⛄一、SVD数字水印简介
1 水印嵌入算法
水印W和载体图像C是水印嵌入算法的输入，含水印图像C是输出。C、W、C的尺寸分别为M×M、N×N和M×M。此外，该水印方法可以容纳多个尺寸不同的水印，并对宿主图像进行r级DWT分解。水印嵌入的过程如图1所示，具体的嵌入步骤为：
(1)基于R级DWT，将C分解为LL、LH、HL、HH的分量，其中R=log2(M/N)。
(2)HD在LL上执行，显示为：
PHPT=HD(LL) (9)
(3)将SVD应用于H：
HUwHSwHVwT=SVD(H) (10)
(4)W与SVD结合使用：
UwSwVwT=SVD(W) (11)
接着使用Logistic映射产生的混沌系统对Uw、VwT的运算加密，加密后的两个组件标记为Uw1和VTw1。
(5)通过将HSw和Sw与缩放因子α的乘积相加，计算嵌入的奇异值HSw：
HSw=HSw+αSw (12)
(6)带水印的子带H是通过逆奇异值分解生成的，即：
H=HUwHSw*HVwT (13)
(7)基于给出的逆HD，重建一个新的低频近似子带LL*：
LL*=PH*PT(14)
(8)水印图像C*是通过执行逆r级小波变换获得的，水印嵌入流程图如图2所示。
图2 水印嵌入流程图
2 水印提取算法
在水印提取算法中，加水印的宿主图像C是输入，提取的水印W是输出。W*的大小为N×N。水印提取过程如图3所示，具体提取步骤为：
(1)经过水印的主图像C*通过r级DWT分解为四个子带，分别为LLw、LHw、HLw、HHw。
(2)对LLw执行HD
PwHwPwT=HD(LLw) (15)
(3)将SVD应用于Hw，
HUwHSbwHVw*T=SVD(Hw)(16)
(4)提取的奇异值Sw为：
Sw=(HSbw*-HSw*)/α (17)
(5)Uw1和Vw1T由混沌系统解密，解密的两个组件被标记为Uw2和Vw2T。提取的水印W通过逆奇异值分解(SVD)进行重构，公式为：
W=Uw2Sw*Vw2T(18)
水印提取流程图如图3所示。
图3 水印提取流程图
⛄二、部分源代码
clc
clear
close all
%% Import image
cover_image=imread(‘lena512.bmp’);
watermark_logo=imread(‘cameraman.tif’);
%% Plot cover image and watermark image
figure
subplot(1,2,1);
imshow(cover_image);
title(‘Cover image: 512 x 512’);
subplot(1,2,2);
imshow(watermark_logo);
title(‘Watermark image: 256 x 256’);
%% Example: watermark embedding and exraction alpha=0.1 Attack: Sharpening
method = ‘DWT-HD-SVD’; % Apply 'DWT-HD-SVD Method
alpha = 0.1;
attack = ‘Motion blur’; % You can choose other attacks
param = 0.5; % attack parameter
[watermarked_image, extracted_watermark] = watermark(cover_image,…
watermark_logo,method,alpha,attack,param);
% Plot results
figure;
subplot(2, 2, 1);
imshow(cover_image);
xlabel(‘a) Cover image’);
subplot(2, 2, 2);
imshow(watermarked_image);
xlabel(‘b) Watermarked image’);
subplot(2, 2, 3);
imshow(watermark_logo);
xlabel(‘c) Watermark logo’);
subplot(2, 2, 4);
imshow(extracted_watermark);
xlabel(‘d) Extracted watermark’);
sgtitle(['DWT-HD-SVD method \alpha = '+string(alpha) attack]);
%% NC vs alpha DWT-HD-SVD figure 5
% Plot normalized correlation for different alpha
method = ‘DWT-HD-SVD’;
alpha =0.005:0.005:0.2;
attacks = {‘No Attack’; ‘Gaussian low-pass filter’; ‘Median’;…
‘Gaussian noise’; ‘Salt and pepper noise’;‘Speckle noise’;…
‘JPEG compression’; ‘JPEG2000 compression’; ‘Sharpening attack’;…
‘Histogram equalization’; ‘Average filter’; ‘Motion blur’};
% Attack papameters
params = [0; 3; 3; 0.001; 0; 0; 50; 12; 0.8; 0; 0; 0];
NC = NC_alpha(cover_image,watermark_logo,method,alpha,attacks,params);
%% plot NC vs alpha figure 5
NC_plot(alpha,NC,attacks);
%% PSNR vs alpha DWT-HD-SVD
method = ‘DWT-HD-SVD’;
alpha =0.005:0.005:0.2;
attacks = {‘No Attack’; ‘Gaussian low-pass filter’; ‘Median’; ‘Gaussian noise’;…
‘Salt and pepper noise’;‘Speckle noise’; ‘JPEG compression’;…
‘JPEG2000 compression’; ‘Sharpening attack’; ‘Histogram equalization’;…
‘Average filter’; ‘Motion blur’};
params = [0; 3; 3; 0.001; 0; 0; 50; 12; 0.8; 0; 0; 0];
