# 臺灣博碩士論文加值系統

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 在本論文中，為了找出強健性較好的浮水印演算法，利用離散分數傅立葉轉換(Discrete Fractional Fourier Transform, DFRFT)及其衍生之轉換來嵌入浮水印，此方法為一種在轉換域中嵌入浮水印的方法，在[1]中曾有利用離散分數隨機轉換(Discrete Fractional Random Transform, DFRNT)嵌入浮水印的方式，我們將此方法延伸，使用了五種轉換取代DFRNT來嵌入與萃取浮水印，並且對已嵌入浮水印之影像進行影像攻擊，包含了裁切、胡椒鹽雜訊、高斯低通濾波器，然後再萃取浮水印，觀察這些轉換忍受影像攻擊的極限，並分析與探討強健性。DFRFT與多參數離散分數傅立葉轉換(multiple-parameter discrete fractional Fourier transform, MPDFRFT)對抗裁切的承受度是最差的，而隨機離散分數傅立葉轉換(random discrete fractional Fourier transform, Random DFRFT)對抗裁切及胡椒鹽雜訊皆有最好的表現，實數離散分數傅立葉轉換(Real discrete fractional Fourier transform, Real DFRFT)與實數離散分數哈特利轉換(real discrete fractional Hartley transform, Real DFRHT)對裁切的攻擊時有不錯的表現，而五種轉換都可承受高斯低通濾波器的攻擊。本文中強健性最佳的是Random DFRFT，因其隨機性較高，是適合用來嵌入浮水印的方法。而兩種實數的轉換(Real DFRFT, Real DFRHT)，其特徵向量為隨機，所有轉換過程均為實數，若為了對裁切的攻擊時也可使用此方法。
 In this thesis, to find robust watermarking schemes, we use discrete fractional Fourier transform (DFRFT) and its other four generalized transforms to embed watermarks. They are methods of embedding watermarks in transform domains. In [1], discrete Fractional random transform (DFRNT) was used to embed watermarks. We extend that method and use five transforms to replace DFRNT for watermark embedding and extracting. Then, we attack the watermarked images. The attacks include cropping, salt-and-pepper noise and Gaussian low pass filter. After attacks, we extract the watermark to observe the limits of these transforms to resist attacks and to analyze the robustness. The resistances of DFRFT and multiple-parameter discrete fractional Fourier transform (MPDFRFT) against cropping are the worst. The random discrete fractional Fourier transform (Random DFRFT) has the best performance against cropping and salt-and-pepper noise attack. Real discrete fractional Fourier transform (Real DFRFT) and real discrete fractional Hartley transform (Real DFRHT) have good performance against cropping. All the five transforms can withstand the attack of Gaussian low pass filter.Random DFRFT has the best robustness in this thesis, because it has a higher randomness. Random DFRFT is suitable for watermark applications. Furthermore, there are two real transforms (Real DFRFT, Real DFRHT). The eigenvectors of both transforms are random, and all the values in the transformation process are real, they are suitable for resist cropping attack.
 目錄摘要…..……………………………………………………… IAbstract…..…………………………………………. ….III誌謝…………………………………………………………V目錄…………………………………………………………VI圖目錄……………………………………………………VIII表目錄………………………………………………………XI第一章 緒論…..…………………………………………………..1 1.1動機與目的………………………………………………….1 1.2數位浮水印的基本性質……………………….………….2 1.3數位浮水印的分類…….………………………………….3第二章 數位浮水印......................................5 2.1離散分數隨機轉換在影像浮水印之應用..................5 2.2分數傅立葉轉換及隨機相位編碼在影像浮水印之應用. .......9第三章 離散分數傅立葉轉換…………….……………15 3.1離散分數傅立葉轉換………………………………15 3.2多參數離散分數傅立葉轉換……………………..…17 3.3隨機離散分數傅利葉轉換……………………..…19 3.4實數離散分數傅立葉轉換……………………..…22 3.5實數離散分數哈特利轉換………………...…..…25第四章 離散分數傅立葉及其衍生轉換在影像浮水印之應用……………………………………………………………28 4.1離散分數傅立葉轉換………………………………28 4.2多參數離散分數傅利葉轉換…………………..……36 4.3隨機離散分數傅利葉轉換………………………...39 4.4實數離散分數傅立葉轉換…………………………42 4.5實數離散分數哈特利轉換…………………………45 4.6數位浮水印強健性比較圖表與結果討論…………48第五章 結論……………………………………………….....63參考文獻......................................................................64圖目錄圖1.3-1 浮現式浮水印…………………………………….…..………3圖1.3-2 隱藏式浮水印…………………………………………...