Digital Watermarking: For Resolving Ownership Disputes
From SkyInsight
This article was originally published in the December 2005 issue of AstroPhoto Insight astrophotography newsletter.
When a dispute arises, it is difficult to prove who the owner of a digital image really is. The image in question may be direct copy or a derivative of another image claimed to be the original. Prior to the days of digital photography, the true owner may have been able to produce a negative or a set of negatives from which the image in question was created. Digital imaging and processing, however, mean that such physical evidence may not exist. "Raw data" from which a digital image was created can lend credence to a claim, but it cannot prove ownership. While it might be difficult, it is possible to create such raw data after the fact with invertible processes.
There is a well established solution to this problem. For a registration fee (currently $30) the Registrar of Copyrights in the U.S. Library of Congress can register the copyright of an image. This registration should be made prior to any publication of the image so as to establish the earliest claim of ownership. Unfortunately, this can lead to a significant expense when a large number of images is concerned, the claims process can run into the hundreds of dollars, and, while this may help with an exact copy, it does not fully resolve the challenge of proving that a suspect image is a slightly modified version of another. Unless the monetary value of the imagery is very high, it can be hard to justify such an expense.
Another approach is to show that the suspect image contains certain artifacts that are unique to one imager. From a mathematical perspective, one needs to show that these artifacts could not have been created in any other way or by any other person and that the likelihood of them appearing randomly is vanishingly small. If the process that created the artifacts is kept as a secret and one party can reproduce those artifacts while the other party cannot, this again lends credence to the ownership claim. However, if the process is explained and described (which must happen to resolve the first such claim), then it is no longer secret. Others could now employ that technique and the artifacts generated would no longer be unique to that one imager.
As you might guess from the title of this article, a technique called digital watermarking can be used to help resolve ownership disputes. Digital watermarking is an image processing technique introducing slight modifications to the colors of each pixel in order to hide information into that image. The goal is to change the statistics of the image to match a desired target while at the same time maintaining the fidelity of the image. The original image and the marked image should look identical. The statistics changed are often chosen to be robust to image processing operations such as slight cropping or rotation, low-pass filtering or sharpening, compression, and a host of other operations.
Digital watermarking essentially introduces invisible artifacts into an image. It can be shown that these invisible artifacts can be reliably recovered and that the probability of them being recovered from an unmarked image is vanishingly small. In addition, the artifacts can be generated from a random process based on a key value or seed value. This allows the revelation of the algorithm without compromising the security of the approach.
As an example consider the image of the Andromeda Galaxy (M31) shown below. The image on the left is the original version and that on the right is watermarked. The watermark is essentially a random noise pattern the same size as the image. It has been spatially filtered to provide robustness and spatially modulated to insure invisibility.
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An example of an original (a) and a watermarked (b) image of the Andromeda Galaxy (M31). The original image is 927x1024, 24-bit RGB that has been previously JPEG compressed. The watermark pattern is a pseudo-random noise pattern that is also 927x1024x3. At each pixel, the watermark pattern takes the value of +1 or -1. The detection strength calculated from the watermarked image is 0.0207. The probability of this obtaining this detection strength from an unmarked image is 1 in 1014. Image provide courtesy of Al Degutis. |
The watermark pattern itself was generated from a pseudo-random noise generator. Given a seed value, this generator will produce a unique noise pattern. It is a pseudo-random generator because, given the same seed, it will reproduce the same pattern. Thus, the pattern is actually deterministic, not random. The seed value (or the whole watermark pattern) is saved for use during detection.
The detection process requires that the seed value, the noise generator, and the embedding algorithm be made public. The seed value and the noise generator are used to reconstruct the watermark pattern. A correlation process then looks for this pattern in the suspect image. Note that since the pattern itself is typically a noise pattern with each pixel value chosen independently from its neighbors, a slight shift or rotation of the suspect image will cause the correlation value to be significantly decreased. Thus, the original image is often used to register the suspect image back to its proper orientation, scale, and translation. If the image is cropped, then the watermark pattern should also be cropped to the same region prior to correlation.
The detection process yields a detection value. This represents the likelihood that the pattern was found in the image. A commonly used correlation measure is the correlation coefficient. This measure ranges from 0 to 1.0. Higher values indicate greater likelihood of the image having been watermarked with that pattern. Unmarked images will have a detection value close to 0.0. However, it will not be exactly 0.0. All images will have some very small, but non-zero correlation with a watermark pattern. Mathematics can help determine whether a particular detection value is from a watermarked image (true positive detection) or from an unmarked image (false positive). In the example shown, with a pattern size of 927 x 1024 = 2,847,744 pixels and a detection strength of 0.0207, the probability that this image is unmarked is 1 in 1014. This is about 1000 times less likely than obtaining a false match on a DNA fingerprint.
To use this approach, one would select a seed value, use a well known pseudo-random noise generator and the seed to create a random noise pattern the same size as the image, and filter and modulate that pattern so that it can be added invisibly and robustly. To prove ownership of that image, one would then simply register the suspect image and provide the pattern (or seed value). A correlation-based detection statistic would then provide a detection value and a corresponding likelihood that it is a false positive. This approach, however, has a well known flaw.
As an adversary who wants to claim ownership of a posted image, I could create a noise-like pattern that has a high correlation with that image. There are a number of ways to do this by processing the image until it looks like noise. I would claim this noise pattern to be my watermark and a correlation analysis would prove that my pattern is in the posted image.
To avoid this problem, it is recommended that the seed to the noise generator be derived from the image itself. The field of cryptography provides a special function called a one-way function or one-way hash. Applying this function to an image yields a single, long number that can be used to seed the random number generator. But the function is one-way in that, given a long number, one cannot feasibly find an image that would hash to that number. Now, you save your original image. The original image and the hash create the seed. The seed creates the watermark pattern that is found in the suspect image. The adversary can create a fake watermark pattern found in the image, but he cannot prove that he didn't fake it. You can.
You watermark an image and put the original away in a safe. You distribute the watermarked copy on the web. If someone copies the image, your watermark will be present in that copy. If someone watermarks your distributed version with their own watermark, both watermarks will be found in the pirated copy, but your watermark will also be found in the pirates original.
In that last example it is important to note that the watermark can prove that the pirate got the image from you. However, it does not prove that you are the owner. You may have stolen the image from someone else. That someone else may not have watermarked the image. Even if he did, he may not be aware of your dispute and may not know that his image was stolen. Thus, the watermark does not strictly prove ownership. Instead it can be used to prove that one image is a derivative of another.
Unfortunately, the digital photography industry as a whole has not been quick to adopt digital watermarking for protection of their imagery. As a result, many of the companies that offered digital image watermarking products have fallen by the wayside. One company still in the business is Digimarc (http://www.digimarc.com). Their product called MyPictureMarc can be used to embed ownership marks in images. The starter package runs $79 and covers your first 1000 images. This comes with a stand-alone detection tool. In addition, some image manipulation packages, such as Adobe Photoshop and Equilibrium Debabelizer, have Digimarc watermark readers built in. Another option is Signum's SureSign (http://www.signumtech.com) with which you can mark an unlimited number of images starting at $220/year. Signum provides Adobe Photoshop plugin for marking and reading. Finally, for those brave downloaders, you can find plenty of free or shareware programs on the Internet that you can use to uniquely identify your images.
Dr. Jeffrey Bloom manages the Content Security Research Group at Thomson Multimedia Research Center in Princeton New Jersey. He is a co-author of the book "Digital Watermarking", published by Morgan Kaufmann in 2001, which is the standard text book in the field.
