離散分數傅立葉轉換在影像浮水印之應用

Image watermarking based on discrete fractional Fourier transforms

蔡豐懋(Fong-Mao Tsai)

指導教授 ： 許文良

中原大學/電機資訊學院/通訊工程碩士學位學程/碩士(2014年)

https://doi.org/10.6840/cycu201400870

摘要

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。

關鍵字

數位浮水印 ； 強健性 ； 實數離散分數傅立葉轉換 ； 實數離散分數哈特利轉換

並列摘要

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.

並列關鍵字

discrete fractional Hartley transform ； watermarking ； robustness ； discrete fractional Fourier transform

參考文獻

[5] 楊景光（2012）。離散分數隨機轉換之研究。中原大學電機工程學系碩士論文，桃園。

[16] 張惟晴（2013）。實數離散分數傅立葉轉換之研究。中原大學通訊工程碩士學位學程碩士論文，桃園。

[1] Qing Guo, Zhengjun Liu,and Shutian Liu, “Robustness analysis of image watermarking based on discrete fractional random transform,” Optical Engineering, vol. 47, no.5, 057003, May 2008.

[2] Khan, A. and Mirza, A. M. “Genetic perceptual shaping: Utilizing cover image and conceivable attack information during watermark embedding.” Inf. Fusion 8, pp.354-365, Oct. 2007

[3] Frank Y. Shih “Digital watermarking and steganography: fundamentals and techniques.” Taylor & Francis, Boca Raton, FL, USA, 2008