera recroca . ocessescre aove w resecoe veo encoern connecon w moon.
  • oaear c moemmoornens m oae sore veoaa suc as an encoe veosream, aa memor mae oane,or veoecoer.
  • veoaa sorene veo source suc as exame,rome soraeevce,rom aoca veo accessn sca a caamae srao,ra vae m werea oer.
  • a reresens veoocs o an encoe v es an encoe veosream ecoer ma receive eorame an assocae snax eemens.e veo e en ee snax eemens ae veorameeve anore veooceve. uaroecon un oe veoecoer enroecoesesreamoenerae eemnenzes.
  • recveocsn oeres orames en e coe rame orornra coe un maeneraereconaaor rarecon un oereconrocessn snaenrarecon mo a veooc oe curren veoramease on a rame. e an reerenceaaromrevousecoeocs oe curren ornee.: .
  • conreeoc aronn sox u acco aec sve o n a sa arem -reeres ee. arrormoannnce,,erena vr-eore eencaoreron ma recursveerormree comnaonereo one conreeocs oe a n,ua-reearonn or a secen.,ex srsvennovoure smeaerns,o e samcaers.
  • oc sze ox.moneour sm avn a s aers an are eacvenoour s o oxx ococ sz se.ze.ewox s an are eacurervenoour earonroce .
  • an rcuresavnree substituted by a ma comrse a sneuma, s, annax srrucocuresso urseumoa,re, ace.e veo encoer maeneraerecve e veo encoer mnrs o eac oe. recveocsor a.
  • ssocae w mores o aere, vee vo eenoco enecroerene mraaeserneeraceve auummaa, res, anrocsor one or suracne’srecveumaocsroms ornauma counaoocore samene’suma resuaocncaes aerenceewee c suca eac 'srecveumaocs an a corresonn sa n auma samen one oe mar,e veo encoer maenerae amene's ornauma conoc.
  • nse veo encoer,e veoecoer reconsrucerames oe veoaaa romesream.e veoecoer ma esream.erocess o r se aeasnar one snax eemens oanerom rocesseror econsrucne veoaasenera recrocaoe enconnverserame e veo encoer.or exame,e veoecoer maerorm resuaoncsosr amssso ocnaee w coeceens oocse a csusorrcenae w.e vse oo ae ccuorreern asoo re reccoonnsruc err ceonnooc cosrr oesoen cunrre snames o aen sruc
  • oeer ornee . reracmones.rucne conocsor eac o arame, veoecoer ma reconsruce.e.,nra-ramse noree acoove, veo con aceves veo comresson usnrmarwo moes,s no nornra-recon anner-ramereconorner-recon.wo meoesa,ner- coraumeer reeacroen a cson ereurensr ma-orraemoeree ccoonn or e acern moe.eweene reconecause oe use o moon vecorsorre cannra-rame reerence v cn a curren veoocrom a oc szeoueo r woc.
  • a moon vecor can eo encoer ane a curren usnoseoena can aesasonown as a “meres”or s anoremora co-o ae moon vecors assocae w saa neorn moon vecor canaes acsa ae moosn o veceo crurrreencor aonree cnu srereencn. one moemne sro,romerees ornee.: .
  • suc ase oer nros overa oeraons oe Chevronmenma aons assocae wsa,aa acuson,aa communcaons, anoereorrmoce ass onr s.omee orocees ssoersn mea aonvce-ueesc one or morerocessorso execuensrucons mancue one or more mou re meos.oreover,erocessor oer comonens esaacaeeneraconeweenerocessor an sne c ma.erocessor mae aenrarocessnn , a mcrorocessor, a ec mneme,o arracas cornoceussrenon , oree.
  • a cncne wraecee,eweenerocessor anererancueu are nomeo, aomeuon, a sa uons, anee.euons manerace cane coue w an enc r scanuon, an a so scanuon.
  • scosure reasessoc moseureoss a rnea aeaora vo usee oor a n cn morneco ov anner.
  • nneers as one eoar was sume nsue oecrca anecroncs enera nernaona sanaror acaons.e sanars one new eceon veo con sanaror veo acaon amn a surassne con enc- oaeseaneesnernaona sanar .narc , ae- meen, sanar.
  • aenreoraxmonae veo con-ra saen saavrn. or euvaene.rceuoauuae coma sraenaorreror sncan conmrovemensansreecessor,eres ev oves ecenc cane aceve w aona conoos o encea sueror con an saree exoraon wor o new conveercno.ase ona,o sanarzaon.neoneoxoraoneam oesoruure veo con an oen sncan su o ava wnacseoermcenoonecs.a co - susana enancemen o con ecenc.ne reerence u enae moe was manane e neran seve soware caeon exoraon e es
  • ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇
  • ane rao ⁇ .3 ⁇ . , ⁇ / , ⁇ .3,/!6 ns mn ⁇ . , ⁇ /, are e:o ⁇ 345 eac ⁇ ⁇ o ⁇ ⁇ e 3 r !6 w an ⁇ 3 o 45 re ⁇ s ⁇ o ⁇ ⁇ s 3!6 ' an e: ⁇ . ⁇ , ⁇ / ' ⁇ .,/ ⁇ *&,*' ' ,s seo.
  • ..onn areeonooceevuemaeraaon aaaon.uma c ⁇ oc-eveer aaaon, suors-eveer cacuaeore area caone use s aces.er s cean c aascou uasee oore curren sce or one oeer ses eacuma , wcerrome co ne oe oneraneer ses. n eermne e cass cac sener se soue aeo eac ⁇ oc,s roma uses onuae-evne euaero anaaoorsoc.
  • comonensn a sce.ac n.o ers cane useor croma ..naxesn can seec one oeseers.
  • ncue uoer c crooemacenesr an cnnces are carren s.n canncueor eac oeusm aan ca osnsees.umaassesera sven we u samoenexe ⁇ rs. snnex ⁇ ? s aso mern eren casses,e numer os ? aree sameer.
  • oere aers ses oers ⁇ ⁇ u amna s ⁇ ame,reeeren cassers ⁇ & , ⁇ ' an ⁇ anreeerenraneor cass & ers ' ⁇ an ⁇ ⁇ a ⁇ re use.es ⁇ & an ⁇ ' conanxeers, w coecens se ⁇ s useor ave & n same ' . s o e e c c e ens a o cass ersn ⁇ are snae.cerrom a ⁇ ! ⁇ ! assneos same usn casser . ! . .
  • sa wmeree ⁇ were ⁇ ⁇ e ⁇ wee,n,e ⁇ n ⁇ e ⁇ rm,ease saem cee ⁇ e ⁇ r,e ⁇ n ⁇ an curren s,ame ⁇ ⁇ , ⁇ , !,0 an curren ceeween a neorn sameeore rane o “”n ⁇ sa .mee ⁇ e ⁇ , ⁇ .ere,e vaue rane o “”n !,0 serenrome vaue resen !,0 r coecens ⁇ !
  • w.oaonaraens are cacuae coverseare ⁇ ocs useor casser eraens wn a ⁇ wnowa ⁇ wnows useor casser ⁇ & ane sum o sameraens wn a aonar s ⁇ ' an ⁇ ! . ! e s ! ums o !
  • oresrw.ser,es ⁇ osse ma.,.,,,., are use.e s !xmumneer suca ⁇ .,/ ⁇ E ! F re -n s !.e s ! ren ! ⁇ ! ⁇ ! ⁇ *',* ,.e.,orzo o na er v w er se c , a ⁇ e s es a e re ma o x m m n u a m n, ne e e ⁇ r suca ⁇ *',* ⁇ -.
  • vaue assascea conasnsers exene w ar casserase onuma resua same nes.ouronr eacx wxnouwmas coc,e sum o asoue vaues oe resua samesn a caasscuae, ane cassnexserve as: e vaue o cassxsne ranx sumsamee –. or eacumaer sen.e oo, same asn -..e casser usaes snae . n ..
  • ocaoneer a weanmon sae.s seenn.,or a co-soews w oeeum evaen numer e croma sames areorzona e r e coumns oeuma sames an vercanersaeween c soaemcees,nse caevnee ar oreaeerameornee os aenxe w c ao croma sameocaon.
  • coecens snce no smmer consran mareo reuar o s are enorce.owever,womaons are enorce: resure,s oenrve seven ne ourae e,e sum o coece cnose neceeno vaeu sess reureoe zero.s a e coecen aocaon ⁇ , ⁇ serve naenesream, an e asoue vaue o ? co ? ecenss re asrceeecooer.
  • e cane enae a a seuenceev eac croma aso enaeore seuence.
  • c e can one enae suma s enae ae corr ane enae acure an sceeve on ..neuereu esonneve.
  • anwo sasescrecno snecon..,euma ane cromaneuerounares areournneumereso,u rnesaercesvea, a areov aeneeor cournomaar a.ore:: cromaorma,s resus cromaormas,e crom numa.owever,or:: an::: s a aneumaneuerounares are no ane w eac oer.
  • amrovneser cooremacnceen.s.ccoer snao euaon sameerences are ceeore ne orn same, ⁇ ⁇ ⁇ , ⁇ ⁇ m , a e ne e c re e n n c e e r sam sc e a , ⁇ ⁇ m ⁇ , ⁇ e ⁇ an . s n on e smar oe asusraenuaon ! oec ! on..
  • . onace sa omeerence maaves own coecesn.s, w aeas one coecen ae .eu coevs cee ra en,anrose maar. ar ssareeowe saemoew coeerocunen asn.n a soomvee exea umeers, sna aona coecen oun usee same . mavx,nenno.
  • sar e aona coecens snaeor eac same a rccorenoor a s sameerencesa are ousee rane.ncan ome exames,vnnoarsseermne snan annex cacnorenmn,o ma sxom,ee exnamexeos, raneeo mrea anane cane coereceennes,.nu sameoweerrenocuesn a,reev oeernaros aarosv,e onee uarers woun a ranemn, max, onearseowe coecensoevears.e se n.erocessor ma a eren coecenore o oe encoer,erocessor ma sna aona erence, orc scoarrenoou r a sosm sa
  • exames aove mae soem seam exea cmooers c,ome soanmen,e suce aresnuces aneareer samene ccorno some exames,e sameerenma an croma.
  • sameerences are u vaues are reresene as sameerences,e e aeas one n comue usn aeas one neorn same an aareer same, oc, aneareorn sames oanerom aeas one neornoc oe curren n one oer moreer e saxmamee cso,rreesonsoe currenoc.
  • oe aeas one neo sameerences are comue usn coor comonens same anerocesrn same o a samen as a coor comonen oeareer resonseoe s sor ma, ae se oeecoer,urererormoown acs:n neorn sameerencesen comue usnuma comonens oe aeas one comonen oameea, an,ase one sameerences, auma ero auma usnrosm,a reer same or,n resonseoe sameerencesen comue erence comonens oe aeas one neorn same, an,ase one same n a onero omr maore exero aroma comonen oeareer same.
  • oe aeas ames,e sameerences are comue usn coor comonens er same a one neorn same o aerennrom a coor comonen oeare acs:n resnerocessor ma, ae se oeecoer,urererormoown on onseoe sameerencesen comue usnuma comonens oe aeas come noeorn same, an,ase one sameerences, an ero aroma usnnernom oa coemaorneens oer saem aeea osr, onne r neesonsoerno seam same, aeenre,nceassee onn ceom samuee ornee.: .
  • eso,erocessor ma ae se oe encoer,er a reconsruce zeroer coecennone ao ae causrr oenne raonce,.nas seom oen e axa rmesues o, ae rene aeas one non- oane an annverseuanzaon un ann consruceoc mae n one or more exame verseransorm unoe currenoc. a comuaon smaros,eoconer “.e.
  • sameerences are comue usn aeas sene as sameerences,e e aeas one neorn sames oan one neorn same an aareer same, oc, aneareer same corr erom aeas one neornoc oe curren n one or more exames,ees soamnseoeer ceunrcreesnoc.
  • oe aeas one neorn same o a sa are comue usn coor comonens same anerocessor ma, ae semen as a coor comonen oeareer resonseoe sameerenc oe encoer,urerormoown acs:n neorn same, an,esen comue usnuma comonens oe aeas one comonen oeareer saase one sameerences, auma ero auma usnroma comone me or,n resonseoe sameerencesen comue erences, arons oe aeas one neorn same, an,ase one same n one omr maore examereos aroma comonen oeareer same.
  • oe aeas one e sameerences are comue usn coor comonens er same an neerorn same o aerennrom a coor comonen oeare acs:n reso ocessor ma, ae se oe encoer,urererormoown on nseoe sameerencesen comue usnuma comonens oe aeas come noeneno orne saamree, aer sanm,eas oer, onn reseo snamseoeee sraemncees, anerenceseerno a comroumea ornee.: .
  • oes,eers ranneu an vauees s are reresene as sameerences, zeroer coecenncues a econ rane, ane aeas one non- e m ana, ae sare non-zeroer coecen, anne ,erocessor ran se oe encoer, a e sare non-zeroer coecenooers rane, anne s e s aoecmo een as e.x oanme neosn,-zeero aeears c one ranencuesoers rane ane secon a secon non oecenncues ars non-zeroer coecen an enco -zeroer coecen, anne ,erocessor ma, ae se oe er ceor,e aceneorse s neon-zeroer
  • meum comrsn aura orosr aamsos,roorv exeam a neo,nn-raens meomro cromue,r e-rxeeacuaaee soraee ornee.: .
  • anrocoesrs soorrn ansere caommeunenra eenvronmee enncon, moreeorormescnre aove-escre meos ecoe eecon meoescre aove.n one exa e aove or asreamoe e execue erocessor ne schizophrenia envronme,eura ororams ma rome veo encoer n.
  • soorra exea mme,e comuerroramrouc mancuee non-ransor comuer- more sn, an eme s,oumm.
