向量量化编码

CompressionCode

VectorQuantization向量量化编码

在向量量化编码中，则是把输入数据几个一组地分成许多组，成组地量化编码，即将这些数看成一个k维向量，然后以向量为单位逐个向量进行量化。向量量化是一种限失真编码，其原理仍可用信息论中的率失真函数理论来分析。

Principleofvectorquantizationencoding衡量两个向量之间接近程度的度量标准可以用均方误差准则：其他准则????在向量量化编码中，关键是码本的建立和码字搜索算法。

码本的生成算法有两种类型:一种是已知信源分布特性的设计算法；另一种是未知信源分布，但已知信源的一列具有代表性且足够长的样点集合（即训练序列）的设计算法。码字搜索是向量量化中的一个最基本问题，向量量化过程本身实际上就是一个搜索过程，即搜索出与输入最为匹配的码字。

DiscreteCosineTransformFFT一个变量的周期函数g(x)能够通过傅立叶级数表示出来：系数（A0、An和Bn）的值按照下面的公式计算：

傅立叶变换(FourierTransform)的物理意义：将信号从时间域（timedomain）变换到频率域（frequencydomain）。DFT正变换：给定一个二维信号的样本序列{x(k,l),k=0,1,…,N-1,l=0,1,…,N-1}，二维离散傅立叶变换（2D-DFT）

：

逆变换：

DCTTheDFTtransformsacomplexsignalintoitscomplexspectrum.However,ifthesignalisreal(asinmostoftheapplications),halfofthedataisredundant.(Theimaginarypartofthesignalisallzeroandboththerealandimaginarypartsofthespectrumaresymmetry.)Asarealtransform,Discretecosinetransform(DCT)transformsrealdataintorealspectrumandthereforeavoidstheproblemofredundancy.AlsoasDCTisderivedfromDFT,allthedesirablepropertiesofDFTarepreserved.一个变量的周期函数g(x)能够通过傅立叶级数表示出来：系数（A0、An和Bn）的值按照下面的公式计算：

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运用filter中：低通滤波器为高通滤波器为的小波变换的LL和LH分量Step1:的每行进行偶延拓得到

的每行进行低通滤波得到

Step2:Step3:的每列进行偶延拓得到

的每列进行低通滤波得到Step4:隔二抽一得到LL分量

的每列进行高通滤波得到

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.多尺度子波图像融合—结构图待检原始彩色图像光线校正YCbCr肤色HIS肤色像素级融合融合不同肤色模型下的肤色图彩色图像转化为灰度灰度图像的小波LL子图像HL子图像LH子图像像素级融合子图像人脸检测和校验原始图像人脸区域及尺寸根据人脸边缘特征，运用多尺度子波图像融合算法:

多尺度子波图像融合--YCbCrRGBYCbCr空间Y分量

YCbCr空间Cb分量

YCbCr空间Cr分量多尺度子波图像融合--肤色图像YCbCr空间的肤色分割多尺度子波图像融合--肤色图像多尺度子波图像融合--HSIHSI空间的肤色分割多尺度子波图像融合—HIS和YCbCr

YCbCrHSI融合结果多尺度子波图像融合