Invariant Image Watermark Using Zernike Moments

766 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003 Invariant Image Watermark Using Zernike Moments Hyung Shin Kim and Heung-Kyu Lee, Member, IEEE Abstract This paper introduces a robust image watermark based on an invariant image feature vector. Normalized Zernike moments of an image are used as the vector. The watermark is generated by modifying the vector. Watermark signal is designed with Zernike moments. The signal is added to the cover image in the spatial domain after the reconstruction process. We extract the feature vector from the modified image and use it as the watermark. The watermark is detected by comparing the computed Zernike moments of the test image and the given watermark vector. Rotation invariance is achieved by taking the magnitude of the Zernike moments. Image normalization method is used for scale and translation invariance. The robustness of the proposed method is demonstrated and tested by using Stirmark 3.1. The test results show that our watermark is robust with respect to the geometrical distortions and compression. Index Terms Feature extraction, geometrical attack robustness, watermark, Zernike moment. I. INTRODUCTION THE DIGITAL watermark is a signal added to digital data that can be detected or extracted later to make an assertion about the data. After its earlier proposal as a method for copyright protection, it has drawn significant attention from many researchers and there has been a very intensive research in this area [1], [2]. Many different watermarks for still images and video contents are vulnerable to small amount of geometrical distortions [3]. This problem is most pronounced when the original image is not available to the detector. Hence, the designing a watermark resistant to geometrical distortions is remained as an open problem. Since the recognition of the need for watermarking schemes resilient to geometric distortion, many research results were reported [4] [6], [8]. Most of them are based on the shift-invariant property of the Fourier transform. Among various approaches, invariant watermark has advantages compared to the others. The invariant watermark schemes are based on a strong mathematical theory. As such, watermarking methods belong to this class will have provable invariance as well as empirical results. Also, there is more potential to design reliable system using the relevant mathematical theories. The invariant watermark which is robust against rotation, scale, and translation (RST) was first reported in [8]. They used the Fourier Mellin transform for their watermark. It is an Manuscript received December 16, 2002; revised March 13, 2003. This work was supported by the Korea Science and Engineering Foundation (KOSEF) through the Advanced Information Technology Research Center (AITrc). The authors are with the Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology (KAIST), Daejon 305 701, Korea (e-mail: hskim@casaturn.kaist.ac.kr). Digital Object Identifier 10.1109/TCSVT.2003.815955 integral invariant. Shift invariance is achieved from the translation invariant property of magnitude of the Fourier coefficients. For scale and rotation invariance, they take the Fourier magnitude spectrum of the log-polar mapped Fourier magnitude of the image. This procedure is equivalent to the Fourier-Mellin transform. By doing that, a scale and a rotation are converted into a translation which is invariant after another Fourier transform. The work by [9] is also based on the Fourier Mellin transforms. Most of the methods using the Fourier Mellin transform suffer severe implementation difficulty. It is mainly due to interpolation error by the log-polar and inverse log-polar mapping during embedding and detection procedure. The nonuniform sampling grid of the log-polar mapping also causes aliasing. Watermarking algorithms using a feature of an image were proposed in [6], [7]. Moments and invariant functions of moments have been extensively used for invariant feature extraction in a wide range of two- and three-dimensional pattern recognition applications [10] [14]. Hu [15] derived seven moment invariants which are RST invariant from the regular moments. The same invariants were used for watermark in [16]. They adopted Hu s moment invariant functions and used them as the watermark. They embed the watermark by modifying the moment values of the image. In their implementation, they had to do an exhausted search to determine the embedding strength. They could not embed watermark systematically. Of various types of moments defined in the literature, Zernike moments have been shown to be superior to the others in terms of their insensitivity to image noise, information content, and ability to provide faithful image representation [17]. Recently, a Zernike moment was used as the invariant watermark in [19]. Image is subdivided into co-centric rings and a watermark signal is modulated into the Zernike moments of each ring. The watermarked image is achieved by reconstructing the image from the modulated moments of the segmented subimages. However, the reconstruction procedure is computationally expensive and there is severe fidelity loss during the process. Hence, we question their performance. Another problem in [19] is that authors have shown only the rotation invariance; they did not mention the scale and translation and other possible distortions. Scale and translation invariance can be achieved by preprocessing the image to a standard image. Image normalization technique has been used for invariant pattern recognition [20]. Once an image is translated to its centroid and scaled to a standard size, we can achieve the invariance against scale and translation. A generalized approach to correct geometric distortion for watermarking schemes using normalization is proposed in [21] and [22]. The image is translated and scaled to a standard size 1051-8215/03$17.00 2003 IEEE