  • aen,nea comrocuesns envronmen maememene w one or s, s, s, conroers, mcrnevces s,rorammaeocevces comonens, o-conroers, mcrorocessors, or oer eecronc n aonr eemroormmnen,e aeroeves a mseoos.
  • resensconsuesres sse ocncanen seaeo oeerwussrea, avne, or aner oe s sees oe meo accornoe resenscosure are nomeoe orer s s oe meo accornoe accornoracca conons.
  • eccaescre aove,u mae cane eresenscosure mae ausne a, comon,n aee oars oeneee o aceco srens ooera mcecao re acucroermenns.o ornee.: .

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  • Engineering & Computer Science (AREA)
  • Multimedia (AREA)
  • Signal Processing (AREA)
  • Respiratory Apparatuses And Protective Means (AREA)

Abstract

Methods for video decoding and encoding, apparatuses and non-transitory computer-readable storage media thereof are provided. One method for video decoding includes: receiving, by a decoder, at least one non-zero filter coefficient; applying, by the decoder, the at least one non-zero filter coefficient to at least one range in a dynamic range of adaptive loop filter (ALF) input values; and filtering, by the decoder, a reconstructed video block corresponding to a current block, based on a result of applying the at least one non-zero filter coefficient to the at least one range.

Description

ornee.: . -aveoo eroreoon caoneresen acaonsase uon an camsroro..rovsona , ,e enore o, wc, ensneco “roraaeveo reoerenceeroorr aeuoroosesn.,”e oneemer s acaoen rereaseensos mcosures reaeo veo con an comresson.ore secca,ooer an cross-ceomoosn aenn a aaaraveuso oonmerrovne c.on ecenc o aave ao oresoa c vomeouser ssu,aoree com au vaerrse o eecroncevces, suc asaeevsons, meaaers, veoamn consoes, smar,oanes c,am vereaos,eecaon recornevces,a sreamnevces, ec.e eecroncevcesransm an receve ore orenecrwnsevces, veo a veoaa across a communcao e communcae ev n newor, anor soreea veoaa on a sorae resoucerc.esu oeoe a somraeeeavncwe, caac oe communcaon newor anme memoro one or more veo con sa vnaeros coenore mas ceom usmeo comresse veoaa accorn con sanar uncae or sore.or exame, veo -censncueersaeeoon ,onxoraonesoe , curexercroueoon c .,vance eoon .,ovn meose on, oree.eo conenera uzesreconnerenn..e, vneero-raea.cone,o cnora-nre acon, oreeaae avanae o reunanc rae, we avon or mnmznemrasaoo cnosmor vesse voeuoaaa.no aorma uses aower e con emcoencme ons a oaevereoseonscerosurero avne c mreos an aaraus onmrovn . oss-comonen aaveooer ccorno ars asec oeresenscosure,eresrove a meo o veo ornee.: . eecoecno,ern,cue ane:a rsec oenven no,n-ze aroecoere cr,o aeecaesn onoe a non-zeroer coecen an, aaveooer nu vaues anern, eeaesco one ranen anamc rane o corresonno a currenoc,ase on a r er, a reconsruce veooc coecenoe a esu o ane aeas one non-zeroer c eas one rane. veo corno a secon asec oeresenscosure,eresrove a meo o e e ennccooner,,nec auenas: s onena nonn-z,ero a enecro coeer, aceeans oon ae noeans-ze ornoe raer coecen an, o aaveooer nu vauesern, e encoer, a recnoen anamc rane corresonno a currenoc,ase a resu o ane aeansruce veooc coecenoe aeas one rane aneneran, e enc s one non-zeroer oern oer, asreamase on a resu cec roerconnsruce veooc. veoecon.e aoa araurs m asaecnc ouee onrees oern morsecorsoucrees,soresre ans aro mvemeor an c aouaerausor one or morerocessors an conureo sorensrucons execu oe rocessors.urermore,e one or moreroces ae e one or more conureoerorme meo sors, uon execuon oensrucons, are or veo enccocorn.neo a aoaurarus a a mscc aeocr n ono cuee ore neeser ons as r mosrceocs.ure,eresrove an aaraus e one or morerocessors an co erocessors an a memor coueo rocessors.urermore,e one onr muorreeoro sceosrseorns,s uruconon exse ecxuecouna oeenesr ounceo or more conureoerorme meo a ns, are ccorno ccornoe secon asec. comuer- a asec oeresenscosure,eresrove a non-ransor execuerea oanee or s mooraree co mmeuuemrroorce sssoorrsn, ca cuosmeueer o-enxee ocur maoensruconsa, wen erorme m re comuerrocessorso cceoro accornoers asec. com no a sx asec oeresenscosure,eresrove a non-ransor execuueer-rea oanee or s mooraree co mmeuuemrroorce sssoorrsn, ca cuosmeueer o-enxee ocuaensruconsa, wen erorme meo accornoe secon ase r more comuerrocessorso ccorno a seven asec oce.resenscosure,eresrove a non- ornee.: . arcacnosronr coomuer-reaae sorae meumor sorn asreamoeecoe e meoransor comcceourrs ern as -roec an. e asec oeresenscosure,eresrove a non- accornoe seconea aaseec s.orae meumor sorn asreamenerae e meo seccaon,e aucscoramea enxamnersaw connsss,e wn wc areencorresoeraen an consue aar os escron, serveo e nscosure an,oeer w e .s axoacnaerramncuessr oaescosure. veoocsn accorance w somememnen aano exnesm oare sresseenmosr encon anecon .s aocaramusran an exemar veocosure. somememenaons oe encoern accorance w somememen.as aocraesreanmsucsorsaurne. an exemar veoecoern accorance w aroneno.ons o mueroueresen arescoocsure.aramsusranow arames recursvememenaons oer veoocs oeren szes an saesn accorance w some .s aoesenscosure. some emomens oecreseanramscoussurrean an exemar veo encoern accorance w some emom.enss o aoecreseanramscoussra.n an exemar veoecoern accorance w resenscosu.s anusraon oure.er saesn accorance w some exames oe exames oe.re.s aecon o susame sameraensn accorance w some accorance w.res somse e anns examucsors eaur s ooe.n oe areseeonmesrccosruanres.ormaon o aamoner saen some exames. ose anreseunsrasconos oure a.n onneer sae usen an n accorance w ornee.: . resenscosu.s anusraon o a arcecure, accorno some exames oeneumaa.re. neosr an::us craroomna o aor rmeaa wveoc caroonm oaere croma same ans suor accorance w some ex ocaone.eusraonsn .s anamusersa oone or aesen-ascosure. resenscosu oner accorno some exames oen accorance w.re. esx aanmuess oraoen ore asener saeor arecon sna oreore a sna exames oe.resesn anscuossurare.on o an ascuosseure. er saen accorance w some accorno so.mems aemaernamaonuss oran a comun envronmen coue w a usernerace, ernn a.ccoranrocue w ex aarmeearraemsesnusscraosunre s.mmerca samean ouma . rou areeas oramseruessernascosure. roose c w scae oeraon sameerencesnoo ana erxesnn accora cnce o wera eoxnam an a oeresenscosure es some exames. os a.ow carusran a meoor veoeconn accorance w meoor ve.oecse o ares noewn a casrcosuurser.an a meoor veo encon corresonnoe scosure. s sownn.n accorance w some exames oeresen areusraeenerenec aec wcom noanwne mraawenns.eaneo soeocwcnmeaemeenaescorns, eoxna,m numeser oo wc mn secceas are seorn orero asssn us non- eren.u varo unersanne suec maerresene suec maer muas aeernraacvcees m waoeu usees we soeuccearnrome scoe o cams ane reseneeren canememene on manes oe eaesc.roonrc exaemvcees, we sueca m vaeeor ornee.: . caaes. escron, c saomus oeeusrreaseenascoseuree,rm asn “rse,” ac “csoemconan,”n anee usene snus oecs, an no useoescre an secc orer rawns are useo unersooaeaa usens wa maenercane une or seuence. soue sucae emomens oeresenscosureesc r an arorae conon, orersesesose sownne accomannrawreeren maememenen .s aocaramusran ann exse omrescreneresenscosure. econ veoocsnaraen accorance w somear ssem or encon an scosure.s sownn.,e ssemncues a smemenaons oeresen encoes veoaaoeecoe a aaerme a ourceevce aeneraes an aneesnaonevce ma comrse a esnaonevce.e sourceevce cou servers, server c n o a we vare o eecroncevces,ncunooxes, aeeovmsuonesr,s, caemseroas, orsaao coevmceuse,rs,aae m ceomauears,e srms,a vreooneasm, se- consoes, veo sreamnevce, oree.n somememenaons,e n eesnaonevce are eue w wreess communcao sourceevce an n somememenaons,eesnaonevce ma rne ccaevaeee esn.oeecoe va an.en ma comrse ane o communcacoone m veoaa evce caae o movne encoe veoaarome sourceevceo eum or evce.n one exame,en ma comrse a communcaon me eesnaon sourceevceoransme encoe veoaarecoeesnaumo enaee me.e encoe veoaa mae mouae accorno a commuonevcen rea a wreess communcaonrooco, anran ncaon sanar, suc as communcaon meum ma comrse an wreesmeoeesnaonevce.e aoreuenc secrum or ss or wre communcaon meum, suc as a meum maor one or morescaransmssonnes.e communcaon newor, or aoma nearwo or a sucac aes-easneer nneew.ore, c soumcmu ansc aaoocna m aereaum ne mwor, a we-area swces,ase saons, or an oer eumena mae u ancue rouers, rome sourceevceoeesnaonevce. seuoacae communcaon ouunernac seome oo aer somraeemeenvaceons.,ues eencuoene v,eeo enacoa mea veeoraansamneer soomra ane ornee.: . eevvccee m maanecu accee asnse o a vaerees onasonruevece oroc vaa an accnesusenearaa sceo.e sorae as aarrve,u-rascs, aersaess s,omacscea-rane mea suc - s,as memor, voae or non-voae memor, or an oer su emores meaor sorne encoe veoaa.n aurer exame,e soraea sorae corresono ae server or anoernermeae soraeev aeevce ma aaenerae e sourceevce.eesnaonevcecea maoe encoe veo rome soraeevce va sreamn orownoa ma accesse sore veoaa comuer caae o sorne encoe veoaa ann.ee server mae ane o esnaonevce.xemare serversncuransmne encoe veoaaoe ranserrooco server,ewor e a we servere..,or a wese, ae eesnaonevce ma accesse enaceorae evces, or aocasrve.ncun a wreess cannee coe veoaarou an sanaraa connecon, e.., auscrerne.., a,reesse - connecon, a wre connecon or accessn encoe ve cae moem, ec., or a comnaon ooas suae aarome so oaa sore on ae server.eransmsson oe encoe veo comnaon oora.eevce mae a sreamnransmsson, aownoaransmsson, or a ane ous suownnernace..,ee v soeuorc seouercvece mancnucuese a a v soeuorc seource, a veo encoer evce, e.., a veo camera, a veo arcve con suc as a veo caurnneraceo receve veorom a annrevous caure veo, a veoeen eneran comue veo conenrover, anor a comuerracs ssemor exame,e vero sraourccesaas a as vee soou carcmee vra oeo, a o sre acu crom sunraveona onc seu scs seources.s one evce aneesnaonevce maorm cameraones or ve m,e sourcememenaonsescreneresen acaon mae aca oones.owever,e an mae aeo eo veo connenera, e ca wreess anor wre acaons. enc ure,re-caure, or comuer-enerae veo mae encoe e veo eo oueru.ne encoe veoaa maeransmerecoeesnaonevce va e so erace oe sourceevce.e encoe veoaa ma asoor aernave orerceo onno aneo sroraaeaecv.cee oourauern acecreascse meaesunraeornnecvucee a m oro oemer anevocres a, ornee.: . croamnsmrsee or.ne oer m enocroe seam vee aorraasa, moa comrse a seuence ocures, eac o wc ma croman r or oom r exame,uma onor monocromeuma anwo or convenence an orreen,ue, an ren asonown as oman. anerms assoca oe no wao enac an seer omnoreoe samne asr aras mcaaon,e rne seormree emo aomens, varaes wereewo croma arras mae reerreo as a suma an croma, reresenaon meon use.e veoa nr, rearess oe acua coor ::,ueresen acaon a maen a cromaorma o::,::,::, or saevceee.sneanonuenvecres no acencm mue aese ncere uno. eu a renceervearce an,or a a veoecoer, an a encoe veoaa overen.e encoe veoaa co moem an recevee rove one soraeevce, mancue a va mmuncae overen, or encoeror use e veoecoe re o snax eemensenerae e veo encue wne encoe vernecone veoaa.uc snax eemens ma sorae meum oaaransme on a communcaon meum, sore on a wc canne s ao, nm oer s nmore eraem o eenn aasoe ans s,erv eveer. cees anna aonn exevece mancueesaevce, communcae weesnaonevce.esrnasaevceas conureo aao a user, an ma comrse an o a vare aevce saseecoe veo sa , aasmasa, anranc omsnaeoveces suc ass aa,ursa e osa or anoer ornusr sean vev arecoe. s, en scuocer as an,e veo,ecoe-r, mara o,erae, ac ocornororear sanars. soue unersooaeresen acaon r exensons o suc enconecon sanar an mae acaeo oer vs nomeo a secc veosenera conemaeae veo encoer eo enconecon sanars. encoe veoaa accorno an o oe sourceevce mae conureo enera conemaea ese curren oruure sanars.mar,s asooecoe veoaa ac e veoecoer oeesnaonevce mae conure e veo enccoorenro a ann oeese