How to do watermarking in the Frequency Domain?

Question

I am new in Matlab and I have an assignment that is asking for watermarking an image using DCT transform:

• Read Lin.jpg color image and apply DCT.
• Threshold the logo.jpg (watermark) into binary and ten times of its strength, and then add it to the coefficient of transformed Lin image.

Here are the two images:

I have three questions:

1. Am I supposed to divide Lin.jpg into 8x8 blocks and logo.jpg into 2x2 blocks or that is not necessary?
2. what does it mean by: "ten times of its strength"? Is that just multiplying by 10?
3. How can I get the coefficient of transformed Lin.jpg image?

Here is what I tried:

img = imread('Lin.jpg');
wImg = imread('njit_logo.jpg');

wImgBinary = imbinarize(wImg) * 10;
[rows, cols] = size(img(:,:,1));
[Wrows, Wcols] = size(wImgBinary);

% make the watermark image as large as the original
watermark = zeros(size(img), 'uint8');
for column = 1:cols
    for row = 1:rows
        watermark(row, column) = wImgBinary(mod(row,Wrows)+1, mod(column,Wcols)+1);
    end
end
watermark = watermark(1:rows, 1:cols);

% apply dct and add with watermark at each channel
for i = 1:3
    imgDct = dct2(img(:,:,i));
    C = imgDct + double(watermark);
    Iw(:,:,i) = round(real(idct2(C)));
end

IIw = uint8(Iw);
figure, imshow(IIw), title('watermarked image');

Answer 1

Watermarking Image by Combining Discrete Cosine Transform Components

In this case, I found that using a Watermark_Strength (strength factor) of 30 in this example shows more prominent results. A pipeline for adding a watermark is as follows:

• Zeropad the watermark image to match the size of the image to be watermarked using the padarray() function or alternatively enlarge the image.
• Split the image and watermark image to their RGB channels/components.
• Take the Discrete Cosine Transform (DCT) of all the colour channels using the dct2() function.
• Multiply the Discrete Cosine Transform (DCT) components of the watermarked image by a strength factor.
• Add the corresponding Discrete Cosine Transform (DCT) components based on colour channel.
• Take the inverse of 3 resultant Discrete Cosine Transform (DCT) components using the idct2() function.
• Combine the inversed components to create the watermarked image in the spatial domain.

Image = imread('Lin.jpg');
Watermark = imread('njit_logo.jpg');

%Grabbing the image and watermark dimensions%
[Image_Height,Image_Width,~] = size(Image);
[Watermark_Height,Watermark_Width,~] = size(Watermark);

%Padding the watermark to match the size of the image to be watermarked%
Side_Padding = (Image_Width - Watermark_Width)/2;
Top_And_Bottom_Padding = (Image_Height - Watermark_Height)/2;
Watermark_Padded = padarray(Watermark,[Top_And_Bottom_Padding Side_Padding],0,'both');

%Binary image of watermark%
Watermark_Binary = imbinarize(Watermark_Padded);

%Converting the watermark image to frequency domain using DCT%
Watermark_Strength = 30;
Red_Channel_Watermark_DCT = Watermark_Strength*dct2(Watermark_Binary(:,:,1));
Blue_Channel_Watermark_DCT = Watermark_Strength*dct2(Watermark_Binary(:,:,2));
Green_Channel_Watermark_DCT = Watermark_Strength*dct2(Watermark_Binary(:,:,3));

%Converting the image to frequency domain using DCT%
Red_Channel_Image_DCT = dct2(Image(:,:,1));
Blue_Channel_Image_DCT = dct2(Image(:,:,2));
Green_Channel_Image_DCT = dct2(Image(:,:,3));

%Adding the frequency components together%
Combined_Red_Channel = Red_Channel_Watermark_DCT + Red_Channel_Image_DCT;
Combined_Blue_Channel = Blue_Channel_Watermark_DCT + Blue_Channel_Image_DCT;
Combined_Green_Channel = Green_Channel_Watermark_DCT + Green_Channel_Image_DCT;

%Inversing the combined frequency domain image%
Combined_Image(:,:,1) = idct2(real(Combined_Red_Channel));
Combined_Image(:,:,2) = idct2(real(Combined_Blue_Channel));
Combined_Image(:,:,3) = idct2(real(Combined_Green_Channel));

%Displaying combined image%
Combined_Image = uint8(Combined_Image);
imshow(Combined_Image);

Ran using MATLAB R2019b