KIM AND LEE: INVARIANT IMAGE WATERMARK USING ZERNIKE MOMENTS 767 Fig. 1. Reconstruction of letter A. From left to right:original image, reconstructed image with order =5, 15, 20, 30. prior watermark embedding and the watermarked image is inverse transformed to its original form for distribution. At the detector, the test image is transformed to the same standard image and embedded signal can be successfully recovered. A scheme of image representation by the moduli of Zernike moments of image appropriately normalized by means of loworder regular moments was studied by Khotanzad and Hong [18] and shown to yield superior results to other moment-based methods in an invariant character recognition task. We, therefore, adopt this scheme for our watermark. In this paper, we propose a new invariant watermark based on Zernike moment. We achieved the rotational invariance from the property of the Zernike moment and scale and translation invariance by normalization. Hence, we follow the procedures suggested in [18]. Our method is different from [19] in that we embed the watermark by directly adding orthogonal patterns to the spatial domain rather than to the Zernike moment. Hence, our method will not suffer the fidelity degradation. Also, our method is RST-invariant while the method in [19] is rotation invariant only. This paper is organized as follows. In Section II, we describe about the Zernike moments and their properties. In Section III, we present our embedding and detection algorithms. In Section IV, we show the experimental results. In Section V, we discuss some of the issues regarding to our method, and in Section VI, conclusions are drawn. II. BACKGROUNDS In this section, we describe Zernike moments and their properties. We explain how we achieve the RST invariance using them. Some of the implementation issues are discussed. Zernike moments have been investigated by Perantonis and Lisboa [23] and by Khotanzad and Lu [24] among others. Some of the materials in the following are based on [18] and [24]. A. Zernike Moment The Zernike moments [25] of order with repetition for a continuous image function that vanishes outside the unit circle are where a nonnegative integer and an integer such that is nonnegative and even. The complex-valued functions are defined by (1) (2) where and represent polar coordinates over the unit disk and are polynomials of (Zernike polynomials) given by. These polynomials are or- Note that thogonal and satisfy with (3) a b otherwise For a digital image, the integrals are replaced by summations. To compute the Zernike moments of a given image, the center of the image is taken as the origin and pixel coordinates are mapped to the range of the unit circle. Those pixels falling outside the unit circle are not used in the computation. Note that. Suppose that one knows all moments of up to a given order. A discretized original image function whose moments are those of up to the given order can be computed. By orthogonality of the Zernike basis, we can reconstruct as Note that as approaches infinity, will approach. The reconstruction process is illustrated in Fig. 1 for a 50 50 binary image of letter. The reconstructed binary images are generated by using (5) followed by mapping to [0, 255] range. It shows that lower order moments capture gross shape information and high frequency details are filled in by higher order moments. In this example, orders 2 30 are used. Order 0 and 1 are omitted, as they are independent to the image feature after normalization. B. Invariance of Normalized Zernike Moment Consider a rotation of the image through angle. If the rotated image is denoted by, the relationship between the original and rotated images in the same polar coordinate is (4) (5) (6)