curren oruure sanars. vare o suae encoer anorecoer v crecourec,o suecr as e oance o mra moree mmcreomreonceesso arss, an oa a ornee.: . anearrraocsessorss,ss,creeocaco,n sowecarec,narewraaree,rmrcwuasre or ans c,omenaroonrammae enmemenearan soware, an eecroncevce ma sorensrusereo. sowaren a suae, non-ransor comuer-reaae meum an consore arware usn one or morerocessorsoeror execueensruconsn scoseneresenscosure.ac oe veome veo enconecon oeraonsncuen one or more encoers orecoer encoer ane veoecoer mae comne encoerecoer n a resse,c eveere o wc maenerae asar o a exame,en v someoe somurceemen,aeo vns,e ao eenacso aerar o ov r c cooc mme. oonneennssn ocuee sonurcee vevecoe or asescreeow w reerenceo., ane ouunerace anor aeas encoer o comonens oeesnaonevceor exame,enunerace,e veoe acar or comonensncuene veoecoer asescreeow w reerenceoo.er anesaevce ma oeraen a cou co , so mun servce newor wc marove ervwcaere,aaao,rm ors,n anrasorrucnurraes arusc auree,rv succe asaao.wnar seom ase amervemceenaaa,aorm as a comonensne sourceevce anoreesnaonevc ons, one or more cou comun servce newor maeroven one or meo wc are noncuene more cenevces ma communcae w serve re cenevces, ane one or neworrou a wreess communcao r comuersne cou comun servce newor, a sor-rane wre n neworor exame, a ceuar communcaon communcaoness communcaon newor, or aoa navaon saee ssem commu newor or a wre communcaon newore.., aoca area newor emomen, anecaaon newor or aowerne communcaon newor.n an servcesr s aar o oeraonsescreeren maememene as cou-ase oe coove one or more server comuers wc arememene e aeas aar esnaomnonens oe sourceevce anore aeas aar oe comonens oe es evcene cou comun servce newor an one or more oer oeraons ec croue coermenu mna seervmcee nmeewnoer mae oen ae orrv maoere c couen, aevucesc. cno suom,e orm aemrena coouns, eerms suc as “cou,” “cou comun,” “cou-ase” ec.eren mae u.nercanea as arorae wouearnrome scoe oeresenscosures.e ornee.: . s coomuune un seervrscoeo newaorereesscernesc aoosvuere.sn nsoeameoenmemenene coumemenen an oere o comun en ,eresenscosure ma asoe uure. vronmens currennown oreveoene w somem.emse aocaramusran an exemar veo encoern accorance erormn naonsescreneresen acaon.e veo encoer ma con reersa o ann sanearrreeccovne coo renuc oe o vr reemooveoc ssa wa renu vnaenocrames.nrarecve ven veorame orcure.nerrecve con rees n veoaa wn a removeemora reunancn ve onemorarecono reuce or seuence.r “ sou oaa wn aacen veorames orcures o a veo “mae” o e noeaeerm “rame” mae use as snonmsoreerm rocessn uns scuorwe , an”nne ecoe.e,ce o u v v reeoeo u en c eco roenr.nc,ues a veoaa memor, arecon , auanzaon un, an an a summer, aransormrocessn un urerncues a moon enro encon un.ereconrocessn un annrare esmaon un, a moon comensaon un, aaron un,memenaoncs,onrocessn un, an annraoco un.n someransormrocessne v uneo e,n acnoe ar sum amseorncuores v aneonveorcse reucaonnzaon un, annverse , suc as aeocner, maeosoneeween srucon.nn-ooer ocounareso removeocness aracsr e summer ane oer suc asameavese e om reconsruce veo.noern-ooer, er anoraven-ooer r,, mraoss asoomonenameaveseoer an ouu oe summer. soueusera usen aonoeeocner resen acaons nomeoe emomensescreeaore ecnue,e mae aeo a suaon were an oses s eren, annsea,e acaon croma comonenswc ma eeceor an o auma comonen anwo oman or, an n reroemseann,or c aonrn roman, anon o acaon asescre aove a nvenence o noaon anermnoons comonenso mo sa an ccocmoronneno aanse o oner oe seeecumea o cosme.onuern aenr, seowuo c asroomae ornee.: . curosmraae comao anenrss, co am seocnoenn m coemnoonneene mreenn monae an oeuma comonen anewo comonen anewo croma comonens, eeren mae an oer oeuma remann one oeuma comone an ar comonen menoneeren mae aooers mae o n anewo croma comonens.n some exames,en- oe .me vee,o an encoeerecoe veooc maerecrove e summer un or maeve amon one maaeeorm o axe orrorammaearware e veoaa memo or more oeusraexe orrorammaearware uns. e veo encoer.e veor ma sore veoaaoe encoe e comonens o rome veo source as aane veoaa memor mae oane,or exame, aaor exame, reer sownn..e s auera sores reerence veo encoere.. encerames orcuresor usen encon veoaa e veo mae,onrmnera ornerrecve con moes.e veoaa memor ane aa memor an o a vare o memorevces.n varous exames,e veo reaveoos mae on-c w oer comonens oe veo encoer, or o-c r se s coowmnonnens.., aer recevne veoaa,earon un wne aseocncouneroacressonnn un a veoarramoensnoe s vcese,oeasaonr eox vameoe, seocs os. vesoarocosn,n maareronnss accornoreene sn srucures suc as aua or oer srucure assocae w e veoaa.e veorames or mae reare-ree mensona arra or marx o sames w same vaues. same as awo- reerreo as axe or ae. numer o samesnorzo ne arra ma asoe oe arra orcureene a sze anor na an vercareconsor axes eveno mue veoocs, ao rresouon oe veorame.e veorame ma aans or mae reare as awo-men exame, usn aronn.e veooc aou o smaermenso sona arra or marx o sames w same vaues, vercareconso nane veorame. numer o samesnorzona an maurerearro anxees oe veoocene a sze oe veooc.e veooc ocs,or ex no one or moreocarons or su-ocswc maorm aan ree aroanmne, orerave usn aronn,nar-ree aronn orre- “veooc” as useere ann m caomen aaoornone,reno.arc suoaur a reeca nnoeuarasuaeree orrm no “n-o scu”ar oer ornee.: . voreoon,o oc a mraamee o orr a corrcesuroen.o a reoerennce,reeor enxame,,o a, a anrecon,neoc o or aransormn anor mae or corresono a corresonnoc, e.. a r oc , aonoc , areconoc o onree a su-oc. r aransormoc anoro con moeereconrocessn un ma seec one o aura oosserecvener s, suc as one o aura onrarecve con moes or one o aura o anereevcev oe cosnor mono.es,eorreec cuorrnenro vceesosno ucnase m oan errroovr reesues ree.su., con raenerrecon coeocoe summeroenerae a resuaoc anonnra oro reconsruce encoeocor use asar o a reerencer e summer rocessn un asoroves snax eemens, ame suseuen.erecon aronnormaon, an oe suc as moon vecors,nra-moencaors, n orero seec arn su acr sonaxnormaon,oe enro encon un. oc,enrareconroces raenrarecve con moeore curren veonrarecve con oe cusrrn un wnereconrocessn un maerorm samerame ase curr en veooc reaveo one or more neorocsne un ane moon ceonocoe coeorove saarecon.e moon esmaon recve con oem censaon un wnereconrocessn un erormner more reerenceramesourorrvene vemeooraocre recaovne.oe on ve oero m enocroeerrec mvaeeorcorsmn m oune or conasses, e..,o seec an arorae con moeor eacoc o veoa e moeor a cnu sroremne vmeoemreanmaeons,eneer maonon a e msomoan voenc uonr, wceernmncaeseseenae.rrecon o a veooc wne curren veorame reaveo arecveoc wnsacemen veorame, accorno areeermneaern wn a seuen a reerence esmaon,erorme e moon esmaon un,ser ce o veorames.oon wc esmae moonor veoocs. mo ocess oeneran moon vecors, sacemen o a veooc wn a curren on vecor,or exame, mancaee wn a reerencerame rea veorame orcure reaveo arecveoc reeermneaern maveoe currenocen coe wne currenrame.enra un maeermnees vencaoers v, e.eo.,raomces vencores, seoruennrcae as coranmesn o ar manrnaemre ssm.aer ornee.: . moae uezeermen maoonon o e msomaono vne ucnorsoee meromonne esemoacon ve ucnorornerrecon, or recveocore veooc mae or m. reeren a corresono aoc or a coeceoc o a reerencerameaseeme as cose macne veoocoe ,nuemrm os ouxeerence, wc maeeermne um osoueerence e v areerence , or oererence mercs.n somememenaons, soreeno eencoer. moar e cxaamcuae,e veau veseoo ern scuo-enree mraxenerosoaoens va oue reserencerames xeosons, one-e xeosons, or oerraconaxe o one-uarer ereore,e moon esmaon un maer osons oe reerencerame. osons anraconaxeosons a orm a moon searc reaveoeuxe e moon esmaon unn ca ouu a moon vecor wraconaxerecson. recon coerame com cuaes a moon vecoror a veoocn anner oc o a reerencerame arneoson oe veoocoeoson o arecve ram seecerom ars reerenceramess or a secon reerence e mess, eac o wcenes one or more reerencerames sorene . anooenn eosmea enonro un enco senns une cac.uae moon vecoroe moon comensaon un ecn oreoneoran cnomeensraeocn,veeroorcmease oe moon comensaon un, manvove esmaon un.on recevne moon vne moon vecoreermne e moon comensaon un maocae are ecorore curren veooc,e moon e reerenceramess, re cveoco wce moon vecoronsn one o ocoe summer.reev seuerecveocrome , anorwarerecve vaues suracnxe vammer enorms a resua veooc oxeerence un romexe vaues oues oerecveocrove e moon comensaon ormne resua ve e curren veoocen coe.exeerence vaues m oo aon comensaon unoo mca m aasonceuneerauem san orax c eroemmaen cosm assooncenae werencees v oreoo.oces e v sneoaxr eamemeenors u mseanceu ve,eoor eecxoamere, snnaexco eenmenes veenonoces m oooen veorame.oen erecveoc, anasncanerecon moe, or an o veecor usenormaonescreeren.oeae moon esmaon un aner m sonoaxn ornee.: . coumroesnessa.on un mae nerae,u areusrae searaeor conceua recvenoc sosmen am maenmneenra smonsa,roenaraescr uen aove man coenerae vecors anec esmaon un ane moon comensaon un,u wennreeccon w e moon e samerame ase currenocen coe an we vecorseveocsenn vecors as ooseo moon vecors.narcuar, n reerreo asoc recon moeo useo encoe a curre enra un maeermne annra- encoe a currenoc usn varo noc.n some exames,enra un ma anesererormancerouus rane-ra-sroerocno anna mosess., ee.x.,,urennr saeara uen enco mna saesseecs, amone varousesenra-recon moes, an aroraenra-rec , enerae annra-moencaor accorn.or exame on moeo use an rae-soron vaues usn a rae-soron an ,enra un ma cacuae an seecenra-recon assore varousesenra-recon moes, moes ase a moeavnees rae-soron caracerscs amoneese eermn roraenra-recon moeo use.ae-soron anassenera ocaes w aans a emnocuone oosrooruocneore er ernocroeeweeonc a,n a esn wcoee as aocr aane an orna, unencoe useoroucee encoeoc.nra un ma cacuae r .e., a numer os raesore varous encoeocsoeermne wc aosromesorons an rae-soron nra-recon moe exsees n v oaueer eoxraeoc. moon comensaon umes,enra un ma usee moon esmaon un ane acoccornoememnena,onns weoscer orenearre,no.ne eroremr c sausce,uonrcnornasoorcn croa, arreeccovne ere mae aocaseeme as cose macneocoe coe,nerms oxe oenrcee, wcvc maeeermne ,, or oererence mercs, anencaon eeoc mancue cacuaon o vauesor su-neerxeosons. ere ererecveocsrome samerame accornonrarecon, or a sunracranme acxceor vanueso oneerrreeccovne,oec vreoom encoeexre v maaueso orm ae r ceusrreuna v veooc en coe,ormnxeerence vaues.exeerence vauesor eooc veooc mancueouma an croma comonenerences. mne resua ornee.: . aernaveoeenrnaerr-erecocnonroceerssonrme un mea monorna- ersemca aon curren veooc, as an comensaon un, orenraoc coreconerorme unen ane moon escre aove.narcuar,enrareconrocessn un mra un, as recon moeo useo encoe a currenoc.oo so aeermne annra ma encoe a currenoc usn varous ,enrareconrocessn un asses, anenrar nrarecon moes, e..,urn searae encon ma see econrocessn un or a moe seecon un,n some examesnrarecc ano anrroocresasennr uanrec moan moroveoe usneorrommaoenensecanvrea oreceo sene mcoees.e recon moeoreocoe enro encon un.e enro encon unn mra- encoeenormaonncane seecenra-recon moenesream. a veooc vear eeerrenecrornercocoenss onrn unrareeceromn,nese suemmreercveormosc a roersuea cu vrren oc suracnerecveocrome curren veooc.e resua veoaeo e resuaoc maencuen one or mores ansroveoeransorm an un.eransormrocessn unransormse resua ve rocessn coecens usn aransorm, suc as asc oaano resuaransorm smarranso reeosneransorm or a conceua uanzaon uermr.ansormrocessn un ma sene resunransorm coecensoe e rae.neua.nzeaounanrzoaceossn m una asou raenuzceeseeranseorm as csooecaceen wso suormeer o rreuce e coecens.eeree ouanzaon mae moe ausn auanzaonar a o n some exames,euanzaon un maenerorm a scan o a ameer. uanzeransorm coecens.ernave,e enro enc marxncune oownuanzaon,e enro encon unon