向量量化編碼

CompressionCode

VectorQuantization向量量化編碼

在向量量化編碼中，則是把輸入數(shù)據(jù)幾個一組地分成許多組，成組地量化編碼，即將這些數(shù)看成一個k維向量，然后以向量為單位逐個向量進行量化。向量量化是一種限失真編碼，其原理仍可用信息論中的率失真函數(shù)理論來分析。

Principleofvectorquantizationencoding衡量兩個向量之間接近程度的度量標準可以用均方誤差準則：其他準則????在向量量化編碼中，關鍵是碼本的建立和碼字搜索算法。

碼本的生成算法有兩種類型:一種是已知信源分布特性的設計算法；另一種是未知信源分布，但已知信源的一列具有代表性且足夠長的樣點集合（即訓練序列）的設計算法。碼字搜索是向量量化中的一個最基本問題，向量量化過程本身實際上就是一個搜索過程，即搜索出與輸入最為匹配的碼字。

DiscreteCosineTransformFFT一個變量的周期函數(shù)g(x)能夠通過傅立葉級數(shù)表示出來：系數(shù)（A0、An和Bn）的值按照下面的公式計算：

傅立葉變換(FourierTransform)的物理意義：將信號從時間域（timedomain）變換到頻率域（frequencydomain）。DFT正變換：給定一個二維信號的樣本序列{x(k,l),k=0,1,…,N-1,l=0,1,…,N-1}，二維離散傅立葉變換（2D-DFT）

：

逆變換：

DCTTheDFTtransformsacomplexsignalintoitscomplexspectrum.However,ifthesignalisreal(asinmostoftheapplications),halfofthedataisredundant.(Theimaginarypartofthesignalisallzeroandboththerealandimaginarypartsofthespectrumaresymmetry.)Asarealtransform,Discretecosinetransform(DCT)transformsrealdataintorealspectrumandthereforeavoidstheproblemofredundancy.AlsoasDCTisderivedfromDFT,allthedesirablepropertiesofDFTarepreserved.一個變量的周期函數(shù)g(x)能夠通過傅立葉級數(shù)表示出來：系數(shù)（A0、An和Bn）的值按照下面的公式計算：

2DDCT2D-DCT:2D-IDCT:The2D-DCTisseparable!

TheDCT,unliketheFouriertransform,isspatiallyvariant.

TheDCTissensitivetophase,sothatanobjectmovingacrossthescreenwillhavedifferentfrequencycontentfromframetoframe.

Thisalsomeansthatthevisibilityofcodingartifactsduetocoefficientquantizationwillvarysomewhatdependingonthepositionofanobject(edge)intheimage.

becausetheDCTisastrictlyboundedblocktransform,lossycodingwillproduceblock-edgemismatchwhichwillbevisibleatsomelevelofquantizationevenifthereisonlylowfrequencycontentinthatarea.Blocksize8×8????smallblockfastercorrelationexistsbetweenneighboringpixelslargeblockbettercompressioninsmoothregions20020218918818917517517520020319818818918217817520320020019520018718517520020020020019718718718720020520020019518818717520020020020020019018717520520019920019118718717521020020020018818518718651565-12412-85-163200-11-23-12611-1301-2-83-42-2-3-5-20-27-540-1-40-3-1041-103-2-333-1-1-3-25-24-22-30ThefirstcoefficientB(0,0)istheDCcomponent,theaverageintensityThetop-leftcoefficientsrepresentlowfrequencies,thebottomright–highfrequenciesZig-ZagScan123451565-12412-85-163200-11-23-12611-1301-2-83-42-2-3-5-20-27-540-1-40-3-1041-103-2-333-1-1-3-25-24-22-30QuantizationIdea:getridofthefrequenciesintheimagethatareirrelevanttothehumaneye.TwodifferentmethodsforquantizationUniform(dividingbyaconstantnumber)UsingquantizationtablesQuantizationtablescanbescaledupordowntoadjustthequalityfactor1611101624405161121214192658605514131624405769561417222951878062182237566810910377243555648110411392496478871031211201017292959811210010399326-100000-10000000-10100000-100000000000000000000000000000000000000051266-1000000-120000000-1401600000-1400000000000000000000000000000000000000019919619118618217817717620119919619218818318017820320320220019518918318020220320420319819118318020020120220119618918217720020019919719218618117720420219919519018618318120720420019419018718518416-227-3-2-1-142-41-1-2-30-3-2-55-22-5-2-3-4-3-1-44804-2-1-1-1520013846-2120511463-406-2-222conclusionDCTenablesimagecompressionbyconcentratingmostimageinformationinthelowfrequenciesLooseunimportantimageinfo(highfrequencies)bycuttingB(u,v)atbottomrightThedecodercomputestheinverseDCT–IDCTRGB?YUVConversionRGBtoYUVY=(0.257*R)+(0.504*G)+(0.098*B)+16Cb=-(0.148*R)-(0.291*G)+(0.439*B)+128Cr=(0.439*R)-(0.368*G)-(0.071*B)+128YUVtoRGBR=1.164(Y-16)+1.596(V-128)

