The main goal of digital watermarking a graphic image is to make sure that someone cannot remove the watermark without seriously damaging the image.
N OT E Various signal processing techniques can be applied to an image to change its formatting without destroying its appearance. A good example of this is taking an image that is in one format and converting it to another format. For example, if a .bmp is converted to a JPEG file and then back to a .bmp, the two images would look the same, but the bit-by-bit composition of the images would be different.
One tool used to attack digital watermarks is Stir Mark, written by Fabien Petitcolas. Stir Mark is used to test the strength of digital watermarking tech- nologies. You can add your own tests to the program, but it comes with three standard tests:
PSNR test. PSNR stands for the peak signal-to-noise ratio, which is essentially the peak signal versus the mean square error. The equation for PSNR is PSNR = 20 log10(255/RMSE), where RMSE is the root mean squared error. Typical values for PSNR are between 20 and 40. Remem- ber, when you are applying a digital watermark or any form of stego to an image, you are introducing errors. This test measures the PSNR before and after watermarking to identify such errors.
JPEG test. JPEG images are a compressed image format, one reason why this format is typically used on the Internet. A .bmp file that is a couple of megabytes in size would most likely be a couple hundred kilobytes in size when converted to JPEG. Because JPEG is a compressed format, when other formats are converted to JPEG they often lose information. This test converts various formats to JPEG to see the impact of the con- version on a watermark.
Affine test. This test performs an affine transformation across the image. An affine transformation requires that two properties of an image must be maintained after the transformation: Any point that lies on a line still must be on that line after transformation, and the midpoint of the line must stay the same. The transformation is performed to see what effect, if any, this action has on a watermark.
What follows is part of a report generated by Stir Mark. Here you can see the different tests and how changing the input values for each of the tests can have an impact on the certainty of the detection. For example, with the PSNR tests an input value has to be provided that tells the program what percentage of noise it should use. You can see how the certainty changes with the various percents of noise.
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Test_PSNR — Sat Nov 02 00.37.30 2002 —————————————————————————-
Test_PSNR 0 Images/Set1/Sample Certainty: 57.1169 1.#INF dB Test_PSNR 10 Images/Set1/Sample Certainty: 59.5881 39.5346 dB Test_PSNR 20 Images/Set1/Sample Certainty: 61.2351 35.1198 dB Test_PSNR 30 Images/Set1/Sample Certainty: 63.7055 32.0288 dB Test_PSNR 40 Images/Set1/Sample Certainty: 65.3515 29.079 dB Test_PSNR 50 Images/Set1/Sample Certainty: 67.8198 27.4019 dB Test_PSNR 60 Images/Set1/Sample Certainty: 69.4646 25.5721 dB Test_PSNR 70 Images/Set1/Sample Certainty: 71.9341 23.9908 dB Test_PSNR 80 Images/Set1/Sample Certainty: 73.5774 23.0663 dB Test_PSNR 90 Images/Set1/Sample Certainty: 76.0416 21.8534 dB Test_PSNR 100 Images/Set1/Sample Certainty: 77.6834 21.1355 dB
Figure 4.15 The original image with no modifications.
In most cases, as Stir Mark performs its transformations and removes a watermark, the resulting image is destroyed. It’s worth looking at several images after transformations have been performed. I’ve used the sample image set that comes with Stir Mark. Figure 4.15 shows the original Lena image.
Looking at the PSNR output, you can see that even when you change the input values, this test reveals a minimal impact on the actual image. Figure 4.16 is an image with a PSNR of 0, Figure 4.17 has a PSNR of 50, and Figure 4.18 has a PSNR of 100 percent.
Figure 4.17 Image after 50 percent noise has been added to it.
Figure 4.18 Image after 100 percent noise has been added to it.
By examining these images carefully you can see that when you increase the peak signal-to-noise ratio the image begins to look more and more faded and you lose some sharpness. As you can also see, the quality of the image is still fairly good in all the examples.
The affine transformation test keeps the image intact but makes it look like it was slightly offcenter when printed, as shown in Figures 4.19 and 4.20.
Figure 4.19 After the transformation a visible change has been made to the image.
Figure 4.20 By changing the input to the transformation a different visual effect can be seen.
The biggest effect comes when direct noise is applied to the image. Figure 4.21 shows 20 percent noise, Figure 4.22 shows 60 percent noise, and Figure 4.23 is an image with 80 percent noise applied.
Figure 4.21 When you apply noise to the image it becomes distorted.
Figure 4.22 As more noise is added, at the 60 percent level, the image can be seen only faintly.
As you can see, the more noise that is inserted in an image, the less clear it becomes.
Looking Ahead
Digital watermarking is an exciting and complex field. Most people consider it a subset of stego, but remember the key differences. Digital watermarking is concerned with hiding small amounts of data in many places across an image and doing it in a way that destroys the image if the data is removed. Other forms of stego are concerned with hiding data entirely.
In the chapters that follow I’ll go beyond the basics of stego to show you the impact it is having on our society, how it is generated, and how it can be detected.