Grey theory 灰色模型.ppt

按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,*,灰色理論,鄧聚龍、郭洪 編著,全華出版,報告：王乾隆,大綱,灰色系統,灰生成,灰建模,灰預測,什麼是灰色,-Grey Theory,1982 Grey System Theory,鄧聚龍提出,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。,信息不完全、不確定的系統,研究少數據不確定性的學科,基本原理,差異信息原理：,a,比,b,高,解的非唯一性原理：同一病，中、西醫不同解法,最少信息原理：直線是最少資訊圖,信息根據認知原理：須以資訊作為依據,新息優先原理：新息的權比舊息的權大,灰性不滅原理：人類認知是無窮盡的,Grey,、,Probability,、,Fuzzy,的區別,灰生成,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,數據生成,數據處理，加工,數據累加，累減,數據差補或剔除,數據組合,數據映射、取代、借用,數據生成的目的,數據相對值化：初值化、平均值化、區間值化,極性變換：效果測度,層次變換：累加生成、累減生成,灰生成,累加生成,AGO,定義,條件,累減生成,IAGO,定義,條件,灰建模,用序列建立具有部分微分方程性質的模型,部分微分方程性質的模型即微分方程模型,微分方程模型,只適合連續可微的對象,屬於無窮信息空間,GM(1,1),定義型,白化型,白化響應式,灰色預測,-1,GM(1,1):gray model one-order one variance,Example:,GM(1,1),之預測方程式為：,灰色預測,-2,建立,GM(1,1),之步驟：,輸入：一原始數據序列。,輸出：,GM(1,1),預測,模型。,步驟,1:,求出累加生成序列如下：,步驟,2:,求出之均值序列如下：,灰色預測,-3,步驟,3:,求中間參數,C,D,E,F,如下：,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,-4,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,先,建立,GM,（,1,1,）,模型，依據此模型進行預測。分為：,數列灰預測,災變灰預測,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,Grey Prediction and Frequency-Domain Based Image Compression,作者：黃詠淮、謝明興、曾定章、莊永達,2000,年灰色系統理論與應用研討會,報告：王乾隆,Architecture,Original Image,DWT,EZW,Grey(1,1),compression,compression image,Huffman code,DWT(Discrete Wavelet Transform),HL1,HL2,HH1,LH1,HH2,LH2,HL3,HL4,LL4,EZW(Embedded,Zerotree,Wavelet),Wavelet tree,EZW(Embedded,Zerotree,Wavelet),Zero tree:if,all,the value of someone wavelet tree elements no more then threshold,T,1,was given.Then we call the sub-wavelet tree is zero tree.,Zero tree imply that the block was,smoothly,and it is not very important to image.,Used Grey Prediction to Compression,After DWT and EZW we have a sequence data.,If some point is no more then the threshold,T,2,then we make the GM(1,1)model else or not.,If n=4 was the worst case,but n4 was not.,n,a,b replace the model sequences.,Apply,Zerotree,to distinguish between the insignificant and significant coefficients,More then threshold,T,1,is significant coefficients that is important for an image.,If no more then,T,1,it is the smooth parts of an image,so we replace them by zero to increase the compression rate.,DWT+GM(1,1)to compression Image-1,Step 1:Original image,4 level DWT then got 13 wave bands.,Step 2:encoding LL4 by uniform quantization.,均勻量化,Step 3:for 13 wave bands set up the,zerotree,.,Store the sign map of significant,Store the relation between significant and insignificant coefficients,DWT+GM(1,1)to compression Image-2,Step 4:apply the GM(1,1)to model the significant sequences.Store the n,a,b.,Step 5:encode the significant coefficients sign map,uniform quantization of LL4,all the n,a,b.,Step 6:decode.inverse the compression steps.,Experiment,CR:compression ration,CR=(bits of the original image)/(bit of compression image),Conclusion,Grey model is good to high compression rate,Sign map problem,store the sign map increase the data.,Only let the grey model to predict the original wavelet tree,dont care the sign problem,then we can raise the compression quality really.,