768 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003 Fig. 2. Watermark detection. It can be shown that the Zernike moments image become [18], [24], of the rotated Equation (7) shows that each Zernike moment acquires a phase shift on rotation. Thus,, the magnitude of the Zernike moment, can be used as a rotation-invariant feature of the image. Scale and translation invariance can be achieved by utilizing the image normalization technique as shown in [21], [22]. An image function can be normalized with respect to scale and translation by transforming it into, where with (, ) being the centroid of and, with a predetermined value and its zero-order moment. Hence, we first move the origin of the image into the centroid and scale it to a standard size. If we compute the Zernike moments of the image, then the magnitudes of the moments are RST invariant. III. ALGORITHM As the magnitudes of Zernike moments are RST invariant after proper normalization, we use them as the watermark. The watermark signal is embedded in the spatial intensity domain after reconstruction of the chosen watermark vector consisting of Zernike moments. Embedding strength is controlled by an iterative feature modification and verification procedure. This procedure avoids the implementation errors that can occur during insertion and detection of the watermark. At the detector, the Zernike feature vector is estimated from the test image and the similarity between the vector and the watermark vector is computed. We use root-mean-square-error (rmse) as our similarity measure instead of the traditional normalized correlation because the feature vectors are not white and the correlation measure can not produce peak value when they are same vectors. Hence, we measure the distance between two vectors using rmse function. If the rmse value is smaller than the threshold, the watermark is detected. The original image is not required at the detector. We define the detector first and an iterative embedder is designed using the detector. (7) (8) A. Watermark Detection Fig. 2 shows the detection procedure. The detector takes a test image and normalize it into a standard image as (8) for scale and translation compensation. Zernike moments of the normalize image are computed. A feature vector is constructed with the Zernike moments of the test image as, where is the length of the feature vector and is on the order of Zernike moments. The similarity defined with rmse between the extracted vector and the watermark as follows: If is smaller than the detection threshold, the watermark is detected. Note that the moments and are not included in the feature vector construction. Those moments are modified to have known values during the normalization procedure. B. Watermark Insertion As we use the Zernike feature vector as the watermark, we try to modify the Zernike moments of the input image. Though watermark signal can be inserted into the Zernike moments of cover image, we have found that this approach causes severe implementation difficulty. After modifying the Zernike moments of the input image, we have to reconstruct watermarked image using (5). However, as we mentioned before, the reconstructed image cannot be the anticipated, and instead we get. The reconstruction procedure requires Zernike moments with high order and this leads to a heavy computation load. We have tried to reconstruct 256 level 256 256 gray images and we could hardly recognize the images reconstructed from Zernike moments even with order. Also, it was very time consuming. Hence, we believe that it is not feasible to embed the watermark by modifying the Zernike moments of the input image directly. A watermark signal can be directly added into the intensity of the image using the Zernike polynomials. If we try to modify of the original image by, then we can compute the contri- (9)

KIM AND LEE: INVARIANT IMAGE WATERMARK USING ZERNIKE MOMENTS 769 bution of the modification as intensity pixel values by the reconstruction equation. The contribution can be shown as with k m n k m l otherwise (10) As,, the distortion added to the original image is bounded as, which means by adjusting, we can exactly control the maximum pixel distortion to the images. Note that for modification of, we also have to change to have real valued intensity after the reconstruction process. We simply add the reconstructed intensity watermark signal into the cover image to achieve the watermarked image for distribution. Ideally, the added signal affects only and the value becomes For all,. Hence, we can modify the Zernike feature vector of the image by adding the reconstructed watermark signal in spatial domain. In some watermarking methods, we may not be able to extract the exact embedded signal at the detector. As reported in previous research ([8] and [9]), there are situations when the estimated signal at the detector is different from the embedded signal in its nature. Embedding functions without exact inverse function or discrete nature of the implementation can be the reasons. In [9], the authors have provided approximation methods to reduce the effects of these errors. Instead of using a similar method, we approach this problem differently. As we have proposed in [7], we use the iterative embedding method. Let the feature vector of the cover image be. After embedding, we intended the feature vector of the watermarked image to be. However, at the detector we get instead of. Hence, after embedding the watermark signal, we apply the feature extractor from this watermarked image and use the extracted feature as the embedded watermark instead of the initially modified feature vector. In this way, we can avoid the inversion errors. However, to guarantee the uniqueness of the watermark and its perceptual invisibility after insertion, we need a validation procedure to use as a watermark. We empirically measure the maximum noise level resulting from geometric distortions with the detector response as follows: (13) where is the feature vector of an image and is the feature vector of the image after RST distortions. We should adjust the embedding strength so that the distance between the two features from the unmarked and the marked image show a higher value than. However, the embedding strength cannot be higher than, which defines the minimum distance between features of the images and (14) (11) By the orthogonal property of the Zernike moment as in (4), we have (12) where and are the feature vectors of different images. We preset and values empirically. With varying the embedding parameters, it is checked if. If this condition is satisfied and the embedded signal is unobtrusive, is accepted as a watermark. We repeat this validation procedure until we get the right result. In this way, we can embed the watermark without exact inversion of the modified signal. From the above observations, we can design the embedding procedure. Fig. 3 shows the whole insertion procedure. The watermark signal to be embedded is defined as follows: if otherwise (15) where are the embedding locations and the locations of the nonzero Zernike moments. We reconstruct the intensity domain representation of as (5) and get. The watermarked image is achieved by adding to the cover image. We extract the watermark to be used for detection by extracting the Zernike moments of after normalization. Then we validate the watermark iteratively until it meets.

