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融合結果多尺度子波圖像融合