灰色理論w鄧聚龍、郭洪 編著w全華出版w報告：王乾隆大綱w灰色系統w灰生成w灰建模w灰預測什麼是灰色-GreyTheoryw1982GreySystemTheory 鄧聚龍提出w針對系統模型之不確定性及資訊之不完整性，進行系統的關連分析及模型建構，並藉著預測及決策的方法來探討與瞭解系統。w信息不完全、不確定的系統w研究少數據不確定性的學科Grey、Probability、Fuzzy的區別灰生成w灰色系統理論：序列的變換為序列生成； 稱序列中的變換為數據生成或數據構造w數據生成n數據處理，加工n數據累加，累減n數據差補或剔除n數據組合n數據映射、取代、借用 w數據生成的目的n數據相對值化：初值化、平均值化、區間值化n極性變換：效果測度n層次變換：累加生成、累減生成灰生成累加生成AGOw定義w條件累減生成IAGOw定義w條件灰建模w用序列建立具有部分微分方程性質的模型w部分微分方程性質的模型即微分方程模型w微分方程模型n只適合連續可微的對象n屬於無窮信息空間GM(1,1)w定義型w白化型w白化響應式灰色預測-1wGM(1,1):graymodelone-orderonevariancewExample:nGM(1,1)之預測方程式為：灰色預測-2w建立GM(1,1)之步驟：w輸入：一原始數據序列。w輸出：GM(1,1)預測模型。w步驟 1:求出累加生成序列如下：w步驟 2:求出之均值序列如下：灰色預測-3w步驟 3:求中間參數C, D, E, F如下：w步驟 4:計算式（1）中之a、b係數如下：發展係數灰作用量灰色預測-4w假設一時間序列如下所示：37471.99, 37460.05, 37222.60, 36895.52, 35734.30 灰色預測-5灰預測w先建立GM（1,1）模型，依據此模型進行預測。分為：n數列灰預測n災變灰預測n季節災變灰預測以灰色預測頻率空間為基礎的影像壓縮技術GreyPredictionandFrequency-DomainBasedImageCompressionw作者：黃詠淮、謝明興、曾定章、莊永達w2000年灰色系統理論與應用研討會w報告：王乾隆Architecture Original Image DWT EZW Grey(1,1)compression compression imageHuffman codeDWT(DiscreteWaveletTransform)HL1HL2HH1LH1HH2LH2HL3HL4LL4EZW(EmbeddedZerotreeWavelet)wWavelettreeEZW(EmbeddedZerotreeWavelet)wZerotree:ifallthevalueofsomeonewavelettreeelementsnomorethenthresholdT1wasgiven.Thenwecallthesub-wavelettreeiszerotree.wZerotreeimplythattheblockwassmoothlyanditisnotveryimportanttoimage.UsedGreyPredictiontoCompressionwAfterDWTandEZWwehaveasequencedata.wIfsomepointisnomorethenthethresholdT2,thenwemaketheGM(1,1)modelelseornot.wIfn=4wastheworstcase,butn4wasnot.nn,a,breplacethemodelsequences.ApplyZerotreetodistinguishbetweentheinsignificantandsignificantcoefficientswMorethenthresholdT1issignificantcoefficientsthatisimportantforanimage.wIfnomorethenT1,itisthesmoothpartsofanimage,sowereplacethembyzerotoincreasethecompressionrate.DWT+GM(1,1)tocompressionImage-1wStep1:Originalimage4levelDWTthengot13wavebands.wStep2:encodingLL4byuniformquantization.均勻量化wStep3:for13wavebandssetupthezerotree.nStorethesignmapofsignificantnStoretherelationbetweensignificantandinsignificantcoefficientsDWT+GM(1,1)tocompressionImage-2wStep4:applytheGM(1,1)tomodelthesignificantsequences.Storethen,a,b.wStep5:encodethesignificantcoefficientssignmap,uniformquantizationofLL4,allthen,a,b.wStep6:decode.inversethecompressionsteps.ExperimentwCR:compressionrationnCR=(bitsoftheoriginalimage)/(bitofcompressionimage)ConclusionwGreymodelisgoodtohighcompressionratewSignmapproblem,storethesignmapincreasethedata.wOnlyletthegreymodeltopredicttheoriginalwavelettree,dontcarethesignproblem,thenwecanraisethecompressionqualityreally.