A DIGITAL IMAGE WATERMARKING TECHNIQUE USING MODULATED PASCAL S TRIANGLES

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1 A DIGITAL IMAGE WATERMARKING TECHNIQUE USING MODULATED PASCAL S TRIANGLES H. Kostopoulos, S Kandiliotis Department of Mathematics University of Patras GR Patras Greece I. Kostopoulos Research Academic Computer Technology Institute R. Fereou 61 GR Patras Greece M. Xenos Hellenic Open University Sachtouri 16, 26223, Patras, Greece Abstract A watermarking process introduces imperceptible changes to a digital image that can be next detected by a computer program. In this paper we present an algorithm that embeds a binary representation of a modulated Pascal s triangle into the blue channel of color images by modifying one of the Bit planes. The proposed technique aims at the protection of the rights of the image owner. The visual quality of the watermarked image has been measured with objective criteria (PSNR) and presented in this work along with subjective results. The proposed method is robust to common image processing operations like Filtering, and Cropping or even combined attacks. Keywords: Digital Watermarking, Color s, Pascal s Triangles, IPR protection 1. Introduction In the beginning of the third millennium, digital imaging has become an inseparable piece of everyday life. Digital photography, video, medical images, satellite images etc. are some indicative examples. In many cases digital images are intended to be published, either on the internet or in widely used mediums. Organizations, museums, digital libraries, need to protect their Intellectual Property Rights (IPR) on this kind of media. In the past, the scientific community along with commercial organizations has invested in order to find reliable methods to protect digital media. During the last decade digital watermarking, based on the idea of information hiding, originally introduced in the 5 th century BC [1], gave a solution to the problem of designing such mechanisms to protect media. Digital watermarking of images exploits the fact that digital images contain redundant data that can be used to hide the information of the image owner. The latter information is called digital watermark. The redundancy of the image data is also exploited by image compression techniques in order to reduce the amount of data that represent an image. The directions that have been followed in the design of a watermarking method are: (a) modification of cover data in the frequency domain [2, 4] and (b) modification of the cover data in the spatial domain [3, 5-7]. Recent advances in watermarking technologies introduce algorithms working in both spatial and frequency domain [10, 11]. Most watermarking techniques applied in the spatial domain are based on the properties of the Human Visual System (HVS). This happened because a fundamental property [1] of a watermarking system is to produce watermarked images that will be identical to their unwatermarked versions according to Human observers. Kutter et al [4] proposed a technique that embeds a digital watermark in the Blue Channel of color images. The Blue Channel has been chosen since the HVS is less sensitive to changes on it. In current watermarking systems for digital images, the watermark represents a bit sequence [5, 6], a binary logo [7] or a piece of the image itself [8]. The present paper provides a new algorithm that embeds a binary representation of a modulated Pascal s triangle [9] into digital images respecting the restrictions of the HVS. The selection of this kind of watermark is based on the capability of constructing such a Triangle without storing any extra information, on the big difference between two modulated Pascal Triangles that minimize the probability of false detection and on the self similarity that is observed in the sub-regions of the Triangle. This paper is structured as follows: Section 2 gives an overview of the proposed method, Section 3 presents quality metrics of the method, and section 4 discusses robustness against attacks and ways of achieving better results. And finally section 5 gives a conclusion and mentions future work to be done. In section 6, references can be found.