en urn maerorme scan.ransorm coecensno a veosream usn, e. o encoeseuanze ,onexavenarrmecon.,onex,anvaex-aarsae ceoenon narrmecon ,roa n nex-aave anoer ervaaronnnro con orransm eenro encon meooo orecnue.e encoesream maene sownno.eor vaeeorraencosmersson aso s oro rwenrenva.e, v or aerocevceoenr.e soer eaneroev ecnecon as ornee.: . u vneor mamae aeso enro encoee moon vecors ane oer snax eemensore currennverseuanen zanv c oeo nrs aee. nuannvezrsaeornan usnorma anon, reesnevcervseer,anos roercmonsrrouccessne r uen a ocnexeomanoreneran a reerenceocorrecon sua veo noe aove,e moon comensaon un maener o oer veoocs.s ocrom one or more reerence ae a moon comensaerecve comensaon un ma aso a oonces o oerames sorene .e moon cacuae su-neerxe va r moreneroaonersoerecveoco e summer auessore us reeconn msorucone es remaon. recveocrouce e moon comenssuaocoe moon comensae soraene .e reerenceo aon un orouce a reerenceocor esmaon un ane moon comcen msaene use enra un,e moon anoer veoocn a suseuen v aon un as arecveoconerrec w somem.emesn aaooncs oaerarme esenuosr araamne. ca aonn. exeme vareo veceooerecoenrcn accorance memor, an enroecon un, areconrocessn u ues a veoaa un, annverseransormrocessn n, annverseuanzaon rocessn un urerncues a mo un, a summer, an a .erecon annra un.e veoe on comensaon un, annrarecon un, anoe enconr coer maerorm aeconrocessenera recroca . ocessescre aove w resecoe veo encoern connecon w moon. veocro erxsa rmeceev,eero mmooen e cnormoenseacoonn un un m,a weenereanerar-ereconaaase on eneraereconaaase onnra-recon moencaor con un ma econ un s receverome enromemenano snosm. oe exeamreseesn, a a unca oon.e vsoeoecoer maeaseoerorme resenscosure maeve a ,n some exames,ememenaons oe exame,enra un mon one or more oe uns oe veoecoer.or orn comn maerormememenaons oeresen acaon, aone, ,enraareonc won o uner un, asn oee e vnreooeceocoern, u sunc as.ne s moomeo enx caommeesn,saeon v uneo ornee.: . eecrooremre ma o noern ccoumeoneennsr oae unrec anoneroucnecssonna un on,r sauc un mae comensaon ase moonoeecoee un veeo. oaear c moemmoornens m oae sore veoaa, suc as an encoe veosream, aa memor mae oane,or veoecoer.e veoaa sorene veo source, suc as exame,rome soraeevce,rom aoca veo accessn sca a caamae srao,ra vae m werea oer. w., areeasss nerwveor or caormmusnc.aoen v o veoaa, or mancue aoecureuer a sores encoe veoaaeoaa memor sream.e oe veoecoer sores reeren rom an encoe veo veoaa e veoecoere..,nnra or ce veoaaor usenecon memor ane maeorme anner ore a vcve con moes.e veoaa namc ranom access memor , are o memorevces, suc as ressve ,essve ncun, onrc oroenrouses o mem ,aneo- usraveurose,e veoaa memor ane areecorevces.or comonens oe veoecoern..u we aareno one se aswosnc e veoaa memor ane maerove e same memoreevcnee ara memorevces.n some exames,e veoaa memo or searae comonens oe veoecoer, or o-c reave r mae on-c w oer urneeconrocess,e veoecoeroo rescee cvomonens. a reresens veoocs o an encoe v es an encoe veosream ecoer ma recev eorame an assocae snax eemens.e veo e en ee snax eemens ae veorameeve anore veooceve. uaroecon un oe veoecoer enroecoesesreamoenerae eemnenzes. coee encroens,e mcooonn u vnecors oernnorrwa-arresceo mno moonencaors, an oer snaxncaors an oer snax eemens vecors ornra-recon moe ene veorames cooee asr aencnoranrreocecssvn un. recveocsn oeres orames,en e coe rame orornra coe un maeneraereconaaor rarecon un oereconrocessn snaenrarecon mo a veooc oe curren veoramease on a rame. e an reerenceaaromrevousecoeocs oe curren ornee.: . moon comenesnaoen v uneor oameesr ceoceo ans arnocensesrn-re uncve croouece.e., orrame,e ocsor a veooc oe curren veorameas s one or morerecve eemens receverome enro e one moon vecors an oer snax roucerom a reerencerame econ un.ac oerecveocs mae ma consruce re wn one oe reerenceramess.e veoecoer ase on re erenceramess,s ans, usneau consruconecnues escreenere re son nmce ,er e eaxmanmes s raeosr,e wn unenee o veeo. reoccosn coroece accornoenra moe ocsore curren veoocase onoc vec ssn un roucesrecve e enroecon un.erec ors an oer snax eemens receverom samecure ase curre veocs mae wn a reconsruce reon oe e moon cnom veneosaoonc unene anore veenor encoer. normaonor a veooc oe curren veora a un eermnesrecon snax eemens, anen useser mearsne moon vecors an oer curren veoocenec econnormaonorouceerecveocsore e receve snax eemensooee.ermorn eexa amree,ceon m mooone ceo.m.,ennsraa oorn unnerre usceso snome oo coe veoocs oe veorame, annerreconrameee.., o usenormaonor one or more oe reerencerame r, consrucon recve encoe veooc ssorerame, moon vecorsor eacner veooc oer oerame,nerrecon sausor eacnerrecve coe rame. ame, an oernormaonoecoee veoocsne curren veo mar,enra un ma use some oe receve snax eemens, e.., anao,rmoaeoenr omn weca vee courreonc vs oeoeorcam wea asrer wecne ues rneconesrnucra moe, consrucon sorene ,oc vecorsor eacnra rece veooce reon an soue recon sausor eacnra rece veooc oerame, oerame,nra ecoee veo an oernormaono e moocsne curren veorame. neroaoneron comensaon un ma asoerormneroaon usne cacuaeneroase as va usueesor sue- vneeoe erncoxeesr o reuerrennce encoocns. onse c vasee,oeo mcosoon ornee.: . coem reecnesvaeon s unnax ee mmaense anerm usneeeenneerrooaaoonneerrss use e veo encoerrom enverseuanzaon un nverseuanzesoroucerecveocs. rovenesream an enroecoe e eneuanzeransorm coecens uanzaonarameer cacuae e veo enc roecon un usne sameoeermne aeree ouanzaon.e oeror eac veoocne veorameransorm, e.., annverse , annversenvnereseerranrasnosrmormr,o ocers as cnon ucneua a smes aanrnverseransormrocess,oeransorm coecensn orero r nverse xeoman. econsruce resuaocsne ocore ceurrrene m voeoon coocmeansseao onn une v orenra un eneraeserecve reconsrucsecoe ve ecors an oer snax eemens,e summer enverseran oocore curren veooc summne resuaocrom moon c sormrocessn un an a corresonnrecveocenerae e er,omenesr,aon une arn aenra un.nn-ooer suc aseocn ourerrocesseecnoeor ve maeosoneeweene summer ane e ome, aneecoe veooc mooc.n some exames,en-ooer ma .eecoe veoocsn avenaramee arreecenrove e summeroe reerencerames useor suseuen moon c sorene , wc sores a memorevce searaerome ,omensaon o nex veoocs.e , or on asaevce, suc a ma aso soreecoe veooraerresenaon rames ornc aures.caac vres aom ceoe mansa nrcocueesv es,c ae r vee se o aom seeu.en.cecancues an orere se o awo-mensona arra ouma sames. s a arras,enoe,, anr.s rs awo-mensona arra wo-mensona arra o croma sames. monocrome an or croma sames.n oernsances, arame mae s sowereorencues on onewo-mensona arra ouma sames. eneraes an encnn.,e veo encoeror more seccaearon un veorame maoenc reuree asennnaeoner o nu amraemr oerss oraerreo cnonnsecuevraemenn ao ra as seer s oc s. rnomeeo o re anr aorme sonaoeoom an orer a e. vaceo encose ararnes a soeuceanc ceoanram uener a sne, suec wa ornee.: . a×e.us sno au veeo n soeeuencaeaevereseen sam ae sczaeoenns n oone n oecessa×r,me×,×, an sze.s sownn., eac ma comrse one ouma same o aarcuar conreeocs o croma sames, an snax ee s,wo corresonnreeocs.e snax eemense mens useo coee sames oe con xes anowe veo se screroeres oerenes o uns o a coeoc o ornrarecon,nrareucenocne m caone,e m reocoonns vruecceors a, ane o veeroaeracmoeeerrs,ncunner cures orcuresavnree searae cooran .n monocrome oc an snax eemens useo co es, a ma comrse a sne conree mae an ee sames oe conreeoc. conreeoc aronn sox u acco aec sve o n a sa arem -reeres ee. arrormoannnce,,erena vr-eore eencaoreron ma recursveerormree comnaonereo one conreeocs oe a n,ua-reearonn or a secen.,ex srsvennovoure smeaerns,o e samcaers. oc sze ox.moneour sm avn a s aers, an are eacvenoour s o oxx ococ sz se.ze.ewox s an are eacurervenoour earonroce . ecs aua-reeaa srucureusrane en resu o corresonno onsse o oe asecen., eacea noe oeua-reen., eac ma co am rersseec ave sze rannromxox.ee ece o croma sames o a ouma sames anwo corresonn conocs e c rame oe same sze, an snax eemens useo coee sames o mao comnrseoc a ss.nne m coononcromoce ancur sesn oarx scruucreusresav usneree searae cooranes, a oc. soue noeaeua-reearonneceo coee sames oe con usraveuroses an one cane snoso aano var.n an s onor ase onuaernarnar-reearons.ne mu oca caracerscs arone aua-ree srucure an eacu -eree srucure, one s nar anernarree srucure a-reeea caneurerarone a o a conocavn a w.s a snownn.,ere areveossearonnes aronn, vercana ae ,.e.,uaernararonn,orzonanar aronn. raronn,orzonaernararonn, an vercaernar ornee.: . ano onne so omr meomreemxenaso.ns,e vs ae roec enacnouearrs muaareu orr neoraron a conoc o on wce samerecon,ner ornra,s ae n-suareoc o sames sames,wo corresonns o croma sa . o a ma comrse a ouma n monocromecures o mes, an snax eemens useoreces. an rcuresavnree searae cooranes, a ma comrse a sneuma, s, annax srrucocuresso urseumoa,re, ace.e veo encoer maeneraerecve e veo encoer mnrs o eac oe. recveocsor a. a usenrarecon ornerreconoeneraee ocs o a,e e veo encoer usesnrareconoeneraeerecve ecoe sames veo encoer maeneraeerecveocs oe ase onoene oerame assocae we.e veo encoer usesnerrecon oeraeaseer oencecvoeeoc sams oe as o, onee o vr meoor eencroameers o mearaenneraeerameer aecveocs e. ssocae w mores o aere, vee vo eenoco enecroerene mraaeserneeraceve auummaa, res, anrocsor one or suracne’srecveumaocsroms ornauma counaoocore samene’suma resuaocncaes aerenceewee c suca eac 'srecveumaocs an a corresonn sa n auma samen one oe mar,e veo encoer maenerae amene's ornauma conoc. , resecve, suca eac samen resuaoc an ar resuaocore eween a samen one oe'sree's resuaocncaes aerence 's orna conoc an eac sacve ocs an a corresonn samene erenceeween ar samen one mene'sr resuaoc mancae ane's ornar cono oe'srecverocs an a corresonn same ar urermore, asuscra.en.,e veo encoer ma useua-ree , anonnrraonseocrommoosces reesuemca,ve,. anransro rersmuaocosc a rse oca a no one or moreuma, oc o sames on wce sameranso nuarsuare or non-suare oc ouma sames,wo corr rms ae. o a ma comrse aransorm eemens useoransormeransesoromnnocr saanmsorems.oucs, esa oc cro om aa sam maes,e a ansso scnaaex ornee.: . weu amuamraanrsanosrmormococ as,so acaera wnsormeoc m, aan ae ar suran-sormoc.n some exames, oc.eransormoc mae a su-oc oe's reoscu oe'suma resua oc mae a su-oc oe'sr resuaoc.n monocroaoc.erransorm ree searae cooranes, a ma comrse mecures orcuresavn useoransorme sames o a sneransormoc an snax srucures aoeneraee v aeuom ean ccooeercen meara oc ansorm or onee oorc . m.o croeeracnsenormsoco a maumaransormoc o arra oransorm coecens.ransorm coece e awo-mensona ma a one or moreransormso n mae a scaaruan.e veo encoer ocore.e veo encoer m aaransormoc o aoenerae a coecen o aoenerae ar coec a one or moreransormso arransormoc oc or arer coeenecraenn ao ccoeen ,co eecno veor oce ence.o..,er aum maa coeuacnenzeoec c,o aec ceonecoen uanzaonenera reerso arocessn wcransorm coecens a c. reucee amoun oaa useo rereseneransorm c reuanzeooss comresson.ere veo encoeruanzes a oecens,rovnurer enro encoe snax eemensncane coecenoc,e veo encoer ma veo encoer maeror uanzeransorm coecens.or exame,e coecens.na,e vem one snax eemensncaneuanzeransorm avcoerms o ar rerare o encoer ma ouu asreamancues a seuence os e senaon o coerames an assocaeaa, wcs eer savene sorae maarseeenrs rm serceee amvno o o ae ases nr sean nmao axen enee ermav eece. nse veo encoer,e veoecoer reconsrucerames oe veoaaa romesream.e veoecoer ma esream.erocess o r se aeasnar one snax eemens oanerom rocesseror econsrucne veoaasenera recrocaoe enconnverserame e veo encoer.or exame,e veoecoer maerorm resuaoncsosr amssso ocnaee w coeceens oocse a csusorrcenae w.e vse oo ae ccuorreern asoo re reccoonnsruc err ceonnooc