現今因為資料壓縮技術進步，壓縮後各種有版權的數位化影像、音樂或軟體在網路上傳輸十分容易，而增加了被大量非法複製或散播的機會。為了解決著作權保護的問題，資訊隱藏技術是目前最常被採用的方法之一。資訊隱藏技術將特別的資訊－浮水印(如所有人簽章、使用者資訊)，嵌入多媒體資料之中，而不被使用者察覺，可以用來保護資料內容或驗證所有權。但資訊隱藏技術同樣面臨了一些挑戰，例如有心人士的蓄意破壞或一般正常處理資料(如壓縮)，都可能會對所隱藏的資訊造成傷害。
本論文使用碎形正交基底編碼(Fractal orthonormal bases)技術來做資訊隱藏。碎形（Fractal）使用在影像壓縮上，已被證實有良好效果，其壓縮方法是先將原影像分割成數個Range方塊，對於每一個方塊，在事先訓練出之正交基底Domain方塊集中找出數個方塊及一個轉換函數，使得這數個方塊經過轉換函數之線性組合係數調整後，會與較小之Range方塊相似。因為各Domain方塊間有其正交獨立性，因此調動各個係數並不會對其他係數造成影響，所以本研究對其係數加以調整以將浮水印資訊隱藏在其碎形碼中，並且利用擴充位元及多數決來增加浮水印擷取後的相似度，最後將每張影像轉換函數集之係數及亂數種子存入資料庫中。
另外本研究將與其他兩個應用在DCT、DFT頻率域之浮水印資訊隱藏技術，進行效能、容量、訊雜比、等之比較，並且透過經由剪裁、縮放、中值濾波、均化、雜訊及JPEGS、SPIHT、EZW影像壓縮等破壞，來比較三者間之強韌性。實驗結果說明，本研究所提出之方法，僅需存取部分壓縮碼以及其亂數種子，不需大量儲存空間，並可以此做為密鑰；另外對於各類一定程度之破壞，皆能有可靠強韌性，且擁有較大資料嵌入空間。

Digital multimedia can be distributed via the internet efficiently with superior compression technologies. The chance of distributing digital intellectual properties, such as image, music, films, and software, being large-scale unauthorized copied and distributed are much increasing one possible and practical solution for the copyright protection is information hiding technology. Information hiding technology embeds a special data into multimedia data for copyright protection. However, the embedded data may be damaged by malicious attacks or common signal processing.
In this thesis, an information hiding technique based on Fractal Orthonormal Basis is proposed. First, the original image is divided into NxN Range blocks, each range block is substituted by several Domain blocks (Fractal Orthonormal Basis), then the watermark information is embedded into the coefficients of the fractal orthonormal basis.
Besides, our technique will be compare with the other two watermarking algorithm (using DCT and DWT). After the attacks of cropping, down-scaling, median filter, smoothing, noise, JPEG, SPIHT and EZW compression, the Fractal Orthonormal Basis watermarking technique shows better result of capacity, transparency and robustness. In addition, we only store parts of compression fractal codes and the permutation seed, and these can be the secret key for the security.

目錄
第一章 浮水印簡介與相關研究……………………………………………………1
1.1前言… …………………………………………………………………………… 1
1.2數位浮水印… …………………………………………………………………… 2
1.3浮水印分類與相關研究… ……………………………………………………… 4
1.3.1 可見式浮水印(visible watermark)…………………… ……………………4
1.3.2 不可見式浮水印(invisible watermark) …………………………………… 5
1.3.3易碎式浮水印(fragile watermark) ………………………………………… 5
1.3.4強健式浮水印(Robust watermark)………………………………………… 6
1.3.5 空間域… ………………………………………………………………… 6
1.3.6 頻率域……………………………………… …………………………… 7
1.3.6.1 離散餘弦轉換域(DCT Domain)……………………………………7
1.3.6.2離散小波轉換域(DWT Domain)………………………… ……… 14
1.3.6.3離散傅利葉轉換域(DFT Domain)…………………………………25
1.3.6.4複合式浮水印技術 ………………………………………………27

第二章 碎形基礎理論與相關浮水印研究……………………………………… 28
2.1前言………………………………………………………………………………28
2.2轉換之收斂性……………………………………………………………………31
2.3碎形影像壓縮……………………………………………………………………32
2.4基於碎形壓縮之浮水印應用……………………………………………………37
2.4.1區域尋找法… ……………………………………………………………37
2.4.2區域尋找改良式………………………………………………………… 39
2.4.3旋轉轉換二分法………………………………………………………… 40
2.4.4亮度偏移量量化法……………………………………………………… 42

第三章 碎形正交基底與浮水印… …………………………………………… 44
3.1 Orthogonal Basis IFS……………………………………………………………44
3.2嵌入演算法…………………………………………………………………… 48
3.3擷取演算法… …………………………………………………………………49
3.4碎形正交基底浮水印之實作… ………………………………………………51

第四章 研究結果 ……………………………………………………………… 55
4.1 評比標準………………………………………………………………………55
4.1.1 信號訊雜比(PSNR，Peak Signal to Noise Ratios) ………………… … 55
4.1.2 正規化相似性(Normalized Correlation tatio，NC) …………………… 56
4.2 實驗結果與效能比較…………………………………………………………56
4.3 幾合轉換破壞(Geometrical transformation attacks)……………………………60
4.3.1 剪裁(cropping)………………………………………………………… 60
4.3.2 縮放(down-scaling) …………………………………………………… 62
4.4 影像處理破壞(Image processing attacks) ………… ………………………… 65
4.4.1 均化(smoothing) ……………………………………………………… 65
4.4.2 中值濾波(median filter)… …………………………………………… 67
4.4.3 加入高斯雜訊破壞(Gaussian noise) ………… ……………………… 69
4.5 影像壓縮破壞(Image compression attacks)……………………………………71
4.5.1 JPEG壓縮………………………………………………………………71
4.5.2 SPIHT壓縮 ……………………………………………………………73
4.5.3 EZW壓縮………………………………………………………………76

第五章 結論…………………………………………………………………… 79
參考文獻 …………………………………………………………………………81

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