……4圖2.1-1 256×256大小之原始影像及50×50大小之原始浮水印....7圖2.1-2原始影像經DFRNT轉換之結果. ……………………….....8圖2.1-3將浮水印嵌入後之影像………………………….……….....8圖2.1-4萃取出之浮水印. …...…….………………………………....8圖2.2-1 一般浮水印演算法...…….………………………………...11圖2.2-2 此篇浮水印演算法...…….………………………………...11圖2.2-3 原始影像...…….…………………………………….……...12圖2.2-4 原始浮水印...…….…………………………………….…...13圖2.2-5 萃取出之浮水印...…….……………………...……….…...13圖2.2-6 將影像從左上角裁切50×50像素後萃取出之浮水印….14圖4.1-1浮水印嵌入流程圖解….……………………...……….…...29圖4.1-2浮水印萃取流程圖解….……………………...……….…...30圖4.1-3 256×256大小之原始影像及50×50大小之原始浮水印...32圖4.1-4 將浮水印嵌入後之影像……………………...……….…...33圖4.1-5 萃取出之浮水印……………………………...……….…...33圖4.1-6 將影像從左上角裁切20×20像素大小……...…………...34圖4.1-7 萃取出之浮水印……………………………...……….…...34圖4.1-8 將影像摻入密度為0.03之胡椒鹽雜訊…...…………...34圖4.1-9 萃取出之浮水印……………………………...……….…...34圖4.1-10 經高斯低通濾波器處理之影像…………………….…...35圖4.1-11 萃取出之浮水印……………………………..……….…...35圖4.2-1 256×256大小之原始影像及50×50大小之原始浮水印..36圖4.2-2 將浮水印嵌入後之影像……………………...……....…...37圖4.2-3 萃取出之浮水印……………………………...……….…...37圖4.2-4 將影像從左上角裁切20×20像素大小……...…………...37圖4.2-5 萃取出之浮水印……………………………...……….…...37圖4.2-6 將影像摻入密度為0.04之胡椒鹽雜訊…...…….……...38圖4.2-7 萃取出之浮水印……………………………...……….…...38圖4.2-8 經高斯低通濾波器處理之影像……….….………….…...38圖4.2-9 萃取出之浮水印……………………………...……….…...38圖4.3-1 256×256大小之原始影像及50×50大小之原始浮水印..39圖4.3-2 將浮水印嵌入後之影像……………………...……....…...40圖4.3-3 萃取出之浮水印……………………………...……….…...40圖4.3-4 將影像從左上角裁切45×45像素大小…………...……...40圖4.3-5 萃取出之浮水印……………………………...……….…...40圖4.3-6 將影像摻入密度為0.04之胡椒鹽雜訊…...….………...41圖4.3-7 萃取出之浮水印……………………………...……….…...41圖4.3-8 經高斯低通濾波器處理之影像…………..………….…...41圖4.3-9 萃取出之浮水印……………………………...……….…...41圖4.4-1 256×256大小之原始影像及50×50大小之原始浮水印..42圖4.4-2 將浮水印嵌入後之影像……………………...……....…...43圖4.4-3 萃取出之浮水印……………………………...……….…...43圖4.4-4 將影像從左上角裁切40×40像素大小…………...……...43圖4.4-5 萃取出之浮水印……………………………...……….…...43圖4.4-6 將影像摻入密度為0.025之胡椒鹽雜訊…...…..……...44圖4.4-7 萃取出之浮水印……………………………...……….…...44圖4.4-8 經高斯低通濾波器處理之影像…………..………….…...44圖4.4-9 萃取出之浮水印……………………………...……….…...44圖4.5-1 256×256大小之原始影像及50×50大小之原始浮水印..45圖4.5-2 將浮水印嵌入後之影像……………………...……....…...46圖4.5-3 萃取出之浮水印……………………………...……….…...46圖4.5-4 將影像從左上角裁切40×40像素大小…………...……...46圖4.5-5 萃取出之浮水印……………………………...……….…...46圖4.5-6 將影像摻入密度為0.025之胡椒鹽雜訊…...…..……...47圖4.5-7 萃取出之浮水印……………………………...……….…...47圖4.5-8 經高斯低通濾波器處理之影像…………..………….…...47圖4.5-9 萃取出之浮水印……………………………...……….…...47圖4.6-1 影像受到裁切後的PSNR值比較圖………...…………...49圖4.6-2 影像受到裁切後的WNR值比較圖………...…….……...50圖4.6-3 影像摻入胡椒鹽雜訊後的PSNR值比較圖………...…...51圖4.6-4 影像摻入胡椒鹽雜訊後的WNR值比較圖………...…...52圖4.6-5原圖………. …..…...….….. ………... ……...….………...55圖4.6-6 使用DFRFT轉換原圖後之影像………... ……...….…...55圖4.6-7 使用MPDFRFT轉換原圖後之影像………...…...….…...56圖4.6-8 使用Random DFRFT轉換原圖後之影像…….....….…...56圖4.6-9 使用Real DFRFT轉換原圖後之影像………... ………...56圖4.6-10 使用Real DFRHT轉換原圖後之影像………..………...56圖4.6-11 256×256大小之Mandrill影像及50×50大小之浮水印..57圖4.6-12 Mandrill影像受到裁切後的PSNR值比較圖……. …...58圖4.6-13 Mandrill影像受到裁切後的WNR值比較圖…. …. ….59圖4.6-14 Mandrill影像摻入胡椒鹽雜訊後的PSNR值比較圖….60圖4.6-15 Mandrill影像摻入胡椒鹽雜訊後的WNR值比較圖….61表目錄表4.6-1 各轉換在不同裁切大小下的WNR值……………………53表4.6-2 各轉換在不同胡椒鹽密度下的WNR值…………………53表4.6-3 各轉換在不同裁切大小下的WNR值……………………62表4.6-4 各轉換在不同胡椒鹽密度下的WNR值…………………62
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 1 數位浮水印強健性之分析與比較 2 應用於所有權保護上的一種結合多個轉換域之浮水印方法 3 使用單工碼與哈達碼應用於籬笆知情編碼之數位浮水印 4 基於混合雙重影像資訊隱藏之演算法改良 5 轉換域數位浮水印之研究 6 以統計分析法進行影像浮水印藏密之研究 7 具能源效率之浮水印演算法研究 8 植基於奇異值分解之強健性的二維條碼浮水印架構 9 以均衡且不完整性之區塊結構資訊辨識之強健型數位浮水印 10 強健的數位浮水印方法使用平衡不對稱區塊設計 11 數位影像浮水印技術用於抵抗幾何攻擊與訊號處理之研究 12 利用小波轉換技術之互補式數位浮水印 13 基於小波轉換之強健且低破壞性的數位浮水印嵌入法 14 以係數平均值量化為基礎的強健性浮水印技術 15 離散餘弦轉換頻域之健全性浮水印方法

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