DRAFT - How to apply DCT for watermarking

When looking at image watermarking, Discrete Cosine Transform is a very common technique:

1. Transform your image (spacial) to frequency
2. Add your watermark on the mid frequency coefficients
3. Reverse frequency coefficient to spacial domain

First Trial

I used OpenCV to do the DCT/IDCT.

I took Lenna to illustrate.

“Low” coefficients of DCT are the right columns and the bottom rows of the image. I have float32, so I am not very happy with that.

img = cv2.imread("lenna.png")
img_freq = cv2.dct(img.astype(np.float32))
img_freq[-1]

If I use many columns, it tends to saturate in the top-left corner.

If I fill with values of large amplitude, I get “waves” within the image

k = 5
ncols = 25
nrows = len(X)
X_fill = 2**k * np.ones((nrows, ncols))
X[:, -ncols:] = X_fill

If I double the number of last columns (while using all possible values on each row) I increase the “wave” frequency.

k = 5
ncols = 50
nrows = len(X)
X_fill = 2**k * np.ones((nrows, ncols))
X[:, -ncols:] = X_fill

Summary

It is not recommanded to do DCT on the full image as by modifying low/mid frequency component, you will get the corner degenerated. Nevertheless, it could be an option as corners are not the main thing we look at.

How to add the watermark

Ok, there are DCT coefficients. In LSB (Lowest significant bit), to hide a message, one would just remove the initial bit and write the message directly.

Here, you should not. You can “add” or “multiply” the watermark with the current image.

Addition

$F’ = F + \alpha W$ (F previous frequency pixel value, $\alpha$: mixing coefficient, and $W$ watermark info)

Multiplication

$F’ = F (1 + \alpha W)$ (F previous frequency pixel value, $\alpha$: mixing coefficient, and $W$ watermark info)

That way, you preserve the information.

Ref

Frequency coefficients

Linkg img

In some papers, it is just said “multiply “ In many papers

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