770 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003 Fig. 3. Watermark insertion. Fig. 4 shows insertion and detection example with 256 256 Lena image. We have embedded a watermark signal with and. Fig. 4 shows the watermarked Lena image. The measured PSNR is 41.78 db and inserted noise is invisible. The reconstructed is shown in Fig. 4. We took the absolute values of and equalized them for better display. Fig. 4(c) shows the histogram of. The added noise is well spread around the zero value, which we have anticipated from (10). Those two orthogonal complex polynomials selected for embedding is shown in Fig. 4(d). We have displayed the real part only. Fig. 5 shows the detected watermark at the detector. We can see the peaks at and. Note that although the detection looks perfect, there are little peaks around the intended moments. Those unwanted peaks are due to the discrete implementation of the procedure as analyzed in [26]. IV. EXPERIMENTAL RESULTS Experiments are performed with 50 images from the Corel image library [27]. For valid watermark generation, and are determined empirically using unwatermarked images. The similarity is measured between unmarked test images and the smallest is chosen for. For the test we use. For the determination of, robustness of the defined feature vector is tested. Similarity is measured between the original image and attacked images. The largest is chosen for. Fig. 6 shows the variation of the feature vector after rotation, scale, random geometric attack, and JPEG compression, respectively. From these graphs, we set. Zernike moments are modified with controlling so that the fidelity of the watermarked image remains over PSNR 36 db. Embedding location is determined randomly excluding, which are the independent terms. We embedded at two or three locations out of ten Zernike moments which are computed with order. is used for the detection threshold. Two experiments are performed to demonstrate robustness. Using images of Lena, Mandrill, and Fishingboat, the watermark detection ratio is measured for each class of attack generated by Stirmark benchmark software. The second experiment is performed to estimate the false positive and negative probability with 50 images from the Corel image library. Table I shows the watermark detection ratio compared to other published results. The ratio of 1 means 100% detection success and 0 means the complete detection failure. Our method shows good performance against scaling, rotation, and JPEG compression. Detection failure was found when we scale the image down to 50%. This is due to the large amount of interpolation errors during normalization. Rotation with large angle causes more detection failures than with small angles. This can be anticipated as larger portion of the image is cut out after the large angel rotation and crop operation. As our watermark is using a global feature of the image, our method shows strong resilience to random geometric distortion. The false positive probability and false negative probability is measured with 50 unmarked images and 50 marked images. For each watermarked image, StirMark generates attacked images. In this experiment, we used only two attacked images for each watermarked image that makes 100 attacked images. We measure the empirical probability density function (pdf) of the computed with histogram. Though we do not know the exact distribution of, we approximate the empirical pdf of to the Gaussian distribution to show rough estimation of the robustness. and can be computed using the estimates of mean and variance. Random geometric attack performance is the worst with and. It shows that our method performs well over

