A Matlab Playground for the JPEG Standard.docx

A Matlab Playground for the JPEG Standard.docx

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AMatlabPlaygroundfortheJPEGStandard

Kolev,Nikolay

Pekarske,Andrew

ECE533

FinalProjectReport

12/12/03

NikolayandAndrewPresent:

AMatlabPlaygroundfortheJPEGStandard

Introduction:

ThegoalofthisprojectistoprovidemoreuseroptionsfortheJPEGEncoderprovidedbyProfessorHuforMatlab,exploredifferentlosslesscompressionapproachesandfrequencytransformperformanceapplicabletotheJPEGstandard,aswellasprovideacorrespondingJPEGDecodercomplementingProf.Hu’sJPEGdecoder.TheMatlabcodefromthisprojectisthoroughlycommentedandlaidoutinorganizedwaysothatanyonefamiliarwithMatlabcouldunderstandwhatistakingplaceintheprogram.Thisprojectintroducesthefollowinguserrun-timeoptionstotheJPEGDecoder/Encoderpair,whichwouldaidothersinunderstandingandlearningoftheJPEGstandardanditsrelatedconcepts.

RuntimeJPEGOptions:

1.ImageSelection:

a）p64int.txt（64x64）

b）Samplefrom8.28（8x8）

c）Zelda（128x128）

d）Barbara（256x256）

e）Lena（512x512）

2.TransformSelection

a）DCT（discretecosinetransform）

b）FFT（fastfouriertransform）

3.QuantizationMatrix

a）Samplefrom8.37

b）CompressionRation=8forSNM_Quantizer

4.EncodingMethod

a）Huffman

b）Arithmetic

Themotivationforthisprojectwastwofold.ThefirstistocreateawaytolearnmoreabouttheJPEGandtheoreticalandtechnicalimplementationofalgorithmsthatsuccessfullycompressinganimageandalsohelpotherstudentsorreadersinterestedinthisfieldtolearnactively.ThesecondreasonforundertakingthisprojectwastohavefunprogrammingandtolearnmoreaboutMatlab.

Approach:

Westartedtheprojectbycarryingoutresearchonlineandinseverallibraries.UsingtheUW-MadisonLibraryJournalsdatabasewesearchedthrougholdIEEEjournalslookingforpapersrelatedtoJPEGStandard（notJPEG2000）optimizations.Aspecificareaofinterestwehadwasadjustableoradaptablequantizationmatrixgeneration.WeinitiallylookedattheWUBAalgorithmbutdeemedittoocomplexforthescopeoftheproject.LaterwefoundapaperbyB.G.Sherlock,A.NagpalandD.MMonrocalled“AModelforJPEGQuantization”whichwasfeaturedinthe1994InternationalSymposiumonSpeech,ImageProcessingandNeuralNetworks（13-16April1994,HongKong）.WedecidedtocallourimplementationofthismodelSNM_Quantizeraftertheauthorsofthepaper.

OncewehadoneruntimeoptionfortheJPEGencoderwestarteddiscussingotherfeaturesoftheJPEGstandardthatwewereinterestedinmodifying,likethediscretecosinetransform,Huffmanencoder,andblocksizes.Althoughchangingblockprocessingsizewaslaterdroppedduetotimeconcernsandcomplexityofparameterizingallofoursourcecode,itwasdecidedtoaddauniqueimplementationofarithmeticencoding,amethodforgeneratingpossiblyadaptivequantizationmatrix,aswellasusinganalternativetransformsuchasFourier.

TherealsowastheadditionaltaskofcreatingacorrespondingJPEGdecoderforthenewandoriginaloptionsoftheJPEGencoder.Someofthecodingforthedecoderonlyinvolveddoingtheexactsameoperationsdoneintheencoderbutcarryingthemoutinreverseorder.Butalargeportionofthecodinginthedecoderhoweverwasslightlymorecomplexthanthis,andprovedtobeagoodchallenge.

TasksPerformed:

ThelayoutoftheencoderanddecoderMatlabcodeissuchthattheyorganizedinseparatedirectoriesandoutputfilestoashareddirectory.Thispromotesthetruenatureofencodinganddecodingimagesbyforcingthedecodertorunonlyfromtheencodedvaluesoutputbytheencoder.Ifbothencoderanddecoderwereinthesamefile,certainvaluescouldbereusedinthedecoderthatcouldonlybemadeintheencoderbyhavingtheoriginalinputimage.ThereforewhentestingtheperformanceofdifferentJPEGalgorithms,onemustfirstruntheJPEGencoder（jpegencode）intheJPEG_EncoderdirectoryandthentodecodethatencodedimageonemustopentheJPEG_DecoderdirectoryandruntheJPEGdecoder（jpegdecode）.

ThisprojectbeganbyexaminingtheEncoderanditsrelatedmodulesprovidedbyprofessorHu.Afterintenselystudyingtheencoderwewereabletostartworkondevelopingthedecoder,andspecificallytheHuffmandecoding,whichprovedtobeconsiderablytimeconsuming.WhiletheHuffmandecoderwasbeingdesigned,anarithmeticencoderanddecoderweremadetomakeuseoftheMatlabsuppliedarithencoandarithdecomodules.Afterwardtheunzig-zagandinversequantizerandtransformcodewasfinished.