cosrr oesoen cunrre snames o aen srucs cu ranseo srammeosc os oeerecsv oeeoc cusrreonrs. oeer ornee.: . reracmones.rucne conocsor eac o arame, veoecoer ma reconsruce.e.,nra-ramse noree acoove, veo con aceves veo comresson usnrmarwo moes,s no nornra-recon anner-ramereconorner-recon.wo meoesa,ner- coraumeer reeacroen a cson ereurensr ma-orraemoeree ccoonn or e acern moe.eweene reconecause oe use o moon vecorsorre cannra-rame reerence v cn a curren veoocrom a oc szeoueo r woc. resee evermrovn veoaa caurnecnoo an more rene veo moon rvneasne veoaa,e amoun oaa reureor reresenn caen veecsoorseonre a curorrmeneraamce aaso nonc ornease as sruousa on nae.onren wa osn overcomns anemoraomansave smar veoaaorrecnuroseueoe saa eweenese neorn s are aso smar.ereore, moon vecorsnormaon o saa neorns anoremora cososseo usee moon oe moonnormaone.., moon vec -ocaes as an aroxmaonemora correaon, wcs as or o a curren exorner saa an . o reerreo as “oonecorrecor ” oe curren eermnnsea o encon,noe veosream, an acua moon vecor oe curren moone e moon esmaon un asescre aoven connecon w .,e o vreocuocrer aecooron oeec courrrenerencse suraceorrome cuer arecnua m.oon voecnor s oe curren neeo encoee moon vecoreermne e moon esma o,eres no ramenoe veosream ane amoun oaa useor on un or eac o a e veosream cane sncanecr reresenn moonnormaonn recon o ae coeeroocces,s a o se c ooo rsunes a neereeas ocev. ee aoocen a reoerencee vrameurnner-rame veoecoeror consrucn a moon vecor can eo encoer ane a curren usnoseoena can aesasonown as a “meres”or s anoremora co-o ae moon vecors assocae w saa neorn moon vecor canaes acsa ae moosn o veceo crurrreencor aonree cnu srereencn. one moemne sro,romerees ornee.: . noec noeeero arnans amnneex m oooen s veeeccoer c manoona veecsorsrerome veo encoeroe veo ss sucenore veo encoer an ecor wne moon vecor canae recor wne moon veco e veoecoero usee same moon vecor . sows a comru cann enavesor encon anecone curren. comun envronmen cane ronmen coue w a usernerace.e ncues ar ar o aaarocessn server.e comun envronmen eroocceessssoorr , a mcaemo cro , an annuuu nerace . , suc ase oer nros overa oeraons oe comun envronmenma aons assocae wsa,aa acuson,aa communcaons, anoereorrmoce ass onr s.omee orocees ssoersn mea aonvce-ueesc one or morerocessorso execuensrucons mancue one or more mou re meos.oreover,erocessor oer comonens esaacaeeneraconeweenerocessor an sne c ma.erocessor mae aenrarocessnn , a mcrorocessor, a ec mneme,o arracas cornoceussrenon , oree. oe comun envronme sore varouses oaao suore oeraon xames o sucaancn .e memor mancuereeermne soware. comun en uesnsruconsor an acaons or meos oerae onememenevro unsmen , veoaases,maeaa, ec.e memor mae ereo, suc as aanc ananome occe vsosaeemo orr non-voa, aen meemcorrcaevcraessa, ore ar coomramnaon ea-nemor , anrasaero mae roram rammaeea-nemor , a aas mmemaore,ea-nemor , aea-nemor , a manec memor,nerace moe a m ues, sna uen crea acc se or oc aera ooavs r,e as. a cncne wraecee,eweenerocessor anererancueu are nomeo, aomeuon, a sa uons, anee.euons manerace cane coue w an enc r scanuon, an a so scanuon.e scosure reasessoc moseureoss a rnea aeaora vo usee oor a n cn morneco ov anner. comresson.ore secca,s er an cross-comonen aaveooer e c.on ecenc o aaveoo arous veo conecnues mae useo comress veoaa.eo cons ornee.: . enrowornm vee aocc coornn soa onnea orrs more veo con sanars.or exame, nowaas, some we- on , asonown as.ncu oerersa-eareo anon , cenc eo nown as. or -ar, wc areoneveoevanceeoon an, a-so success.oroseraeceo waseveoe anceorenea as a an a veo coemnres ssaonar .uoeoon , wc reersoa auo e n sanar,s anoer veo comresson sanar sereseveoe sanaruso aneoonanarorrou ona.os oe exsn veo con recon a mreeous ue.o.n,neer-armeoucson,nrra- vreeoc coonno rreamuceew roeru.e., usnoc-asemaes or seuences an usnransorm co nancresenn veo nmoranoa o veo con no comace ener oerecon errors.ower rae w ecnuesso comress veoaano aorma uses a eres aveonernao onr mnm szannareraaonso veoua. ecnoo,vanceuoe ncuesnese naona sanar “normaon ecnoo,vanceuoeooon,ar:eo”nown as an “normaon can oer aroun -rae saonar:aoeevsoneo”nown as . sanar.e sanar veovnar ae sameerceuaua comareo - eruar .e secone wasromuae asenese naona sanarn sanar “nor neraon sanarncuese seres onese naona manareem aaoenrecnoo,cenumeaon”nows as , wcssoue oa oeansm.snson o exra rorams.e con ecenc oe eanwe,e sanar va ,e wasssue asenese naona sanar. nneers as one eoar was sume nsue oecrca anecroncs enera nernaona sanaror acaons.e sanars one new eceon veo con sanaror veo acaon amn a surassne con enc- oaeseaneesnernaona sanar .narc , ae- meen, sanar. wasnse, wcroves aroxmae -rae savns overes manane uerren,rouereos oenme roenserreanece a s roeewreanrec,e cameemenaeronormance moe , or.e.evese,eoca sraamn oar aseneurc u oe sanar. ramew oocn-easeoc-rase veo ernco vneo s cosenm. ornee.: . en wu vceoa srnoanssoroccess osneoasce onouca-cae con unss.erenromes sno rees,ne , one conree un o so aao varnoca caracerscsase onuanarexene-ua-ree. searanoan o,e, croence o muearon un ene s remove,.e.,e eac s awas usceon as une anransorm un oes no exsne nsea, arons.nereearon srasc unororecon anransorm wouurer ua-ree srucure.en, eacuucure oe , one srsaronease on a an exene-ua-ree a-reeea noe caneureraronease on anar erorme.aa srucure.n., saarecon anoremorarecon mae neorn reconor “nrarecon” usesxesrome sames o area coe e curren veoocsocw.ca arae careec reoenre rencuec seasm saesa rneuen saamnce vneeorencunrese vceeoo srenc emorareconaso reerreo as “nerrecon” or “moon come a. uses reconsrucexesrome area coe veocures nsaerecon” emorarecon reucesemora reunancn orece curren veooc. recon snaor avens usua snae oneer oernne veo sna.emorancaee amoun anerecon o mooneween more moon vecorss wc so, mue reerencecures are e curren ansemora reerence. wcs useoenrom w suore, one reerencecurenexs aona sen, recon sna c c reerencecurene reerencecure soreeemora encoer c omes.er saa anoremorarecon,e moeecsonocne m ooseseesrecon moe,or examease one rae-soron omzaon reesuoa.see-croerrecaoen uoscnsranesno srum arnaceenromuanez ceur.rene vueaonzeoc res anuae coerecon arenverseuanze annverseransormeoorme recons cens aeacoereconocoorme reconsruce snrauce resua, wcsen ern, suc aseocner, same aave ose an a oaveen-.urern-oo mae ae one reconsruce eoresune reerencecure soooreer reerenceo coeuure veoocs.oorme ouu veo-sre an use asnra,recon moenormaon, moonnormaon, am, con moener or a senoe enro con unoeurer com anuanze resua coecens are ers verson oe sanar wreasssen aanzeacne.coer , wc oers ornee.: . aenreoraxmonae veo con-ra saen saavrn. or euvaene.rceuoauuae coma sraenaorreror sncan conmrovemensansreecessor,eres ev oves ecenc cane aceve w aona conoos o encea sueror con an saree exoraon wor o new conveercno.ase ona,o sanarzaon.neoneoxoraoneam oesoruure veo con an oen sncan su o ava wnacseoermcenoonecs.a co - susana enancemen o con ecenc.ne reerence u enae moe was manane e neran seve soware caeon exoraon e es m ra aona conoos ono o eon n wco a.e sssue,e.on- ca anorroosa.snr. on v,eo com rersesoson w caa an evauae ae- meen, wcemonsrae nses were receve e aroun .ase on suc evaua comresson ecencan over eveoe neweneraon ve on resus,e aunce a newroeco ne same mon, one o con sanaras name asersaeeoon . esaseor reerence soware coease, cae es moe , was eemons,raen a reesrenuce umemenaon oe sanar. .veseocaram o aeneoneoc-ase r veo conramewor. veo snasrocesseo rcoc-ase r veo encon ssem.enuox xes.owever,cereoccae con unss.n -., a cane urees,ne , one conrnrome wcaronsocs onase onua- caracerscsase onuanaree un s snoso aao varnoca unene s removeernar-ree. ona,e conce o muearon un oes no ex ,.e.,e searaon o,recon un anransorm ororecon ansrannseorm w anoumourreenrseaar, eoancs.nes m awua-s useere aes sreucausrec, un srsarone aua-ree srucure.en, eacua-reeea one arone anar anernarree srucure.s s noe caneurer es,uaernararonn,orzonana ownn.,ere areve sn orzonaernararonn, an raronn, vercanararonn,emorarecon maeerorm veer.caaeranarreacronononr “.nnrar.e, scaona” urseescxoens anroomr ornee.: . vee soamceusre os acreeaor ceoce nee curroenrn veoocsocw.ca aare craeec roenerence samesne samenerenne veo sna.emorareconaso ree reuces saa reunanc comensaerecon” uses recon rreo as “nerrecon” or “moon rece curren veooc.emsrucexesrome area coe veocureso veo sna.emorar orarecon reucesemora reunancnerenne vecorss wcneccon snaor avens usua snae one or more moon semora reere aee amoun anerecon o mooneweene curren annexs aonanc see.n,s wo,c msu usee roeereenncerocmur wes acre r seuereonrcee, ocnuere renerenec reeercure cure soreeemorarecon sna comes.er saa anoremora ence moeecsonocne encoer cooseseesrecon moe,or e recon,e rae-soron omzaon meo.ereconocsen suracexamease one oc anerecon resuase-correae usnranso rome curren veo resua coecens arenverseuanze annv rm anuanze.euanze resua, wcsen aeacoere erseransormeoorme reconsruce .urern-ooern, suc aseoconocoorme reconsruce sna oen-ooer mae ae one rceconnsrucere, same aave ose an aave sore an useo coeuure veoocs.oo eoresune reerencecure ornra,recon moenormaon rme ouu veo-sream, con moener a senoe enro c , moonnormaon, anuanze resua coecens are .veso anen uenraooeurer comresse anaceoorme-sream. sreamsrs enroecoe a ecnaram o aoc-ase veoecoer.e veo-normaon are seno eere saaroreecon un.e con moe anrecon un ner coeoormereconcoco.n un nra coe oreemorareconnverseuanzaon un annv e resuaransorm coecens are seno reconoc ane res erseransorm uno reconsruce resuaoc.e ureroroun-ooeruanoc areen aeoeer.e reconsruceoc ma vueroe vn reeoer eores soren reerencecure sore.e reconsruce u encecure soresen sen ouorve asaevce, as we as useorec comonen aeo a mcas. venooocus oerescosu.reseo remaerovaecer aouanvneowooeeers eaora ane cnrosse- ornee.: . o.own secons. .. enrnaes,,neasr aeerno aen ouua samvees on sae an .woer saes,×amon sownn×..anmon. s,a eaec, a sreu saure coorreresoornusmoa a anum croma comonens, resecve, as suare corresonso a cu a or a croma same ane cener an e rreno-e-ere same.eer coecens useon-smmer sum oac coeneceerns oer o cnoeecerens esu raeroesen,e w wcs-erxaec-onoan rreecrson.n aon,e -raconarecson: esenaon o. w , wer "!%#& ^^! ^^"#' = e re ee cr o ee ns s n ru aumm ce eer o sa v m aue ^^
Figure imgf000030_0001
Figure imgf000030_0002
^*^ ^^, ^^ =^"# ^^ ^^ ^ ^^^ e ^ v ^ au ^ e ^ s , ^ ^^^ x − ^^ , ^ ^ asoows: , ^^ ^!%&! ! ^! ^^ − ^ ^^^ ^^ − ^^! , ^^ −^ ^^! ^^"#' ^^ ^^, ^^ : wren as: , ^^ ^^ ^^ ^^ ^^^ ^^ ^*^ ^ ^ ^ ^ , ^^ ^ = ^ ^^ ^^, ^ ^ ^ ^ ^^ ^^ ^^ ^^ ^^ ^^ on-e-
Figure imgf000030_0003
, were ^^! = mn ^^! = ^^ ^^ ^^− ^^ ! ! ^^ ^^ !% ^& ^! ^ ^ ^ ^ ! ^^ ^ ^ ^ ^ ! − ^ ^ ^ ^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ervsee as c n
Figure imgf000030_0004
Figure imgf000030_0005
, weres ! #' , # ^^ *! ^^ ^ ^ ^ ^ ^ ^ ^ ^^ ornee.: . ^^ = ! ^^ ^ = ^ ^^ ^^ ^^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ..umae same nu-,o sc
Figure imgf000031_0001
umaocs cassu re- orase on × sameraenso srecona an aacan acv.rs,e vaues o ^ ^ z^ ^ +o,n- = =a, v ^e ^ ^ ^r ^c^,a ^ ^ ^ ^ a −n ^^w ^^o −a, ^o^n −a ^^r ^e^con,s ^^ ar,e cacuae: ^^ − ^^ ^^ − − ^^ ^^ ^^
Figure imgf000031_0002
, , − waosea ononae sraamenes,ra ^^*&en asn, su ^^*-,o acre caocruzoanea asraen, ^^., vercaraen, ^^/, an ^' ^ =!12012 ^^ cnancees se ^^en anrom ^^ r eeueraoone,
Figure imgf000031_0003
coverseare×ocs useor cassnaoc.o reucee c a raen o ever secon samen a× wnows cacua omex, on vaues o o e asusraen..e eecro snam,oe asrsanense arere sceoona.,e rao oe maxmum ane mnmum o e su-ocorzona an vercarae ornee.: . ane rao ^^.3 ^^. , ^^/ , ^^.3,/!6 = ns mn ^^. , ^^/, are
