Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/5998
標題: 以貝氏定理尋找影像壓縮之最佳相鄰關係
Finding the Optimal Context Modeling for Image Compression by Bayes' Theorem
作者: 林峻德
關鍵字: 貝氏定理;條件熵編碼;算術編碼;離散小波轉換;最佳相鄰關係
出版社: 電機工程學系
摘要: 
由於一般影像相鄰像素之像素值有很大的相關性,而條件機率模型正可以用來表示這種相關性。本篇論文就是要利用這種性質,利用包含25張8 bit表示的灰階影像,來估測此條件機率 P(X|X1,X2,...,Xn)。此式子經由貝氏定理並且在給定 X 的情形下,X1 、X2 …和 Xn 互為獨立的假設成立下,可以得到:
P(X|X1,X2,...,Xn)αP(X|X1)P(X|X2)...P(X|Xn)P(X)
如此便可使計算時所需要使用的式子減少維度,自然也可以減少
記憶體使用量。而當 X1=x1,X2=x2 ,… Xn=xn 已知時,可以得到所需要的估測條件機率模型:
P(X|X1,X2,...,Xn)=P(X|X1)P(X|X2)...P(X|Xn)P(X)/(ΣP(X|X1)
P(X|X2)...P(X|Xn)P(X))
最後利用此模型進行條件熵編碼來找出其影像壓縮的最佳相鄰關係,並且應用於算術編碼上對影像進行編碼壓縮。之後我們也對經由一階離散小波轉換後的四個頻帶進行同樣的處理,也將得到的估測機率模型一樣應用於算術編碼上。
論文方法最後的結果發現對於以影像像素值所得到的估測機率模型應用於算術編碼上,對其它影像進行編碼可以比使用傳統算術編碼得到較好的壓縮率;一階離散小波轉換後的LL頻帶亦同;但是LH、HL和HH頻帶則由於頻帶相鄰係數的相關性已經被破壞,論文方法已經不能改善,對於此三頻帶反而以傳統算術編碼比較適合。
關鍵詞:貝氏定理,條件熵編碼,算術編碼,離散小波轉換,最佳相鄰關係。

The neighboring pixels of an image are highly correlated and conditional probability can be used to represent the correlation. In this thesis, we use twenty five 8-bit gray-level images to estimate the conditional probability
P(X|X1,X2,...,Xn). Using Bayes' theorem and under the assumptions that X1 , X2 , …, and Xn are independent when X is given, we known that
P(X|X1,X2,...,Xn)αP(X|X1)P(X|X2)...P(X|Xn)P(X)
The relation can decrease the dimension to store the conditional probability. Therefore, the memory needed can also be decreased. When , , …, and are given, we can obtain the estimated conditional probability model as follows:
P(X|X1,X2,...,Xn)=P(X|X1)P(X|X2)...P(X|Xn)P(X)/(ΣP(X|X1)
P(X|X2)...P(X|Xn)P(X))
Conditional entropy coding using this estimated model is used to find the optimal context model for image compression. The optimal model is applied to compress image using arithmetic coding. The same procedure is used on the LL, LH, HL and HH bands which are obtained by first-order discrete wavelet transform. Arithmetic coding is then used to compress images.
The results show that the method using the conditional probability model can get better compression ratio than general arithmetic coding. When the method is used on the coefficients of LL band, we can obtain the same result. But at LH, HL and HH bands, because the correlation between neighboring coefficients is low, general arithmetic coding can gets better compression result than the method of conditional probability.
Keyword: Bayes' theorem, conditional entropy coding, arithmetic coding,
discrete wavelet transform, optimal context model.
URI: http://hdl.handle.net/11455/5998
Appears in Collections:電機工程學系所

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