2 2. Watermarking model The proposed algorithm is used to embed watermarks in medium and large sized color images (256x256 or bigger). The watermarking process consists of four steps: In the first step, the Original Io is decomposed to three channels corresponding to the three colors Red, Green and Blue. The Blue channel, in which the watermark is to be embedded, is decomposed to eight Bit Planes ranging form level 7, which is the plane containing the Least Significant bits of the image data, to level 0, which is the bit plane containing the Most Significant bits. In the second step Pascal s Triangle is created and put into an n x n matrix M, where n is equal with the original image side, using (1). Let x ij be the i,j element of matrix M then : x xi 1, j 1 + xi 1, j, i > j, j = 1, i = j j = 1 (1) 0, j > i i In the third step, matrix M is reduced modulo k, k [2,1000] thus creating a series of matrixes M 2 to M Number k that is used is chosen in a way that the patterns created differ from one another significantly, (see section 4). This way a database of a large number of different Pascal's Triangles is created. These matrixes are modified so that a 1 represents each element of the matrix that is not equal to 0. In the final step, one of these patterns is embedded into one of the bit planes. The bit plane is selected by the end-user and provides a tradeoff between the robustness and the desirable quality of the watermarked image. In practice the suitable bit planes range from 5 to 7. A pseudorandom number that corresponds to a second key k 2 is used to indicate the pixel from which the pattern will begin. As mentioned before, the dimensions of the matrices Mi that correspond to the watermark are equal with the image dimensions. In the case that the watermark exceeds the positions range it is embedded in the complementary positions. The position of the pixel combined with number k, used to reduce matrix M modulo k, create a composite key consisted of two parts, therefore offering greater security. Figure 1 illustrates the procedure of watermarking embedding. Pascal's Triangle offers a variety of different patterns that are self similar [9], see table 1. As the number of rows increases, self similarity is reinforced. This makes the detection process discussed later in this section, more robust to attacks, since less information is needed in order for the detector to extract the watermark with great accuracy. The hidden information that corresponds to a modulated Pascal triangle is assigned next to the owner of the image. User s details can be held in a database and after the extraction of the watermark they can be retrieved. Original Pascal s Triangle k1 Key Figure 1. The watermark embedding process The recovery of the watermark is achieved by comparing the pattern embedded in the image to the database of patterns that have already been created by reducing Pascal s Triangle modulo k, k [2, 1000]. The detector scans the bit-plane of the blue channel, that has been previously selected, using key composite k 2 (k 2 indicates the pixel from which the pattern starts and is pseudo randomly selected), comparing every bit of the plane to the patterns in the database. It exports as a result the number k used to reduce Pascal s Triangle modulo k and creates the specific pattern. In the ideal case where there is no alteration of the watermarked image the detector is able to detect the hole of the pattern. In any other case where modification has been inflicted to the watermark, the process ends when the similarity of the pattern and the watermark is over a threshold T. (mod 2) 2 1 i th bit plane k2 Modulated Pascal s Triangle Table 1. Modulated s (mod 5) Watermarked (1) Modulation (2) Bit plane decomposition (3) Bit plane composition (K) Key k1: number k Key k2: pseudorandom position of watermark embedding (mod 60) In order to increase detector s performance we can break down the bit plane into small square regions. These regions must be large enough to contain the smallest triangles that appear in every modified Pascal s Triangle. In this manner, self-similarity of the patterns is best exploited. Even after great loss of watermark data pending an attack, the detector is able to find a number of sub regions of the pattern that, combined with the position these are found in, are indicative of the pattern used. Hence giving assurance that the extracted key (number k, used to reduce Pascal s Triangle modulo k) is correct. 3

3 In comparing the sub regions, the detector must use a similarity threshold t 2 90%, to determine whether the triangle examined is identical to the triangles in the pattern created by reducing Pascal s triangle modulo k. The detection procedure is illustrated in Figure 2. Watermarked K 1 i th bit Plane D Similarity Measurement Detection Result (1) Bit-plane decomposition (K) Composite key (D) Detector 3. Quality Metrics The proposed method was tested by using an image database of 100 color images. Some indicative examples are presented in this section to show the effects of the modifications caused to the image after embedding the watermark. Up to now, the research community has not deployed a general benchmarking platform for watermarking systems considering the quality of the produced watermarked image. The common practice is to measure the quality of the watermarked image using objective and subjective criteria. The subjective results are presented in table 2 where the original image along with the watermarked one can be viewed. The method produces a high quality watermarked image. Table 2. Subjective results Original Watermarked Figure 2. The watermark detection process Furthermore it has been observed that in a given region, the number of triangles to be found and their size is indicative of the number k used, thus giving another property of the patterns that the detector can exploit to draw safe conclusions of the pattern in use. An example of the above property is given in [9]. The example refers to the properties of the pattern created by reducing Pascal s triangle modulo two. A regular pattern of inverted triangles with various sizes differing by powers of two is clear. Large inverted triangles spanning the whole of Pascal s triangle begin at rows n=2 j. Consider the pattern down to the beginning of one such large inverted triangle (say down to the sixty-third row). A striking feature of the pattern is that the largest upright triangle contains three smaller triangles whose contents are similar (except at the scale of very small triangles) to those of the largest triangle but reduced in size by a factor of two. The pattern created by reducing Pascal s triangle modulo 2 is shown in Table 1. It is a very difficult task to calculate the distribution of 1s and 0s in an image bit plane. For practical reasons we consider the probability of finding a 1 or a 0 in a bit plane position equal to ½. The basic hypothesis is that the probability P of finding a=n 2 /2 preexisting random bits identical to a pattern created by Pascal s Triangle in a n x n image is 1/2 a. Therefore the probability of false detection of a watermark is extremely low (almost 0). Then, all of our experiments since we measure the similarity between a specific pattern (modulated Pascal tree) with the extracted information of a bit plane follow the Binomial Distribution. A fair threshold for our experiments considering attacks is to set the similarity threshold equal to 2/3. This value is giving very good results in watermark detection and keeps the probability of false detection very low. Boat.bmp Stones.bmp Lena.bmp Boat-wat.bmp Stones-wat.bmp Lena-wat.bmp The objective criteria include Peak Signal to noise Ratio, Mean Square Error, Bit by Bit compression between the original and watermarked image. The most common metric in watermarking field is PSNR (2). The results of the proposed method considering PSNR are presented in Table 3. PSNR=20 log 10 (255/RMSE) (2) where RMSE represents the Root of the Mean Square Error between the Original and the Watermarked image.