G=1.164(Y-16)-0.813(V-128)-0.391(U-128)B=1.164(Y-16)+2.018(U-128)ChrominanceSub-SamplingHumaneyeismoresensitivetowardschangesinluminanceratherthanincolorLuminanceQuantizationTable

ChrominanceQuantizationTableLimitationoftheDCTTimesignaltransformthefrequencyinformationNotemporalapplicationDatacompression(JPEG)SignalanalysisWatermarkingWaveletTransformCodingMulti-resolutionanalysisofthesequence:takingaveragesanddifferenceandkeepingresultsforeverystep.Forimages,thiswouldbeequivalenttocreatingsmallerandsmallersummaryimages,one-quarterthesizeforeachstep,andkeepingtrackofdifferencefortheaverageaswell.Mentallystackingthefull-sizeimage,thequarter-sizeimage,thesixteenthsizeimage,andsoon,createsapyramid.thefullset,alongwithdifferenceimages,isthemulti-resolutionanalysis.Theobjectiveofthewavelettransformistodecomposetheinputsignal,forcompressionpurpose,componentsthatareeasiertodealwith;havingspecialinterpretations,havingsomecomponentsthatcanbethresholdaway.Furthermore,wewanttobeableatleastapproximatelyreconstructtheoriginalsignal,givethesecomponents.Supposewearegiventhefollowinginputsequences:Considerthetransformthatreplacestheoriginalsequencewithitspair-wiseaverageanddifference.Wavelettransformdecomposesasignalintoasetofbasisfunctions.Thesebasisfunctionsarecalled

waveletsWaveletsareobtainedfromasingleprototypewavelet

y(t)calledmotherwavelet

bydilationsandshiftingwhereaisthescalingparameter

bistheshiftingparameterThecontinuouswavelettransform(CWT)ofafunctionfisdefinedasIfyissuchthat

fcanbereconstructedbyaninversewavelettransform:

DiscretewaveletsDiscretewaveletsareformedamotherwavelet,butwithscaleandshiftindiscretesteps.Notethat:

1):wechangethescaleoftranslationalongwiththeoverallscale2j,soastokeepmovementinthelower-resolutionimageproportion.

2):AlargeindexjcorrespondstoacoarserversionoftheimageMulti-resolutionanalysisprovidethetoolto

adaptsignalresolutiontoonlyrelevantdetailsforparticulartask.Mallatdecomposesasignalintoanapproximationcomponentandadetailcomponent.Theapproximationcomponentisthenrecursivelydecomposedintoapproximationcomponentanddetailsuccessivelycoarserscales.Waveletsaresetupsuchthattheapproximationatresolution2-jcontainsallthenecessaryinformationtocomputeanapproximationatcoarserresolution2-(j+1)Waveletsareusedtocharacterizedetailinformation.Theaveraginginformationisformallydeterminedbyakindofdualtothemotherwavelet,calledthescalingfunctionWeperformthe2-Dwavelettransformbyapplying1-Dwavelettransformfirstonrowsandthenoncolumns.LHLLLHHLHHLL1HL1LH1HH1LL2HL2HL1LH2HH2LH1HH1HL2HL1LH2HH2LH1HH1LL3HL3LH3HH3firstSecondThird運用filter中：低通濾波器為高通濾波器為的小波變換的LL和LH分量Step1:的每行進行偶延拓得到

的每行進行低通濾波得到

Step2:Step3:的每列進行偶延拓得到

的每列進行低通濾波得到Step4:隔二抽一得到LL分量

的每列進行高通濾波得到

Step5:隔二抽一得到LH分量

96.64%0.41%0.92%0.35%0.94%0.27%0.43%ApplicationsSignalprocessingTargetidentification.Seismicandgeophysicalsignalprocessing.Medicalandbiomedicalsignalandimageprocessing.Imagecompression(verygoodresultforhighcompressionratio).Audiocompression(achallengeforhigh-qualityaudio).Signalde-noising.多尺度子波圖像融合—結(jié)構圖待檢原始彩色圖像光線校正YCbCr膚色HIS膚色像素級融合融合不同膚色模型下的膚色圖彩色圖像轉(zhuǎn)化為灰度灰度圖像的小波LL子圖像HL子圖像LH子圖像像素級融合子圖像人臉檢測和校驗原始圖像人臉區(qū)域及尺寸根據(jù)人臉邊緣特征，運用多尺度子波圖像融合算法:

多尺度子波圖像融合--YCbCrRGBYCbCr空間Y分量

YCbCr空間Cb分量

YCbCr空間Cr分量多尺度子波圖像融合--膚色圖像YCbCr空間的膚色分割多尺度子波圖像融合--膚色圖像多尺度子波圖像融合--HSIHSI空間的膚色分割多尺度子波圖像融合—HIS和YCbCr

YCbCrHSI融合結(jié)果多尺度子波圖像融合