DuringthetestingphaseitwasfoundthatthearithmeticencodingasdesignedhadfilesizesthatwerequitelargewhencomparedtoHuffmanencoding.ThedecisionwasmadetoaddEOBsymbolstothisencodingwhicheventuallymadetheencodedfilesizesrelativelycomparable.

Onceallthemoduleswerecompletelycoded,changesandrefinementstotheuserinterfacewereintroduced.Thisallowedtheusertoeasilyselectwhichtransform,quantizationmatrix,image,andencodingmethodistobeused.Inthefinalstage,codewasaddedattheendofthedecodertoaidthevisualcomparisonbetweentheoriginalandcompressedimages.

Results&Discussion（TransformSelection）:

ThepurposeofthetransforminaJPEGstandardistoeliminatehighfrequenciescomponentsinanimage,whichareinpracticenotessentialforimagequalitybecausetheyaregenerallynotwelldiscernedbythehumaneye.Thisstepattemptstopackasmuchinformationaspossibleinaslittlespaceaspossible.Tothiseffect,accordingtoGonzalez&Woods,theperformanceofDCTissuperiortothatofFouriertransform.

TheresultsfromtheactualJPEGcodehoweverproducedaresultthatwasslightlyinconsistent.Thisisaknownunder-exploredareaoftheprojectaswewereunabletogetthealternateFFTworkingtoproduceavalidoutputimage.Somevisualresultsfollowbelow:

Original

DCT

FFT

Results&Discussion（QuantizationMatrixSelection）:

UsingHuffmanencoding,theDCT,andimages0through4weobtainedthefollowingcompressedimagesizeswithdifferentquantizationmatrices.

InherenttotheJPEGStandard,quantizationisthelossystatethatdoescertainportionofthecompression.Thelargerthevaluesinthequantizationmatrix,themoreinformationisremovedwhichinturnresultsinsmallercompressedfiles/coefficientruns.IngeneralwhentheSNM_Quantizerisusedatacompressionratioof8,thequantizationvaluesarelargerthanthoseofthedefaultquantizationmatrix.Aftertheimageissentthroughatransformandzig-zagordered,themajorityofthe“valuable”imageinformationispackedintheupper-rightcorneroftheprocessedblock.Ifthevaluesofthequantizationmatrixarelargerthanthevaluesintheprocessedblockatthepointwhenthequantizationoccurs,thevaluesintheprocessedblockaresetto0（retainingonlytheintegerpartoftheresult）,effectivelyremovingcoefficientsofsmallmagnitude.Whentherearemorezeroes,thesizeoftherunlengthofzeroesincreasesandanEOBsymbolcouldbeusedtorepresentthem,whichyieldsremarkabledatacompression（describedintheencodingselectionsectionbelow）.

Ontheotherside,removinginformationfromtheoriginalimageinordertoreducethesizeoftransmittedencodedimagealsomightdrasticallyreducethequalityoftheimageandmakesitappearmore“blocky”.Therefore,dependingupontheapplicationforwhattheencodedimagesareneededfor,onemightneedtoevaluatethetrade-offbetweenimagequalityorlowerfilesizes–smallerimagesizespeedsuptransmissionalongbandwidthconstrainedchannels.

Iftimepermitted,itwouldhavebeeninterestingtoaddadditionalquantizationmatrices,orevenanimage-adaptivequantizationmatrixgenerator.Thiswouldprovidetheoptimalquantizationmatrixforeveryprocessedblockoftheimage,maintaininghighvisualquality,whilealsodrivingdownthefilesize.

BelowarethreeimagesoftheeyeofLenawithdifferentquantizationmatricesselected.Thereissomenoticeabledifferencebetweentheoriginalandthedefaultquantizationmatrixasthewhiteintheeyeappearsslightlygrainier.OnecouldnoticedefinitelymoregraininessintheresultproducedwiththeSNMquantizationmatrix.

Original

DefaultQuantizationMatrix

SNMQuantizationMatrix

Results&Discussion（EncodingSelection）:

UsingthedefaultquantizationmatrixandtheDCTforencodingimages0through4weobtainedthefollowingcompressedimagesizeswithdifferentencodingmethods.

（*Sizedoesnotincludeadditionaloverheadfilesnecessaryfordecoding）

ItisclearlyshownthatourspecialimplementationoftheArithmeticEncodingAlgorithmistypicallynotasefficientastheHuffmanEncodingalgorithm.Atfirstglancethisdoesnotseemtomakeanysense,asarithmeticencodingtypicallydoesabetterjobofreachingacompressionthatiscomparablewithasequence’sentropy.Therearehowever,severalfactorsthatcomeintoplaythataffecttheresultsfromthisMatlabfile.

Firstitisimportanttonotethatadifferenceintransform,orquantizationmatrixwouldaffectthesizeofrunlengthsofzerosthataparticularimagemighthaveafterblockprocessingtheimagewithaparticulartransformandthenquantizingit.Bothencodingmethodshandlerunlengthsimilarlysuchthatwhenablockof64valueshasnomorepositivevalues（onlyzerosremain）,anEOB（endofblock）symbolisinsertedintothesequencetobeencoded.TheonlydifferencebetweenthetwoisthatHuffmanusesadefaultvalueof999foranEOBsymbol,whileArithmetictakestheadaptiveapproachbysettingitsEOBsymboltooneplusthemaximumvalueinthesequence.Thearithmeticencodingchoosesthisi