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A New Method of Robust Image Compression Based on Embedded Zerotree Wavelet Algorithm

A New Method of Robust Image Compression Based on Embedded Zerotree Wavelet Algorithm. Charles D. Creusere IEEE Transactions on Image Processing, Vol. 6, No. 10, October 1997 學 生 : 戴 錦 輝. OUTLINE. 1. Introduction 2. Wavelet Transform

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A New Method of Robust Image Compression Based on Embedded Zerotree Wavelet Algorithm

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  1. A New Method of Robust Image Compression Based on Embedded Zerotree Wavelet Algorithm Charles D. Creusere IEEE Transactions on Image Processing, Vol. 6, No. 10, October 1997 學 生 : 戴 錦 輝

  2. OUTLINE 1. Introduction 2. Wavelet Transform 3. EZW Image Compression 4. Conclusions 5. References Ref

  3. 1. Introduction • The author proposes a wavelet-based image compression algorithm that achieves robustness to transmission errors by partitioning the transform coefficients into groups and independently processing each group using an embedded coder.

  4. 2. Wavelet Transform Fig.1(a)An example of Haar wavelet transform using lifting

  5. Fig.1(b)An example of Haar wavelet transform using lifting

  6. 離散小波轉換可用以偵測音高週期 Fig. 2 (a)

  7. Fig. 2 (b)

  8. Fig. 2 (c)

  9. Fig. 2 (d)

  10. Fig. 2(e)Application in 1-D Wavelet Transform “ㄚ”音經五次離散小波轉換後的波形，兩高點(peaks)的距離就是音高週期

  11. Fig. 3 (a)

  12. Fig. 3 (b)

  13. Fig. 4

  14. Fig. 4 左上角是原影像在V(x,y)的低解析度影像，右上角是列向量經一次離散小波轉換後的影像，左下角是行向量經一次離散小波轉換後的影像，右下角是經一次離散小波轉換後的影像。

  15. % p.290 凌波初步 • load Tiffany.mat • Y = dwt(3,Origin,1); • [Ya Yb Yc] = split(Y,128,128); • Ya = saturate(round(Ya), 1, 256); • Yb = 1 + 255* (abs(Yb) <4); • Yc = 1 + 255* (abs(Yc) <4); • image([Ya Yb; Yc]); • colormap(g256); • print -deps Tdtwo • sum(sum(Yb==1 )) + sum(sum(Yc==1 ))

  16. 3. EZW Image Compression • EZW這個方法是由Shapiro於1993年發表的，它是一種對離散小波轉換後係數編碼的方法。當影像作離散小波轉換後，高頻部份的係數會小於低頻部份的係數。 • 係數大的部份是影像低頻的部份，由這部份可得到模糊的影像。低頻的部份比較重要。係數小的部份是影像高頻的部份，它可使影像更加清晰。

  17. 影像壓縮編碼程序 • 步驟一:設定門檻值: N=5 • 步驟二:計算EZW的重建數值 • 步驟三:建立重要係數表 • 步驟四:建構第一次精鍊值 • 步驟五:先前重要係數的再精鍊 • 步驟六:重新設定重要係數的係數值 • 步驟七:(重複步驟三四五六) • EZW 重複步驟三四五六，找出每一次切割的重要係數，並精鍊先前取出的重要係數，直到門檻值為0或使用者認為可以停止。

  18. 表1:第一次切割所建立的重要係數表

  19. 表2:第一次切割之精鍊表

  20. Fig. 4:第一次切割結束前的係數重新設定

  21. 表3:第二次切割所建立的重要係數表

  22. 表4:第二次切割所建構之第一次精鍊數值

  23. 表5:第二次切割之精鍊值建構

  24. Fig. 5 “winter”的影像

  25. Fig. 6是編碼後的影像,Bit planes 1-10 during zerotree encoding of the “winter” image, using Haar wavelets.

  26. Fig.6 Original image

  27. Fig. 7 “Lena”的影像

  28. Fig. 8是解碼後的影像, Progressive decoding of the “Lena” image, which was encoded with the zerotree algorithm using Daubechies D6 wavelets.

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