4 Table 3. Objective Quality Measurements (5 th bit plane) PSNR (db) Boat Stones Lena The PSNR results of our method are over 32.5 db which is considered as an acceptable distortion of the Original. 4. Attacks After a series of experiments were conducted, it was observed that, pending an attack, patterns with k that is a power of a number already used to create a pattern do not differ sufficiently enough to provide secure detection results. Therefore such numbers are not used in the same set of patterns. It was also observed that patterns where k is a prime number that is close enough to another prime number couldn t be accepted as a candidate k, to be used to reduce Pascal s triangle modulo k. It is proposed that for better results numbers differing by at least 10 should be used to create the modulated Pascal s Triangles, for best detector performance. Our method is found to be robust against Median filtering, Blurring and Cropping. In some cases the proposed method is robust even under Jpeg compression as can be shown in Table 4. Combined attacks using both blurring and Median Filtering were also performed, having good results. In these experiments a predefined similarity threshold (T=65%) was satisfied. This threshold is considered as acceptable, since the probability of having an unmwatermarked image bit plane similar to a pattern (modulated Pascal triangle) at 65% or higher is too low. 5. Conclusion and Future Work In this paper a new watermarking method of color images is presented. The method achieves to embed a large binary object (modulated Pascal s Triangle) in a color image, having at the same time robustness to common image processing operations. Since the amount of the data that correspond to the watermark is large, the three color channels can be used to embed the watermark. The main advantage of the method is its self similarity which giving to the detector extra strength comparing to classical spatial domain methods working in LSB. However, the self-similarity properties of the modulated Pascal s triangles combined with a more sophisticated embedding process can be used in order to design more efficient watermarking systems, providing robustness under JPEG compression and geometrical transformations. The method can be used as an image copyright protection mechanism, but the incomplete legal framework along with the big variety of attacks cannot completely safeguard the copyrighted material. Table 4. Indicative results of watermark survival (%) under common image processing operations (5 th bit plane) Blurring Boat Stones Lena Median Filtering 1 2 Boat Stones Lena Jpeg Compression High (10) High (9) High (8) Boat Stones Lena Cropping 10% Boat 89.1 Stones 88.9 Lena 89.3 Blur + Median Filtering 0.1, 1 0.2, 2 Boat Stones Lena References [1] Stefan Katzenbeisser, Fabien A.P. Petitcolas, Information Hiding Techniques for Steganography and Digital Watermarking, Artech House, [2] I. J. Cox, J. Kilian, T. Leighton and T. Shamoon, A Secure, Robust Watermark for Multimedia, First Workshop on Information Hiding, Newton Institute, Univ. of Cambridge, May [3] Kutter, M., F. Jordan, and F. Bossen, Digital Signature of Color s Using Amplitude Modulation, in Proceedings of the SPIE, Storage and Retrieval for and Video Databases V, 1997, pp [4] S.A.M Gilani, I. Kostopoulos, A.N. Skodras, Adaptive Color Watermarking, 14 th IEEE International Conference on Digital Signal Processing, 1-3 July 2002,Santorini, Greece. [5] S. Armeni, D. Christodoulakis, I. Kostopoulos, Y. Stamatiou, M. Xenos, A Transparent Watermarking Method for Color s, First IEEE Balcan Conference on Signal Processing, Communications, Circuits, and Systems, June 2000, Istanbul, Turkey. [6] R. G. van Schyndel, A. Z. Tirkel, C. F. Osborne, A Digital Watermark, Proc. IEEE International Conference on Processing, ICIP-94, 1994, Vol.2, pp

5 [7] M.Yeung and F.Mintzer, An Invisible Watermarking Technique for Verification, Proc. ICIP 97, Santa Barbara, California, at [8] J.Fridrich and M.Goljan, Protection of Digital s using Self Embedding, Symposium on Content Security and Data Hiding in Digital Media, Newark, NJ, USA, May [9] S. Wolfram Geometry of Binomial Coefficients, American Mathematical Monthly, Vol. 91, pages , November [10] G.-J. Yu, C.-S. Lu, H.-Y. Mark Liao, A Messagebased Cocktail Watermarking System, Elsevier, Pattern Recognition 36 (2003), pages [11] F. Y. Shih, S. Y. T. Wu, Combinational Watermarking in the Spatial and Frequency Domains, Elsevier, Pattern Recognition 36 (2003), pages