Digital watermarks are associated with the protection of the copyright property of digital products.

The watermarks are represented by digital signals and legal owners use them in order to sign their products. Watermark existence can be shown exclusively by the owner himself or by an authorised company. Watermarking algorithms have bee n developed in our laboratory in last few years. The algorithms are applicable to digital products that represent still images, video and audio.

Watermarks possess the following features:

Perceptual Invisibility: The watermark signal is embedded in the digital data producing alterations. These alterations should not degrade the perceived quality. The owner can decide about the strength of alterations. Large alterations are robust and can be detected with great certainty, but they produce degradation of the product.

Complexity: Watermark signals are characterized by great complexity. This is necessary in order to avoid the construction of similar watermarks. Subsequently, watermark determination by a third person , becomes more difficult. Another advantage of ``complex’’ (complicated) watermarks is that they provide reliable statistical properties and their detection can be shown with great certainty.

Watermark key: Any watermark signal is associated (one by one) with an integer number (or a set of integer numbers) which is the watermark key. This key is used to produce, embed and detect a watermar k. The key is private and characterises exclusively the legal owner of the digital product. The number of available keys is enormous.

Statistical efficiency: The detection of a particular watermark is successful when the suitable key is used. We note that each watermark corresponds to a unique key.

Statistical invisibility: The possession of a great number of digital products, watermarked by the same key, does not dispose the watermark. Different products watermarked by the same key, transfer di fferent watermark signals. We can claim that the extraction of the owner's key by a third person is impossible. Counterfeit watermark keys can not be determined, i.e. keys, which detect a watermark that had never been embedded in the digital image before.

Multiple Watermarking: A sufficient number of different watermarks can be embedded in the same image. Each of these watermarks could be detected by using the corresponding unique key. A creator can use the same key f or watermarking a large set of products.

 Robustness: Various kinds of modifications should be performed on a digital product in order to improve their quality or to compress their size or to remove the watermarks. Watermarks use effici ent ways to produce invisible and, simultaneously, robust alterations to various modifications like filtering and JPEG (or MPEG) compression. Therefore the watermark is still detected in a modified image that demonstrate high quality.

 We have proposed the following watermark types:
  1. Pseudo-random noisy binary patterns. They are applied to still images. The watermark embedding and detection algorithms are very fast; however, such watermarks do not resist to high JPEG compressi on ratio and low-pass filtering.
  2. Low-pass pseudo-random or chaotic signals. They are applied to still images and audio data. Their robustness is satisfactory under filtering and JPEG compression.
  3. Mixing watermarks. These watermarks represent binary copyright logos, which are embedded in still images and video sequences. The watermark logo can be either reconstructed from the watermarked im age or they can be detected statistically. Statistical detection provides certain decisions about the watermark existence even after high JPEG or MPEG compression.
  4. DCT constraint : The watermark is expressed by constraint in DCT space.
  5. Region-based watermarks : A pseudo-random watermark is embedded in several regions of the image, and is adapted according to certain features of these regions. It is therefore robust to certain geometric operations like rotation scaling and translation, apart from the usual filtering and compression..
  6. Circularly symmetric watermarks : A pseudo-random watermark is embedded in a certain band of DFT coefficients. It is constructed so that it can withstand geometric alterations.
  7. Fourier descriptors : The watermark is embedded in the Fourier descriptors of polygonal lines represented as vector graphics images.
  8. Self-similar watermarks : A self-similar watermark is embedded in several levels of DWT coefficients.
  9. Multi-bit watermarks : The watermark that is embedded corresponds to a multiple-bit message and can be decoded even after geometric attacks.
            In addition to the above, a theoretic investigation of Markov chaotic sequences and their relative performance in watermarking compared to pseudo-random sequences has been carried out.

 Generally, the watermarking scheme is distinguished in three particular algorithms:

a) The Watermark Production algorithm (WPA)

b) The Watermark Embedding algorithm (WEA)


c) The Watermark Detection algorithm (WDA)

The above algorithms are public and can be applied by anyone. The security of the watermark hiding is based exclusively on the privacy of the watermark key. WPA is applied having as input the private key and the data of the digital product. Each pair (key, product) is transformed to a watermark digital signal. By passing the data of the product in the algorithm, we manage to achieve the statistical invisibility of the watermark. WPAs are based on pseudorandom number generators or/and strongly chaotic systems. The determination of a key which produces a predefined watermark signal is impossible, i.e. watermark production is a non-inve rtible procedure preventing an attacker to define counterfeit watermarks. WPA can be considered as a part of the embedding and detection algorithms.

WEA requires as arguments the digital product and the produced watermark. It embeds the watermark in a digital still image or in a video frame by producing alterations in the luminance of the pixels. For audio signals, alterations are p erformed on the amplitude of the signal. Alterations are of low energy and they are designed by taken into account the main characteristics of the human visual and auditory system. Watermark embedding in transform domains (e.g. the DCT domain) can be used . Since video and audio signals require large amounts of memory, data are input in WEAs and watermarked sequentially. For video watermarking, the motion vectors that calculated by a MPEG encoder-decoder should be used to increase the performance of the al gorithm.

Detection is the most crucial part in the watermarking framework. WDAs should be trustworthy producing insignificant false alarm errors. Therefore, the result of the detector should be an indisputable indication about the ownership of a digital product. WDA’s based on statistical hypothesis testing. They provide the certainty, which characterises a possible decision that accepts the existence of a particular watermark. Numerical experiments indicate that watermark detection is en ough reliable and suitable to prove copyright ownership. In video frame sequences, the watermark can be detected to each frame separately. WDA does not require the original digital product in order to proceed to the watermark detection. This characteristi c is a great advantage since it provides fast and automatic implementation and ``web-crawling’’

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