Figure imgf000032_0001
e:o ^^345 eac^ ^^ o ∙ ^^e3r!6 w an ^^3 o45re^s ^^o ∙ ^^s3!6 ' an e: ^^. ^,^/ ' ^^.,/ ^^ *&,*' '
Figure imgf000032_0002
,s seo. n
Figure imgf000032_0003
cacuaene, ee:
Figure imgf000032_0004
e ^ ^^^ ^ ^^ ∙ ∙ s seo,, oac
Figure imgf000032_0005
o
Figure imgf000032_0006
va oerw uess oe sn c esx seecuoe eres no vaue assne = +,- +, ^^ ^^ − acuae ,, s +%!# -%0# - ,,,
Figure imgf000032_0007
,,,,,,,, ^^ ^^ ^^ casses: ,,. ac cass canaves owner = ^^ roaon,aeoonrae oern eac a×ssunmea.oc, aeomercransormaon, suc as-eree eenn one sur- veorccarae,ns va aue aes soeceenera coeec.ens, asusraen., ua-oecreaomeenr vcaruaenssormaonase on su-ocranrsaoremna voanues
Figure imgf000032_0008
ornee.: . ..onn areeonooceevuemaeraaon aaaon.uma c ×oc-eveer aaaon, suors-eveer cacuaeore area caone use s aces.er s cean c aascou uasee oore curren sce or one oeer ses eacuma , wcerrome co ne oe oneraneer ses. n eermne e cass cac sener se soue aeo eac ×oc,s roma uses onuae-evne euaero anaaoorsoc. comonensn a sce.ac n.o ers cane useor croma ..naxesn can seec one oeseers. ncue uoer c crooemacenesr an cnnces are carren s.n canncueor eac oeusm aan ca osnsees.umaassesera sven we u samoenexe ^^rs. snnex ^^?s aso mern eren casses,e numer os ?aree sameer. reuce.e asoue reureo rereseneer coecenss coeoowe a sn vaueo or a a non-ezre crooe coececnens. rereesnen ce unsns e ana orerx-ooms aso snaeor eacer coecen usn awo e, a cnnex or coecens an cnnce -xe-en coe.e sorae neee cane use eecoer ae samesm wen an s a mos s.o s are snae ae sre cuoennrcoe, sncuaxre e, semceen ansnc.ueevwoes onormaon.rs, onoas sceeve onuma s en es.roma cane enae acure ans snae acure, sce anaee ave,e corresso ennaneev ae.aecoenve,.eere uresnaenormaon s are coe a a sceeve or a acureeve ae sces ce s s.uma comonen can reeren wnecure usee same .or a ce uo s an croma comonens can reerenceumaer se uma , annexs snaencan wc or oneranes u s use.or a croma,enexncaes wcerne reerence ..se.ne rocessn.ou n reeruce ,euc neeo u snoerraoeun rearuersem areenacoerum,a sam eems anos cnroemau saemreosu anoavre ornee.: . saomrzoensa one oouern saree os.eenn aeuenrounaor a s caamnnoe oen u osnee s.e o aneuerounar, ... n sm szeor casscaroaca nesnon re s ruem ucseaomva romn axnox v.ruaer sounarrocessn are remove.oc coecens ar zeorouma an croma,or wc .. wxe snae,sncreaseox. oere aers ses oers ^^, ^^u amna s ^ame,reeeren cassers ^^&, ^^' an ^^ anreeerenraneor cass&ers' ^^ an^ ^ a^re use.es ^^& an ^^' conanxeers, w coecens se ^^s useor ave & n same '.soeecceens a o cassersn ^^ are snae.cerrom a ^^! ^^ ! assneos same usn casser .! .. ern nermeae samrs,ewso ^^ ^x^, ^^ aanmon ^^ s ^^,a ^^e.xeeraer,s ^ ^^^& asn a ^^'e areo a ^^e ^^,oervewo ne orn sames, an & sameseo ' reeocn er oerve a & ere ^^ sa,m ^^' e ^^ a,s ^^, ^*^ ^^, ^^ = ^^ ^^, ^^ '!%@& ^^! ^^!,& ^^!,' : !%'& ^^! ^^! !%A ^^!!,& !,' : , sa wmeree ^^
Figure imgf000034_0001
were ^^^ ∈e ^wee,n,e ^^^n ∈e ^rm,ease saem cee ^^
Figure imgf000034_0002
e ^^r,e ^n^ an curren s,ame ^^ ^^, ^^,!,0 an curren ceeween a neorn sameeore rane o “”n ^^ sa .mee ^^e ^^, ^^.ere,e vaue rane o “”n!,0serenrome vaue resen !,0 r coecens ^^!,=,…,, are snae.eer sae o ^^s ..eassn.. acsaeo onnrecona ^^! ^ = ^! ^ a ^ n ! ∗ a ^ c ^, v ! ^^ ^ ! ^!, a cass ^^!s assneo eacxoc: ,! ornee.: . were ^^ or eac sams re enresens usn, v-aeueo asa o nu acaem n.oerrz o eo snuare m,c o veorna eca sa,e m asn ^^!w.oaonaraens are cacuae coverseare×ocs useor casser eraens wn a× wnowa × wnows useor casser ^^& ane sum o sameraens wn a aonar s ^^' an ^^! .!e s!ums o!orzona, verca anwo eermneae cnoms araernenoe, resecve, as ^^. , ^^/ , ^^*' an ^^* .erecona ^^!s w a se oresos. ^^.!,/ = 77B89C^^DD"!"! , ,DD#!#!, ^^*!',* = 77B89C^^DD$!$! %% , ,DD$!$! && or ^^ an e
Figure imgf000035_0001
^^ cacuae ^^', s ! oresrw.ser,es ^^osse= ma.,.,,,., are use.e s !xmumneer suca ^^.,/ ^^E ! Fre -n s !.e s!ren
Figure imgf000035_0002
! ^^! ^^! ^^*',* ,.e.,orzo o na er v w er se c , a ^^ e s es a e re ma o x m m n u a m n, ne e e ^ r suca ^^*',* ^^ -. en o.,/erw*'s,*e,aona ees areomnan,e ^^!s ^!serve usnaea !erve ! usnae. ae.an o ^^ an ^^EFo ^^! o
Figure imgf000035_0003
ornee.: . n. a.ner_nav,e uxoumaer ses are snae, eac se maave uo ers. snaeumaassecra seo,n an cassesr exene w an aona aernave casser.or a eomercaransormaonas nso s anaeeooncae weere aernave cassers ae. cassers ae,e sum o same vaues oe a aerxnauvmeaano casser.enean-ase cassnexs cacua cs cacuae ars.ene esua casse_n aseeow, .. x =sum * samee . vaue assascea conasnsers exene w ar casserase onuma resua same nes.ouronr eacx wxnouwmas coc,e sum o asoue vaues oe resua samesn a caasscuae, ane cassnexserve as: e vaue o cassxsne ranx = sumsamee –. or eacumaer sen.e oo, same asn -..e casser usaes snae . n .. eraes anr rocess.s so uwsenseecusmoan same vaueso renee croma same vaues wnenu aneneraese cornreco.n v, anearern oeraonaeseuma same vaues asneenenor eac croma comauesore croma same vaues.e correconsenerae ^ onen ^^, ^^ ∈ ,r an cane reresene : were ^ ^^ = ' ^^G ^^? & ^^? ^^& ^^!& ^^ ocaon ^^,e ^r^vese
Figure imgf000036_0001
^s^ , ^e^u,ma er suor reonnumaore croma c ?? ^^!s eermnease one saa scanacoromewoneeenn ^^e.umeau amnaocaon ^^
Figure imgf000036_0002
^^ vauesneuma suor reon are asonusoe uma sa cero anma corresoneo samee ornee.: . oueuum oa samee va suaese w.n sonmee examres,e croma same vaues m e useo rene :: veo ses sueonwcne, wn c.rom,ae ocess. ocaoneer,.aes., a weanmon sae.s seenn.,or a co-soews w oeeum evaen numer e croma sames areorzona e r e coumns oeuma sames an vercanersaeween c soaemcees,nse caevnee ar oreaeerameornee os aenxe w c ao croma sameocaon. coecens, snce no smmer consran mareo reuar o s are enorce.owever,womaons are enorce: resure,s oenrve seven ne ourae e,e sum o coece cnose neceeno vaeu sess reureoe zero.s a e coecen aocaon ^^ , ^^serve naenesream, an e asoue vaue o ? co?ecenss re asrceeecooer. owo, secca ,,,,,,, e eer zero or anneerower -s oeraonsna .s enaesmemenaonso use varae ..nax ce o mucaonsor ,esre. na ee msaxnmum numer oerser croma comonen o acure wasourne cromaes conm oonen..ssereen ca ssee oore reu caorecen csoe canceen sse,eceor c eac o a snae wn an .ac conans uoour ersoorecens are comonen. e cane enae a a seuenceev eac croma aso enaeore seuence.mar, c e, can one enae suma s enae ae corr ane enae acure an sceeve on ..neuereu esonneve. anwo sasescrecno snecon..,euma ane cromaneuerounares areournneumereso,u rnesaercesvea, a areov aeneeor cournomaar a.ore:: cromaorma,s resus cromaormas,e crom numa.owever,or:: an:: s a aneumaneuerounares are no ane w eac oer. row as resruee o anosu mr ssaamnemse ano,voere:: anou:n:a cr.romaormas,- s no aeoe . n ornee.: . resua correceonorer cocreosmsa u ssaems aeneareroeruma same vaues anenerae asusnrae cann s..or aven s.-aareers usen rocess, wc em a sce,e encoer can coece sascs oe sce, anaze accorance w.na u examuso ersa oes aers ereesrro en suaseor. arecon sna oreore a snan e saa neornx cosure.n some emomens,sroveoae saes ma esnrecon sna as aona euaonnu.arouser mae×,e× us oero× ex asra scowenormaonnrecon sna.or exame,eer sae eresensc.osureusraes ann anuse..er saen accorance w some exames o rom .n some emomens,sroveo canee croma er sae er saameo.n saeoon cross sae as sownn., wcs une weuman a . rou usrae smmerca samean ouma ern accnorasn ace we e wxaemnees oere sraeseen osceo asure.onna somneu emomens, smmerca same weoeere same crossese vrua ws cenraoson ane eounar.or exam ounarneuerounar orcuresce, eer sae oexee, aesrsuomee o anneeoe reersaueas s resnaua or sameeesr a ssa ae oonae onnune, cenerra wcosornec a anee wso reseuoa senaersex sa,mee cerors ssease oenee resuuea sna ws smmerca sameans conuce as sownn .-, rounar,e coocae resuaxe oeoeere same, ^ were ^^' masse ^^′o ^^′ aree moe resua same vaues, ^& o o n ^^ es A ar a e re ne e o u r er na o r u e n s a u r a es s . am a es, sa&mes reAresenae resua sames.n a wor, w smm e aonanu sames wc are none sameou erca samean,enu same oeoeere same ane a nar se we coocae aonane sameounar se we c onanu smmerca sames wc are areo moen a smm oocae aonanu same oeoeere same ou aner manner.aseenmroven ,eres roomourer ornee.: . amrovneser cooremacnceen.s.ccoer snao euaon, sameerences are ceeore ne orn same, ^^ ^^ ^^ , ^^ ^^m, aenee creennceer samscea, ^^ ^ m^, ^e^an.sn one smar oe asusraenuaon! oec!on.. e or more exameso ^^were “ern”,e sameerences ma correson oera!,0onees ^^^n ∈o ^rm,aon, ^^^ w ∈ ^en,e s oarm!e,0weererenc ^^^ ∈ ^,, ^^^ ∈ ^,.e cnormaoneerences ou es wn a rane, anscars mea see rane.owever,escarenormaon mae sarenrnaun a anre usoze, caonmer socvaeee coownn ecenc.enormaon, or sameerences sow an oe comne w oer nus..- secon, menu osssra arescon roo. vsuree,oo aurreesrs esme nrosvseues sse a c es oxsuson rene oune “roem saemen” maneaures oerooseecnoo aree ssumnm oarzee aso.nowes.nera,e .evoree anonars cose ancnenese,reasn namoces rsanaen o, onneu saarms oer serences are wn a ranemn, max,e oerars ore oe omears are eren coecensoevearrars are ousee rane. . onace sa omeerence maaves own coecesn.s, w aeas one coecen ae .eu coevs cee ra en,anrose maar. ar ssareeowe saemoew coeerocunen asn.n a soomvee exea umeers, sna aona coecen oun usee same . mavx,nenno. exoar rasn meaeeermne snan annexncan a ranemn, nex manae maereene.n one or more exames,e one or m maoree ex aam-esn,eexnnecxa mna ae ra ane- on,exn, orcan, a ra,n ore o,,.,n ,, or, . or . suce s aasmumeaeren ances c anromaeare.er same canee same coor comonen, ornee.: . . coeor sa cmoeerencesuma aneareer samecroma maeeren ccomronnens, suc as . erences areveono somears e,x oanmeeasr,se woren a a rannemn, ma cxoe,cee onse,nu same e rane.erocessor ma a eren coecen rars ouse o an encoer,erocessor ma sna a soevears. a se ccorno some exames, ona coecenore ousear. erence, or sar e aona coecens snaeor eac same a rccorenoor a s sameerencesa are ousee rane.ncan ome exames,vnnoarsseermne snan annex cacnorenmn,o ma sxom,ee exnamexeos, raneeo mrea anane cane coereceennes,.nu sameoweerrenocuesn a,reev oeernaros aarosv,e onee uarers woun a ranemn, max, onearseowe coecensoevears.e se n.erocessor ma a eren coecenore o oe encoer,erocessor ma sna aona erence, orc scoarrenoou r a sosm saee m exaar em.eesr,ene aona coecens snaeor eac same oun. cesa areeoweoweroun or aovee uer snan ancncoerxnncoa sonme a e raxnamemes,n, meaxroc aecscsoorr mnao svomeenoarsseermne mana exames,enexo rane cec coarnneoreene. exames aove mae soem seam exea cmooers c,ome soanmen,e suce aresnuces aneareer samene ccorno some exames,e sameerenma an croma. cromane exames aove ma cesuma aneareer same n some exames, eeren coor comonens, suc as . .s aowcareusscrose meos mae aeneenen oron. oeresen an a meoor veoecon accorno an exame zeroer coneescosure cen.n,. soemreo ecxesasmores, mea no,n a-zereo see or c aoeeccoeenr, m reacev reee areoas a n oonne- nzoenro- ornee.: . s ccoaence wne or noon-zeero a scaen woenu m vaauees. anr one or more exames,e non-zeroer s Keccane rane o,., or m ese vauene rane o,., or more ex M2 a A. m ##KK e = as .. usrae . ,oes a seceasca onen none-z rearnoe oer. coe,.cen.n m aaeansc ounee
Figure imgf000041_0001
ceoece,erocessor ma, ae se oeecoer, a e aeas one nu vaues.n some exnamoe as,eaes onneam ranc reanne a reenrasmoc a r raannee o o anau vvaeuoeosorer , anenu vaues mae reresene as sameerences.n use e aeas one ranenenam 6 o1n'e or m6ore exam6es6,1'e or aosveneer n.n one ocr rane o nu vaues mae− , − or, o zeroenr cuoe vacueens moaenc aueae m swo oore ne ra rnan ane osn e, oe exames,e a erocnessu vaues.