PSNR = PSNR_alpha(cover_image,watermark_logo,method,alpha,attacks,params);
%% plot PSNR vs alpha
PSNR_plot(alpha,PSNR,attacks);
%% SSIM vs alpha DWT-HD-SVD figure 7 paper (see README)
method = ‘DWT-HD-SVD’;
alpha =0.005:0.005:0.2;
attacks = {‘No Attack’; ‘Gaussian low-pass filter’; ‘Median’; ‘Gaussian noise’;…
‘Salt and pepper noise’;‘Speckle noise’; ‘JPEG compression’;…
‘JPEG2000 compression’; ‘Sharpening attack’; ‘Histogram equalization’;…
‘Average filter’; ‘Motion blur’};
params = [0; 3; 3; 0.001; 0; 0; 50; 12; 0.8; 0; 0; 0];
SSIM = SSIM_alpha(cover_image,watermark_logo,method,alpha,attacks,params);
%% plot SSIM vs alpha
SSIM_plot(alpha,SSIM,attacks);
%% FIGURE 8. Invisibility performance: Watermarked images and corresponding extracted
% watermarks with various sizes and their corresponding PSNRs, SSIMs and NCs.
method = ‘DWT-HD-SVD’;
alpha =0.05;
attack = ‘No Attack’;
param = 0;
figure
for i=1:3
watermark_logoi = imresize(watermark_logo,2^(-i+1));
[watermarked_image, extracted_watermark] = watermark(cover_image,watermark_logoi,method,alpha,attack,param);
PSNR = psnr(watermarked_image, cover_image);
SSIM = ssim(watermarked_image, cover_image);
NC = nc(watermark_logoi,extracted_watermark);
subplot(2,3,i);
imshow(watermarked_image);
title([‘watermarked image’;‘watermark size ‘+string(length(watermark_logoi))+‘x’+string(length(watermark_logoi))]);
xlabel([‘PSNR=’+string(PSNR);‘SSIM=’+string(SSIM)]);
subplot(2,3,i+3);
imshow(extracted_watermark);
title(‘extracted watermark’);
xlabel(‘NC=’+string(NC));
end
sgtitle(‘DWT-HD-SVD: Invisibility performance: watermarks with various sizes; alpha=’+string(alpha)+’; No Attack’);
%% plot watermarked image for different attacks and watermark sizes
method = ‘DWT-HD-SVD’;
alpha =0.05;
attacks = {‘No Attack’; ‘Gaussian low-pass filter’; ‘Median’; ‘Gaussian noise’;…
‘Salt and pepper noise’;‘Speckle noise’; ‘JPEG compression’;…
‘JPEG2000 compression’; ‘Sharpening attack’; ‘Histogram equalization’;…
‘Average filter’; ‘Motion blur’};
params = [0; 3; 3; 0.001; 0; 0; 50; 12; 0.8; 0; 0; 0];
for i=3👎1
watermark_logoi = imresize(watermark_logo,2^(1-i));
figure
for j=1:length(attacks)
attack = string(attacks(j));
param = params(j);
[watermarked_image, extracted_watermark] = watermark(cover_image,watermark_logoi,method,alpha,attack,param);
PSNR = psnr(watermarked_image, cover_image);
SSIM = ssim(watermarked_image, cover_image);
subplot(3,4,j);
imshow(watermarked_image);
xlabel(['PSNR='+string(PSNR);'SSIM='+string(SSIM)]);
title(attack);
end
sgtitle(['DWT-HD-SVD: Attacked watermarked image; Size = ‘+string(length(watermark_logoi))+‘x’+string(length(watermark_logoi))+’; \alpha = '+string(alpha)]);
end
⛄三、运行结果
⛄四、matlab版本及参考文献
1 matlab版本
2014a
2 参考文献
[1]甘志超,刘丹.基于HD和SVD的DWT变换的数字图像水印[J].现代信息科技. 2022,6(01)
3 备注
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