I have a problem with the watermark in the svd image. The NC value does not change. When extracting the protected image, it appears black, which means that there is a problem

orig_img = imread('C:\Users\info\Desktop\dfd\foto\1.tif'); 
watermark_img = imread('C:\Users\info\Desktop\dfd\foto\3.png'); 
if size(orig_img, 3) == 3 
orig_img = rgb2gray(orig_img); end 
if size(watermark_img, 3) == 3 
watermark_img = rgb2gray(watermark_img); end 
orig_img = im2double(orig_img); watermark_img = im2double(watermark_img); 
watermark_img_resized = imresize(watermark_img, size(orig_img)); 
alpha = 0.03; 
[U,S,V] = svd(orig_img); 
watermarked_img = U*(S + alpha*watermark_img_resized)*V'; 
[Uw,Sw,Vw] = svd(watermarked_img); 
extracted_watermark = (Sw - S)/alpha; 
psnr = 10*log10(1/mean((orig_img(:)-watermarked_img(:)).^2)); 
nc =sum(extracted_watermark(:).*watermark_img_resized(:))/sqrt(sum(extracted_watermark(:).^2)*sum(watermark_img_resized(:).^2)); 
figure; 
subplot(2,2,1); imshow(orig_img); title('Original Image'); 
subplot(2,2,2); imshow(watermark_img); title('Watermark Image'); 
subplot(2,2,3); imshow(watermarked_img); title('Watermarked Image'); 
subplot(2,2,4); imshow(extracted_watermark); title('Extracted Watermark'); 
disp(['PSNR = ', num2str(psnr)]); 
disp(['NC = ', num2str(nc)]);

Answer 1

[Gayathri]

Hi @salaheddine,

I was able to reproduce your issue. The issue is happening because the watermarked image is not being generated properly.

watermarked_img = U*(S + alpha*watermark_img_resized)*V'; 

The SVD of “watermark_img_resized” image should also be calculated and then the singular vectors should be used to generate the watermarked image.Correspondingly, extract the image back from the watermarked image. As this issue is solved, “nc” parameter will also change.

You can find below the Code Snippet for your reference.

[U,S,V] = svd(orig_img); 
[U1,S1,V1] = svd(watermark_img_resized);
watermarked_img = U*(S + alpha*S1)*V'; 
[Uw,Sw,Vw] = svd(watermarked_img); 
extracted_watermark =U1*((Sw - S)/alpha)*V1';

Hope you find this information useful and resolves the issue.

[DGM]

For example:

orig_img = imread('cameraman.tif'); 
watermark_img = fliplr(orig_img); 

if size(orig_img, 3) == 3 
    orig_img = rgb2gray(orig_img);
end 
if size(watermark_img, 3) == 3 
    watermark_img = rgb2gray(watermark_img); 
end

orig_img = im2double(orig_img); 
watermark_img = im2double(watermark_img);
watermark_img_resized = imresize(watermark_img, size(orig_img)); 

alpha = 0.03; 
% --->
[U,S,V] = svd(orig_img); 
[U1,S1,V1] = svd(watermark_img_resized);
watermarked_img = U*(S + alpha*S1)*V'; 

[Uw,Sw,Vw] = svd(watermarked_img); 
extracted_watermark =U1*((Sw - S)/alpha)*V1';
% <---

psnr = 10*log10(1/mean((orig_img(:)-watermarked_img(:)).^2)); 
nc = sum(extracted_watermark(:).*watermark_img_resized(:))/sqrt(sum(extracted_watermark(:).^2)*sum(watermark_img_resized(:).^2)); 

subplot(2,2,1); imshow(orig_img); title('Original Image'); 
subplot(2,2,2); imshow(watermark_img); title('Watermark Image'); 
subplot(2,2,3); imshow(watermarked_img); title('Watermarked Image'); 
subplot(2,2,4); imshow(extracted_watermark); title('Extracted Watermark'); 

disp(['PSNR = ', num2str(psnr)]); 

PSNR = 36.04

disp(['NC = ', num2str(nc)]);

NC = 1