Figure imgf000041_0002
zeroer coecen ase non-zero s or ma a e aeas one non- e nu vaues conanenoc ran weoo ranes o nu vaues, soa ne oraer use.n anes are scaeown e scan we as receve vaues are r.esec aeas one exameusrae .,ewo ranes o ncues. ve-, - an,, ane aeas one non-zeroer coecen veoocn correeson,neo aro ccuersrseonroc m,aa,se a one s a rees ou oe aecoenr,ee ar ae reconsruce zeroer coecenoe aeas one rane.n some e as one non- oane an annverseuanza xames,e reconsruceoc mae n one or more exames,oere reconosnr uunce an venoversoecr,anseorrmoc uenssoroe c murareneroc. e comuaon smaroecon “..ern” aove.n one or mor orm wen comun ^^ or e “ce”erenceeween ean one exames, samex,,ns!e,0a o c!,0n awa a neorn same an curren e aeas one rane,e nu vau.e. an we o nu vaues conanen aove are use.n aeas one es scaeown ane scan we asne vauesncues-, - an, exameusrae .,e aeas one rane o n aeas one exame asusrae, anuaeo aneas, oonre n ^^!o,0n,-zeero “” rearn coeserocmenoncu aens.e. ornee.: . “” ranesrnom someo exa amneosr,!e,0,roece “s”so rran maes,r aome soe o aneeec “o”e rra,nuesromo.nexncan aoweroun an an uerounenn annerme rer receve anoweroun ane ueroun, weree aeas one ranen ae raneeweene eoweoweroun oenermeae rane, or cues aeas one o ars ranenermeae rane an wereers ran a secon rane aovee ueroun oe n one or more exames,nee an,e secon rane are non-aacen. oown acs:n resonseoeermn erocessor maerorm aeas one o ane aeas one non-ze nae aeas one rane comrsesers rane, ae aeas one ra roer coecenoers rane orn resonseoeermnn coeecsen ne comrsese secon rane, ane aeas one non-zeroer ran -oe secon rane.n aeas one exame asusraen.,enermeae n, som,ee exarms raens,ees-, -n, ane secon ranes,. sameerences are u vaues are reresene as sameerences,e e aeas one n comue usn aeas one neorn same an aareer same, oc, aneareorn sames oanerom aeas one neornoc oe curren n one oer moreer e saxmamee cso,rreesonsoe currenoc. oe aeas one neo sameerences are comue usn coor comonens same anerocesrn same o a samen as a coor comonen oeareer resonseoe s sor ma, ae se oeecoer,urererormoown acs:n neorn sameerencesen comue usnuma comonens oe aeas one comonen oameea, an,ase one sameerences, auma ero auma usnrosm,a reer same or,n resonseoe sameerencesen comue erence comonens oe aeas one neorn same, an,ase one same n a onero omr maore exero aroma comonen oeareer same. oe aeas ames,e sameerences are comue usn coor comonens er same a one neorn same o aerennrom a coor comonen oeare acs:n resnerocessor ma, ae se oeecoer,urererormoown on onseoe sameerencesen comue usnuma comonens oe aeas come noeorn same, an,ase one sameerences, an ero aroma usnnernom oa coemaorneens oer saem aeea osr, onne r neesonsoerno seam same, aeenre,nceassee onn ceom samuee ornee.: . examerenecse,s,n reesonseoereo sa amuema coemrenonen oeareer same.n one or severa eroma comonens cesen comue usneuma comonens or omonen oe aeas one neorn same,e ers aross- n o er. e aeas onen rean ore mnocreu exeasmoes,eers ranneu an vauees s aerceo reresene as sameerences, zeroer coecenncues a sa n rane, ane aeas one non- ma, ae se re non-zeroer coecen, anne ,erocessor rane an oeecoer, a e sare non-zeroer coecenooers rane, anne s e s aoecmo een as e.x oanme neosn,-zeero aeears co one ranencuesoers rane ane secon a secon non- ecenncues ars non-zeroer coecen an ecoer, azeroerser n coone-zercoene arn coenceeno,eersr roanceses,o arn a ma,e a secoen s ne oe er coecenoe sec on-zero n some examones, ranne. a aeas onereene ce ,erocessor ma, ae se oeecoer, rane. onsan aseeas one non-zeroer coecenoe aeas one uerounn saosmee o enxa amrees,e annenenrmeex-oa-era rnanee masenneeween aoweroun an anncues aeas one o ars ranee ae, weree aeas one rane rane aovee ueroun oeneorwmeeaoew rearnoeun an o weereneermersa raen raen ane, ore a s seeccoon rane are no n a annenn- rm oaneea oce arn e m. -roanree ex naomes,erocessor ma, ae se oeecoer,urer .s aow cna-rzerousraer coecenoenermeae rane. meoor veo encon a n a meoor veo encon corresonnoe scosure. s sownn.n accorance w some exames oeresen zeroer coneecen.n, soemreo ecxesasmores, mea no,n a-zereo se o an encoer, sna aeas one non- scan we oe aeonu vau er coecen ma reero a non-zero coecen or non-zero scan we maees. anre osnee v oaru meorne eexa rmanees o,e, no.n-z,er oor moerer ornee.: . s e K xe M2 ac A. mc ##KK ea = asnuser raanee o,.., or, moes a seceasca onen none-z rearnoe oer. coe,.cen.n m aaeansc ounee non-zeron.. er ceoe,erocessor ma, ae se oe encoer, a e aeas onenu vaues.n somec eexnamoe as,eaes onneam ranc reanne a reenrasmoc a r raannee o o anau vvaeooer , anenu vaues mae reresene as sameere uesor use e aeas one ra nces.n6 o1n'e or m6ore exam6es6,1'e or aosvenneeneenamc rane o nu vaues mae− , − or, r naonn-eze oroern coue vr ca n. eunens m one or morean one exames,e a oaen acuease owno ranes o nu
Figure imgf000044_0001
non-zero coecen e rane,erocessor ma a e aeas one nu vaues co ansanee nonn-zeoro sc raannes w aere scaoeoow rannes oe non-zneruo v scaaues, soae recevene oraer use.n aeas one exameusrae n we as o vaues are resecve-, - an ,, ane aeas.,ewo ranes coecenn one non-zeroer veoocncu correes.. eso,erocessor ma, ae se oe encoer,er a reconsruce zeroer coecennone ao ae causrr oenne raonce,.nas seom oen e axa rmesues o, ae rene aeas one non- oane an annverseuanzaon un ann consruceoc mae n one or more exame verseransorm unoe currenoc. a comuaon smaros,eoconer “.e. reconesrrnuc”e a vovee.on oonce, or meorreocesasno or maerorm comun ^^ or e “ce”erenceeween a n ne exames, wen samex,!,0, !,0 o cn awa.e. an eorn same an curren e aeas one
Figure imgf000044_0002
e nu vaues scaeow we o nu vaues conanen asne are use.n aeas one exa n ane non-zero scan we vauesncues-, - an,,meusrae .,e aeas one rane o ..n aeas on ane aeas one non-zeroer coecenncues ane “” raneser eoxmamoe asorusra,ee “” raunaeosnrom,o
Figure imgf000044_0003
r ^^!,0, ane “”e r “a”n raesnerosmromo ornee.: . ase on a rensue oer,nereo rceecsosor ma, ae se oe encoer,enerae asream n some exames nsruce veooc. ncan aow ,erocessor ma, ae se oe encoer,urer sna annex oun a eroun an an uerounenn annermeae raneeweeneower eowneroeu un oerouenn,e wrmeereaee a raneaes, o onre a ra sneceonnc ruanese a aeoavse onee o u aerrs raneeownermeae rane an wereers rane ane secon rane are n oun oe n one or more exames,ne ,erocessor moan-aeraocremn a. oown acs:n resonseoeermnnae aeas one rane co eas one o ane aeas one non-zeroer coecenoers ra mrsesers rane, ae aeas one rane comrsese secon ne orn resonseoeermnn coecenoe secon rane.n ae rane, ane aeas one non-zeroer ranes-,,ers ranes-as one exame asusraen.,enermeae n some exames,e, -nu, a vnauees s aerceo rner reanes,. sameerences are comue usn aeas sene as sameerences,e e aeas one neorn sames oan one neorn same an aareer same, oc, aneareer same corr erom aeas one neornoc oe curren n one or more exames,ees soamnseoeer ceunrcreesnoc. oe aeas one neorn same o a sa are comue usn coor comonens same anerocessor ma, ae semen as a coor comonen oeareer resonseoe sameerenc oe encoer,urererormoown acs:n neorn same, an,esen comue usnuma comonens oe aeas one comonen oeareer saase one sameerences, auma ero auma usnroma comone me or,n resonseoe sameerencesen comue erences, arons oe aeas one neorn same, an,ase one same n one omr maore examereos aroma comonen oeareer same. oe aeas one ,e sameerences are comue usn coor comonens er same an neerorn same o aerennrom a coor comonen oeare acs:n reso ocessor ma, ae se oe encoer,urererormoown on nseoe sameerencesen comue usnuma comonens oe aeas come noeneno orne saamree, aer sanm,eas oer, onn reseo snamseoeee sraemncees, anerenceseerno a comroumea ornee.: . usnerencerosm,ae comonenesr oo ae aumeaas co omneo nneen oorne saame, an,ase one same exames,n resonseoe sa reer same.n one or severa eroma com meerencesen comue usneuma comonens or omonen onens oe aeas one neorn same,e ers aross- e aeas onne on rean ore mnocreu exeasmer. oes,eers ranneu an vauees s are reresene as sameerences, zeroer coecenncues a econ rane, ane aeas one non- e m ana, ae sare non-zeroer coecen, anne ,erocessor ran se oe encoer, a e sare non-zeroer coecenooers rane, anne s e s aoecmo een as e.x oanme neosn,-zeero aeears c one ranencuesoers rane ane secon a secon non oecenncues ars non-zeroer coecen an enco -zeroer coecen, anne ,erocessor ma, ae se oe er ceor,e aceneorse s neon-zeroer coecenoers rane, an a e secon non-zero n some examcones, ranne. aane. aeas onereene e ,erocessor ma, ae se oe encoer, r consan aseeas one non-zeroer coecenoe aeas one uerounn saosmee o enxa amrees,e annenenrmeex-oa-era rnanee masenneaeween aoweroun an anncues aeas one o ars raneeo e, weree aeas one rane rane aovee u weoweroun oenermeae rane, or a secon rane are no eroun oenermeae rane an wereers rane ane secon a annenn- rm oaneea oce arn e m. -roanree ex naomn-zes,erocessor ma, ae se oe encoer,urer n some exames,eerreoser coecenoenermeae rane. ncues arocess rove an aarausor veo con.e aaraus roce or an a memor conureo sorensrucons execuae e meosso ars wuereerocessor, uon execuon oensrucons,s conureoerorm an n asnra emeonmen.,e-re. meum comrsn aura orosr aamsos,roorv exeam a neo,nn-raens meomro cromue,r e-rxeeacuaaee soraee ornee.: . anrocoesrs soorrn ansere caommeunenra eenvronmee enncon, moreeorormescnre aove-escre meos ecoe eecon meoescre aove.n one exa e aove or asreamoe e execue erocessor ne comun envronme,eura ororams ma rome veo encoer n. asream oraame sn o receveor exame,normaonor exame, veoocs reresenn reamncun encoe veo or more snax eemens, encoe veorames, anor assocae one envronmen oe ec., an ma asoe execue erocessor ne comun sream oraa rormeecon meoescre aove accornoe receve rocess sream.n anoer exame,eura ororams mae execue e aoveoor encoen veeo cnomormuanon envorro enxmamene, veooeorcorsm rerees eennconn v meoeroamese,scre assocae one or more snax eemens, ec.no asream or anor execue erocessor ne comun envronm aa sream, an ma asoe aa sreamor exame,oe veoecoern.en.eoransmesream or comuer-reaae sorae meum maave so rnave,e non-ransor comrsn encoe veonormaono reeren asream or aaa sream rames, anor assoca r exame, veoocs reresenn encoe veo e veo encoerne one. or u msonre, sonra exxa ememee,nse e ecn.coennera meeo ane esnccroeer aoorv eexaomre,ran asoerco ceormoure er-xraemaae,e seo vraeeo meecoumer mane,or. examneec,o an v,e aoaanao.e n uosne- emor , a- , a manecae, ao sc, an ocaaa