Optimum watermark detection and embedding in digital images

One of the problems arising from the use of digital media is the ease of identical copies of digital images or audio files, allowing manipulation and unauthorized use. Copyright is an effective tool for preserving intellectual property of those documents but authors and publishers need effective techniques that prevent from copyright modification, due to the straightforward access to multimedia applications and the wider use of digital publications through the www. These techniques are generally called watermarking and allow the introduction of side information (i.e. author identification, copyrights, dates, etc.). This work will concentrate on the problem of watermarking of still images using the luminance component, through the use of spread spectrum techniques, both in space (Direct Sequence Spread Spectrum or DSSS) and frequency (Frequency Hopping or FH), following the guidelines of [1]. This is not the only approach to the subject. Other authors apply the watermark on other characteristics of the image, like the DCT transformed coefficients [6]. The system described below is based on the system developed in [1] in the sense that it is able to embed watermarks and recover them with zero probability of error. The problem is faced from a statistical detection point of view through the analysis of the density function of the image to be marked. A Cauchy model is found to be very accurate and some tests are performed in order to assess improved detection quality. Moreover, the resulting system turns out to be easy to encrypt and very robust to low pass filtering, resizing, JPEG compression, dithering and Xeroxing. 1. DIGITAL WATERMARKS It is interesting to attack the problem by considering the watermark as a signal to be buried in noise, that is the image. The signal design may be obtained as a compromise between the following factors: a) The watermark has to be difficult to detect by a nonauthorized user, therefore some kind of encryption has to be done, if possible both in space and frequency. Spread spectrum techniques in space (DSSS) and in frequency (FH) adapt specifically to the requirement. b) Visual quality of the marked image should be indistinguishable from the original. The contribution in [1] is a pioneering work on the use of psycovisual criteria in the watermark embedding process, by modeling the 1 This work was partially supported by the European Commission under ACTS, AC347 SUNBEAM, the Spanish National Plan of Research, through the projects CICYT, TIC98-0412 and TIC98-0703, the AECI and Generalitat de Catalunya, through the project CIRIT, 1998SGR-00081. behavior of human visual system with Gabor filters [4]. The well known masking effect is used there: Any watermark whose bandwidth is less than or equal to the Gabor filter bandwidth will be invisible provided that its energy be lower than the image energy in that band. With this regard, the instantaneous Gabor filter output is used to modulate the amplitude of the watermark. c) The amount of information this signal can convey: large amounts might increase the signal bandwidth beyond the Gabor filters bandwidth which implies visual noticing of the watermark. d) The probability of error in the detection of each symbol constituting the watermark should be as low as possible, implying high power for the mark and, at the same time, noticeable effect on the marked image. DSSS techniques again allow the use of low power signals while maintaining probability of error in reasonable levels thanks to the processing gain. e) The watermark should be robust enough to low-pass filtering, compression, or any other not noticeable modification of the image. In particular the central frequency of the watermark should be placed at frequencies that are generally preserved by a low compression JPEG procedure. Having those conditions in mind, the watermark to be included in the image consists in a series of K=31 orthogonal symbols being each of them a pseudorandom minimum length sequence (MLS). Each chip in the MLS is sized to a block of 8x32 pixels in order to accommodate to the Gabor filter bandwidth [1] (see figure 1.1).