Jeffrey A. Bloom

Rotation, scale, and translation resilient watermarking for images

Many electronic watermarks for still images and video content are sensitive to geometric distortions. For example, simple rotation, scaling, and/or translation (RST) of an image can prevent blind detection of a public watermark. In this paper, we propose a watermarking algorithm that is robust to RST distortions. The watermark is embedded into a one-dimensional (1-D) signal obtained by taking the Fourier transform of the image, resampling the Fourier magnitudes into log-polar coordinates, and then summing a function of those magnitudes along the log-radius axis. Rotation of the image results in a cyclical shift of the extracted signal. Scaling of the image results in amplification of the extracted signal, and translation of the image has no effect on the extracted signal. We can therefore compensate for rotation with a simple search, and compensate for scaling by using the correlation coefficient as the detection measure. False positive results on a database of 10,000 images are reported. Robustness results on a database of 2000 images are described. It is shown that the watermark is robust to rotation, scale, and translation. In addition, we describe tests examining the watermarks resistance to cropping and JPEG compression.

Watermarking applications and their properties

We describe a number of applications of digital watermarking and we examine the common properties of robustness, tamper resistance, fidelity, computational cost and false positive rate. We observe that these properties vary greatly depending on the application. Consequently, we conclude that evaluation of a watermarking algorithm is difficult without first indicating the context in which it is to be applied.

Informed embedding: exploiting image and detector information during watermark insertion

Usually watermark embedding simply adds a globally or locally attenuated watermark pattern to the cover data (photograph, music, movie). The attenuation is required to maintain fidelity of the cover data to an observer while the watermark detector considers the cover data to be noise. We refer to this as blind embedding. Cox, Miller and McKellips (see Proceedings of the IEEE, vol.87, no.7, p.1127-41, 1999) observed that the cover data is not noise, i.e. it is not random but completely known at the time of embedding. This knowledge, along with knowledge of the detection algorithm to be used, allows a new category of informed embedder to be realized. We describe a simple watermarking algorithm and then compare the performance of blind embedding with three types of informed embedding. Note that in all four cases, the watermark detector is unchanged, only the embedder is altered. Experimental results clearly reveal the improvement of informed over blind embedding.

Rotation, scale, and translation resilient public watermarking for images

Many electronic watermarks for still images and video content are sensitive to geometric distortions. For example, simple rotation, scaling, and/or translation (RST) of an image can prevent detection of a public watermark. In this paper, we propose a watermarking algorithm that is robust to RST distortions. The watermark is embedded into a 1-dimensional signal obtained by first taking the Fourier transform of the image, resampling the Fourier magnitudes into log-polar coordinates, and then summing a function of those magnitudes along the log-radius axis. If the image is rotated, the resulting signal is cyclically shifted. If it is scaled, the signal is multiplied by some value. And if the image is translated, the signal is unaffected. We can therefore compensate for rotation with a simple search, and for scaling by using the correlation coefficient for the detection metric. False positive results on a database of 10,000 images are reported. Robustness results on a database of 2,000 images are described. It is shown that the watermark is robust to rotation, scale and translation. In addition, the algorithm shows resistance to cropping.

Computing the Probability of False Watermark Detection

Several methods of watermark detection involve computing a vector from some input media, computing the normalized correlation between that vector and a predefined watermark vector, and comparing the result against a threshold. We show that, if the probability density function of vectors that arise from random, unwatermarked media is a zero-mean, spherical Gaussian, then the probability that such a detector will give a false detection is given exactly by a simple ratio of two definite integrals. This expression depends only on the detection threshold and the dimensionality of the watermark vector.

Watermarking in the real world: an application to DVD

The prospect of consumer digital versatile disks (DVD) recorders highlights the challenge of protecting copyrighted video content from piracy. Digital watermarking can be used as part of a copy protection system. We describe the copy protection system currently under consideration for DVD. We also highlight some implementation issues that are being addressed.

A rotation, scale and translation resilient public watermark

Summary form only given. Watermarking algorithms that are robust to the common geometric transformations of rotation, scale and translation (RST) have been reported for cases in which the original unwatermarked content is available at the detector so as to allow the transformations to be inverted. However, for public watermarks the problem is significantly more difficult since there is no original content to register with. Two classes of solution have been proposed. The first embeds a registration pattern into the content while the second seeks to apply detection methods that are invariant to these geometric transformations. This paper describes a public watermarking method which is invariant (or bares a simple relation) to the common geometric transforms of rotation, scale, and translation. It is based on the Fourier-Mellin transform which has previously been suggested. We extend this work, using a variation based on the Radon transform. The watermark is inserted into a projection of the image. The properties of this projection are such that RST transforms produce simple or no effects on the projection waveform. When a watermark is inserted into a projection, the signal must eventually be back projected to the original image dimensions. This is a one to many mapping that allows for considerable flexibility in the watermark insertion process. We highlight some theoretical and practical issues that affect the implementation of an RST invariant watermark. Finally, we describe preliminary experimental results.

Watermarking to track motion picture theft

The music industry suspects that unauthorized P2P trading of music flies has had a negative impact on revenue. The motion picture industry fears the same thing happen to movies. However, the piracy problems in these two domains are different. In this paper we take an interesting look at movie piracy as we compare it to music piracy in the two areas of the piracy source and the potential impact on revenue. We do not directly address issues of politics, business, ethics, sociology, or copyright law, but identify relatively uncontroversial areas where technology, specifically digital watermarking, can make a significant contribution.

2 – Applications and Properties

This chapter discusses several possible applications of watermarking, and ways to judge a systems suitability to them. It examines the advantages that watermarking might have over alternative technologies. This discussion includes several examples of planned or actual watermarking systems in use today. Watermarking distinguishes from other techniques in three important ways. First, watermarks are imperceptible and do not detract from the aesthetics of an image. Second, watermarks are inseparable from the Works in which they are embedded. Finally, watermarks undergo the same transformations as the Works. This means that it is possible to learn something about those transformations by looking at the resulting watermarks. These three attributes make watermarking invaluable for some applications. Further, this chapter describes several properties of watermarking systems, discussing how their relative importance and interpretation varies with application. The performance of a given watermarking system is evaluated based on a small set of properties, like robustness, which describes how well watermarks survive common signal processing operations; fidelity, which describes how imperceptible the watermarks are; and so forth. This chapter concludes with a discussion on ways in which performance of watermarking systems is assessed.

Models of Watermarking

This chapter introduces several conceptual models of watermarking. It describes models of watermarking systems based on the traditional model of a communications channel. These models provide ways of thinking about actual watermarking systems. They fall into two broad groups: models based on a view of watermarking as a method of communications, and models based on geometric views of watermarking algorithms. This chapter begins with some background material by providing basic notational conventions used in equations. Works are viewed as points in a high-dimensional media space and within this space, there are probability distributions and regions of interest. Parts of a watermarking system are viewed as an extraction process that projects or distorts media space into a marking space. The rest is then viewed as a simpler watermarking system that operates in marking space rather than in media space. Many watermarking systems fall into the class of correlation-based systems, in which the detector uses some form of correlation as detection metric. This subclass of possible watermarking algorithms encompasses the majority of proposed systems. Linear correlation is computed as the inner product between two vectors divided by their dimensionality. Applying a threshold to this measure leads to a detection region bounded by a hyperplane. Normalized correlation is computed by normalizing two vectors to unit magnitude before taking their inner product. Applying a threshold to this measure leads to a conical detection region. Correlation coefficient is computed by subtracting the means from two vectors before computing their normalized correlation. The terms normalized correlation and correlation coefficient are used interchangeably.