soraeevmce occess e. re es n an emomen,eresrove asreamenerae e encon meo emcoreme an,oveer oers arovsreeam aosreeamec coomersne enceocoen v meoenoormeascorneen aeraove.n an encon meoescre aove or encoe veonormaonoeecoe eee e meoescre con rocessorsno arn ex e a amo move. e,meen,roceessso arsorov ane ae comunevce comrsn one or more meum ore memor avn sor non-ransor comuer-reaae sorae or morerocessors, weree one or moreeroceersesonr as, uuoran exe ocuroon oramse exuercaua oerorea omnse, ornee.: . are conurneoerorme aove-escre meos. ns an emomen,eres asorove a comuerroramroucavn enreuraceonsore s eonrcaoen or mreansomssesocnr oe a aovsere oarm en ccomrsn encoe veonormaon eecon meoescre aove.n an e oe veonormaonoeecoe roramrouc comrsn au momen,eres asorove a comuer erocesso ra ororams,or exame,ne memor , execuae meos r ne comun envronmen ,orerormne aove-escre reaae. soorra exea mme,e comuerroramrouc mancuee non-ransor comuer- more sn, an eme s,oumm. aen,nea comrocuesns envronmen maememene w one or s, s, s, conroers, mcrnevces s,rorammaeocevces comonens, o-conroers, mcrorocessors, or oer eecronc n aonr eemroormmnen,e aeroeves a mseoos. sornesream on a no rove a meo o sorn asream, comrsn meu n-ransor comuer-reaae sorae meum or aa sorae meom,e wscreree aeovesr oeram enconceue vs eenoconeorm vaeoonnooremaecooneeneraeeee encon escre a con meo eneraenov ae en. e enmcooermeesncr,eer aeosve a.sno anrove a meoorransmn asream recevn asreamoeec emomen,eres asorove a meoor eescron ooeereseneseccoosuerreeasscre aove. ans noneneoe exausv eenreseneoruroses ousraon varaons, an a e ormeoeresenscosure.an mocaons, avneeneer onaveeemacemnesnareosennse wne aeoarreenonooesscer o oornsn aanr se asnsocea aer rawns. resensconsuesres sse ocncanen seaeo oeerwussrea, avne, or aner oe s sees oe meo accornoe resenscosure are nomeoe orer s s oe meo accornoe accornoracca conons. eccaescre aove,u mae cane eresenscosure mae ausne a, comon,n aee oars oeneee o aceco srens ooera mcecao re acucroermenns.o ornee.: . scosure ane eoxam enaese w oereer cso ssene annesecr areon u onreero exanernces oememenaons anoes uzee rsanescosureor varous varous mocao unernrnces an varousmemenaons w unersooaen ssco ase a ore sueescoosureesar nocuoar uesem coneemoaee s.ecerce eoxrae,soememenaonsscose ana mocaons an oermemen mes oencue wne scoe oeresenscosure. aons areneneoe

Claims

orne e.: . .a mes c r aecoam ev oe nn vs: ,,eo aec eeoceon coere,, r a com ,eea asrs on enae: s n oonne-z neoro er coecen a namc n-zero er coeceno aeas one ranen ase on ae r rran ene su, o aa o aeev nceooeo er, a a reee acr son osnreu ncoenu n-z v v eroeaoues eroc an coe corcreesnonone aoe aas cu ornreen ranoec., . e meo o nee recevn a cnanmex,unrcear cnom arsn: ra oweroun an an ueroun enn annermeae o en wweereenneeo aweeraso ounne r aanne ceom uresreso auneas one o ars rane weremreenaee ranrse r,a onr ae s aencone r saencoen a roavnee aere u noenr-aouancen o.eneeromweeaeow raenreou ann e.as oen mee ranoe o com cam, weren a n e aeas one non-zero er coecenoe a n resonseorseese aeas one ooown acs: e aeas one non-zerormern conecaeneo aeeasrs o rne rane comrsesers rane, a n n resonsen-ozereoermern cnoecaene aoeeas se ocnoea n rnae or e aeas one no rnanee c.omrsese secon rane, a n . e m weeroen o cea samm,e wereerenncees are cnu vaues are reresene as same erencesare er omue usn aeas one ne orn same an a o e c wurreenr seamne oce a an , aneas oenear nee oerr snam same coerrse osoannseorome c aurreeans onoec n.e orn oc o.ee a meeaos o one c naem,o wrnere sanmee s oam a seameerennce ass a are co coomr cuomeo unsenn o coore coamreonenesr ornee.: . same w an eas onene ne rreesnoonrsee m noeo same sau emre , aer com ne,rerns ace ses es: oenne co sammuee usenrenceusm,a a coumonens oe a uma com a aeasr oonme ro a nen cese ma ero a nonns o omooe nroea enn o ser am saem eeeer samerenece osren comue usnroma comonens oeo a,r aener, saamsee o.ne sameerences, aroma er . saem ae m eeae aso n one o ne camor,n w searmenee o sa ameerenerenncesro amre a co cmoour ceom usonne cno oor coemaroneens oer w ceoams oonnee nne ne rreesnoonrse ne moeo same seau ,mre aer com ne,rer ans sce eess: onene s caommeuee ursennces,u amna comoenrenos a oroem aa aeas onne r oe nseoensaer oroe nee a sra smarm sam ee,ee o e aerr r samnen e,ces .aseen on comue usnroma comonens oe uma comonen oe e sameerences,e ero a co.moene mneso o cam, werene sameerences are comue usneumas aross-o omroenenroma comonens oer.e aeas one neorn same, ane er .e m weeroen o cea ameas, w oneere rannee c nu vaues are reresene as sameerences aeas one non-zeroer coecen coommrrsseessoers rane ane secon rane, ane comrs aens: weren ane aeas one no an- szearroe neorn- czoeeroceenr cooeec aeneas one rane ane sare non-zeroer coecenooers rane ane secon rane. ornee.: . se.cone m raeo o cam, werene aeas one rane comrsesoers rane ane coecenn ane, a an see aeas one non-zeroer coecen comrses ars non-zeroer comrs weeren aconn none-ze aroeaser o cnoee nocne-nzero aner coecenoe aeas one rane non-zero as: er cnoeecenrso none-z seercoone rran coee.cenoers rane, an ane secon ea.s onee m raenoe o cam, weren ane aeas one non-zeroer coecenoe a coec aenon co e am aeer aas sses: o onnee ranree.ene non-zero consan ase aeas one non-zeroer an. ueer meouno oas cea om, weren annermeae raneseneeween aoweroun an werene aena areenenex-o-rane manae oenermeae ranes, o orn ae s reane comrses aeas one o ars raneeoweoweroun wereners rane ancone r saencoen a roavnee aere u noenr-aouancen o.enermeae rane an .e a meon o an cnaemrme,uare-erran come norns-nzer:oer coecenoenermeae rane. . m senoa on, veo an en encoconer,, a comeasrs onne: no anam ac rn, e encoer,e aeas onen- nzoenro-zeroer coeer coceenceno aeas one ran ase on a rran ene su, o aa o ae env en e nceooeore, a a ree ecr aosns onruec nenu on- v v zerea ooues eorc an co ceorrcesenonone ao ae causrrenoc, an one rane oc.eneran,e encoer, asreamase on a resu oerne reconsruce veo ornee.: . .e ranee s me wneao enn o e an ca ownm eerxon,u uncrae annr c aom eo uwres ern ro:un an an uerounenn annermeae oen weremreenaee r aaneaes, o orn ae s reacnone c roamner aseso ov aun eeaes u oneer oo aunrs o raneeneeromweoweroun wereners rane ane secon rane are non-aacen. eae rane an ea.s onee meo o cam, weren ane aeas one non-zeroer coecenoe a n r raense comrses aeas one ooown acs: e aeas oneo nnosen-zoeroeermern conecaee aeas one rane comrsesers rane, an n re osneon nsoen-ozereoermern cnoecan ene ao oee easrs rane or e aeas se ocnoen ra rnanee c.omrsese secon rane, an .e meo o cam, werene nu vaues are reresen e werene sameerences e as sameerencesar are comue usn aeas one neorn same an a oe c wer urreenr seamne oce a an , aneas oenear neeoerr snam same coerrse osoannseorome c aurreeans onoec n.eornoc o. samee e a meeaso o one c naemo,r wne sraemnee o sam a saemeernenc aess a ar ceo coorm coumeo unsenn o coore coamreonenesr w an eas onene ne rreesnoonrsee m noeo same sau emre , aer com ne,rerns ace ses es: oen comue usnuma comonens oe a uma comonen ne sameerences, auma ero a n resons oeoeaer saemeer samerenec or aeas on esen comue usnroma comonens oeo aromea n ceomoonrenn o sameea,r aener, saamsee o.ne sameerences, aroma er ornee.: . o.e meo o cam, werene sameerences are comue usn coor comonens ere sa aeas one neorn same o aerennrom a coor comonen oeare wm nee rree a snn onsee moeoe saumreer comererses:ea ncesen comue usnuma comonens oe a coms oonnee nne ooernar seameer, s an,ase one sameerences, an ero aroma aeas onne re nseonseoe samamee oerrencesen comue usnroma comonens oe uma comonen oornea sramee,e ar samne,.ase one sameerences,e ero a com.oneen mse oroe o croamma com, woneernene sameerences are comue usneumas aross-omonen s oer.e aeas one neorn same, ane er .e w meereon oe c aameas o,n we rearnene coemrsesnuo vaueesr asre ra renresene as sameerences aeas one non-zeroer coecen comrses a sare non-zeroe ane secon rane, ane an weren ane aeas one non-z er coecen comrse eroer coecenoe aeas one rane as:ne sare non-zeroer coecenooers rane ane secon rane. sec.one r maneeo, an o caem ae,a wse orneen none-z aeroeas one rane comrsesoers rane ane coecen an a secon non-zeroer coecener a cnoecen comrses ars non-zeroer comrs weeren ane aeas one non-zeroer coecenoe aeas one rane non-zero as: er cnoeecenrso none-z seercoone rran coee.cenoers rane, an ane secon orne e.: .ea.s onee m reano o cam , weren a n e aeas one non-zero er coecenoe a coec aenone co e am aeer aas sses: o onnee ranree.ene non-zero consan as e aeas one non-zero er an. ueer meouno oas cea omn a,r weeerenne annnexer-moe-ranae ranesene eween aoweroun an werene aeas one rane comrses a e ma nae o enermeae rane, or a secon rane aoveeaes u oneer oo aurs raneeoweoweroun wereners rane an e secon rane are non-aancen o.enermeae rane an . e a meon o an cnaemrme,aure-rearn coem nonr-szenro: er coecenoenermeae rane. .n a onea orar musoor veoecon, comrsn: execua ae memorre e o cnoeuroc oeessoors aen one or morerocessors an conureo sorensrucons w r morerocessors, erormeer meneoe onne an or m onoere or coacemsssors-, u.on execuon o ensrucons, are conureo .n a onea orar musoroer vroceeoss eonrcso an, comrsn: execua ae memore o coueoen one or morerocessors an conureo sorensrucons erorm weer meneoen oe nn oer an o mro mr onoe erero orc coe acsseo mssr sos,rs,- uo.n execuon o ensrucons, are conureo ns.ruc noonns-raan,s woren c eoxmecuueer-rea oanee or s moroaree co mmeuuemrror sorn comuer-execuae comuerrocessorsoerorme meon an one o camsoce-sso.rs, causee one or more ornee.: .ns.ruc noonns-raan,s woren c eoxmecuueer-rea oanee sorae meumor sorn comuer-execuae comuerrocessorsoerorme meo orn m aonre o cnoem ou cearmrsoces-sor.s, causee one or more e. me nono-rann asnor on ceo om cuaemr-rsea-a.e sorae meumor sorn asreamoeecoe me.o nonn- arnans onoer o c comamuser-r-ea.ae sorae meumor sorn asreamenerae e com.u mere-reoaaoer s soorrane m aeusmr,ea wm,er ceomrsn sornesream on a no mnse-.sream n-ransor enerae e meon an one o ca comrses encoe veonormaon com.u mere-reoaaoer s soorrane m aeusmr,ea wm,er ceonmresnsr seaomrnesream on a non-ransoroeecoe e meon an one o cams-. comrses encoe veonormaon me.o men aono ornera ons cmamns a-s.ream, comrsnransmnesreamenerae e me.o men aon oonre re oce cvanms a-s.ream, comrsn recevnesreamoeecoe e
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