Robust image watermarking in the spatial domain
Introduction
Digital media have revolutionized the way still images and image sequences are stored, manipulated and transmitted, giving rise to a wide range of new applications (digital television, digital video disc, digital image databases, electronic publishing, etc.) that are expected to have an important impact on the electronics and entertainment industry. One of the main features of digital technology is the ease with which images can be accessed and duplicated. However, this feature has an important side effect; it allows for easy unauthorized reproduction of information, i.e. data piracy. Due to this, protection of intellectual property rights, i.e. copyright protection of stored/transmitted digital images is a very important issue. One way to help protect images against illegal recordings and retransmissions is to embed an invisible signal, called digital signature or copyright label or watermark, that completely characterizes the person who applied it and, therefore, marks it as being his intellectual property. Obviously, the secure and unambiguous identification of the legal owner of an image requires that each individual or organization that produces, owns or transmits digital images (artists, broadcasting corporations, image database providers, etc.) uses a different, unique watermark.
Copyright protection is just one of the potential applications of embedding invisible data within images or other types of signal (e.g. audio signals), a technique usually referred to as data hiding or steganography. Other applications include authentication control, tamper-proofing (i.e. checking whether the content of an image has been altered or not) and insertion of invisible image annotations (e.g. scene/object description). For each of these applications, the embedded signal should possess a different set of properties. In this paper we would limit our discussion to digital watermarks serving the purpose of copyright protection. Digital watermarks of this type should be [14]:
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undeletable by an ‘attacker’;
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easily and securely detectable by their owner;
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perceptually and statistically invisible;
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resistant to lossy compression, filtering and other types of processing.
The basic operating principle of the proposed algorithm presents certain similarities to the so-called Patchwork technique that has been independently developed in MIT Media Lab [1]. However, the two methods differ in the statistical approach adopted for the watermark detection. Furthermore, an extensive part of our paper is devoted to important extensions of the basic method (image dependent watermarks, robust watermark design by means of optimization techniques, handling of geometric distortions) that are not addressed in [1]. The proposed algorithm bears also certain similarities with other methods 6, 9, 17 developed independently at about the same time or afterwards. However, the differences between our method and the above-mentioned techniques are rather important. For example, the algorithms proposed by Cox and Ruanaidh require the original image during the watermark detection whereas our method does not. The outline of this paper is the following. The basic algorithm is described in Section 2. Design of watermarks that are robust to filtering and compression is discussed in Section 3. Section 4deals with ways to incorporate properties of the human visual system in order to generate invisible watermarks. A method to handle geometrical distortions is presented in Section 5. Image dependent watermarks are proposed in Section 6as a means of further robustifying the algorithm. Extension to color images is treated in Section 7. Experiments on real images are presented in Section 8.
Section snippets
Basic watermarking algorithm
Consider an image I of dimensions N×M:A watermark pattern S is a binary pattern of the same size where the number of ‘ones’ equals the number of ‘zeros’:
Using S we can split I into two subsets of equal size:The digital watermark is superimposed on the image as follows:where ⊗ is a superposition law (in our case addition), xsnm are the pixels of the watermarked image Is and fnm is
Immunity to subsampling
An important issue that should be examined about the proposed watermarks is their immunity to subsampling. Only the case of mean value subsampling is considered here. In this case, if the original image I was of size N×M, the subsampled image Isub is (N/2)×(M/2) pixels large, and the intensity levels x′nm of its pixels are given by
In order to apply the detection algorithm on Isub, we generate a subsampled version S′ of the N×M
Robust watermark design
Unfortunately the method outlined in Section 2is not robust to compression using the well-established JPEG standard which achieves efficient image compression by combining the Discrete Cosine Transform (DCT) with appropriate DCT coefficient quantization schemes. This is due to the fact that the watermark signal fnm (8) is essentially low-power, white noise. As a consequence, it is heavily distorted by JPEG. Furthermore, the watermarks can be easily deleted by other operations such as mean or
Invisible watermarking using properties of the human visual system
Since watermarks are essentially additive noise superimposed on the image, they should be invisible so as not to affect the image quality to a great extent. Another important motivation for generating invisible watermarks is the fact that such watermarks would be difficult to be detected (and destroyed) by visual inspection. From this point of view, watermarking exhibits significant resemblance to lossy image compression [18], an application where invisible distortions are also highly
Handling geometrical distortions
A weak point of the watermarking methods described in the previous sections is that the pixels that form the subset A are specified only in terms of their spatial location and therefore, any geometrical distortion (e.g. line removal) can ‘fool’ the detection algorithm. However, this type of distortion can be treated using a correlation-based preprocessing module. The output of this module is an index d(n) that gives the translation that line n has undergone. d(n) can be fed into the detection
Image dependent watermarks
Using a single watermark on all images of equal size whose copyright is owned by the same individual is very convenient in terms of implementation simplicity and speed. However, such a practice is not a safe one. If, for example, someone can manage to obtain both the original and the watermarked version of the same image, he can easily recover the watermark signal by performing a simple subtraction of the two images and then eliminate the watermark from all images in which it exists. Another
Watermarks for color images
The watermarking techniques presented in the previous sections can be easily extended to handle color images. In this case, watermark casting is done by generating three different watermark patterns SR,SG,SB, one for each RGB channel, and modifying, for each channel, the intensity of the pixels that belong to the corresponding sets AR,AG,AB. The watermark casting and detection procedures for color images are exactly the same as for the corresponding procedures for grayscale images. Sets A, B
Experimental results
The resistance of the proposed watermarking algorithms to various distortions was studied in a series of experiments on grayscale images. The first set of experiments dealt with the resistance of the various techniques to JPEG compression. As it was mentioned in Section 4, when an image is subject to a certain distortion (in our case compression), both the probability 1−β of correct detection in a watermarked image and the probability α of erroneous watermark detection in an image that bears no
Conclusions
A new method for the copyright protection of images using digital watermarks has been proposed in this paper. The proposed method produces watermarks that are not detectable by visual inspection but at the same time are robust to JPEG compression and lowpass filtering. Variations that produce watermarks that are immune to geometric transformations and also image-dependent were also presented. An extension to color images was also presented.
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