KIM AND LEE: INVARIANT IMAGE WATERMARK USING ZERNIKE MOMENTS 771 (c) (d) Fig. 4. Watermark insertion and detection in Lena image. Watermarked Lena image. Reconstruced ^g(x; y). (c) Histogram of ^g(x; y). (d) Added polynomials. A. Rotation Fig. 7 shows the histogram of and ROC curve after rotation by 1 and 30. Different from other invariants, we do not need to shift the computed vector as Zernike moment is rotationally invariant. The performance of rotation by a large angle is poor because we used the rotation-and-crop option for attack. With, is and is. False negative probability shows better performance than false positive probability in this attack. This is because the pdf of the similarity between unmarked images and watermarks has relatively large variance that resulted into the larger false positive probability. B. Scaling Fig. 5. Detected watermark. the intended attacks. The similarity histograms and receiver operating characteristic (ROC) curves ( versus for several thresholds) are produced for analysis. In this section, four attacks are examined: rotation, scaling, random geometric distortion, and compression. The detection histogram was measured using 75% scaled down images and 150% scaled up images. As the histogram in Fig. 8 shows, the watermarked images show strong resistance to scaling attack. The ROC curve shows that is and is. These values are relatively lower than the other attacks, which means that our method performs well with scaling attacks.

772 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003 Fig. 6. (c) (d) Histogram of s between features from original and attacked unmarked images. Rotation (1.0, 30.0 ). Scaling (20:75; 21:4). (c) Compression (Q =30; 70): (d) Random geometric attack. TABLE I STIRMARK TEST RESULTS COMPARED TO OTHER METHODS C. Random Geometric Distortion This attack simulates the print-and-scanning process of images. It applies a minor geometric distortion by an unnoticeable random amount in stretching, shearing, and/or rotating an image [3]. In Fig. 9, the histogram shows large variance in the similarity between the watermark and unmarked image. As a result, is and is, which are relatively large compared with others. Not many previous methods survive this attack and our algorithm works well even with those numbers. D. Compression JPEG compression with Q and 70 was applied after watermark embedding. With Q, the watermarked image fidelity is unacceptable. However, our method survives the

KIM AND LEE: INVARIANT IMAGE WATERMARK USING ZERNIKE MOMENTS 773 Fig. 7. Robustness: Rotation 1, 30. Histogram of s. ROC curve. Fig. 8. Robustness: Scale 75%, 150%. Histogram of s. ROC curve. harsh compression attack. Fig. 10 shows the histogram and ROC curve. is and is. These numbers show that our method has strong resilience to JPEG compression. V. DISCUSSIONS A. Implementation Errors Due to the discretization error, perfect invariance cannot be achieved during implementation. There are two error sources in computation of Zernike moments of discrete images. The first is the geometric error that occurs due to the fact that the area used for the moment calculation, the summation of the square pixels, is not equal to the area of the unit disk. The second source of the errors is the numerical error caused by the fact that during the computation of the moment, there are points whose values are not initially given. In this situation, we have to interpolate the value according to a known interpolation methods which introduce errors. These errors can be reduced by using pseudo- Zernike moments [17] instead of standard Zernike moments or various interpolation methods [26], [28]. B. Complexity Analysis It takes about 5 min to compute the Zernike moments of 256 256 gray image with. We have implemented our algorithm using Matlab on a Pentium 1.5-GHz PC. With,we compute the first nine moments of the image. The most time consuming part is in the computation of Zernike polynomial. There are four factorial operation to compute one value which is dependent on the order and repetition variables. If we want to have more moments for better reconstruction and watermark capacity, we need to increase the order and repetition values. This leads to a heavy computational load. This problem can be improved by using the table lookup method. We compute the value once and store it in a table. Whenever is called, we simply look up the table and return the

774 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 13, NO. 8, AUGUST 2003 Fig. 9. Robustness: Random geometric distortion. Histogram of s. ROC curve. Fig. 10. Robustness: JPEG Compression Q = 30 and 70. Histogram of s. ROC curve. value immediately. With this method, it takes about 1 min for embedding procedure. C. Capacity Current implementation works for zero-bit watermarks. With simple modification, we can embed more bits. After the iterative procedure to generate the valid watermarks, we can construct a code book such as a dirty-paper code [29]. Information is assigned to each valid watermark code during embedding. At the detector, the code book is implemented within the detector. During detection, the detector compares extracted feature with the vectors registered in the code book. When a measured similarity value reaches a previously determined threshold, it shows the assigned information from the code book. D. Embedding Without Exact Inversion If an embedding function does not have exact inversion function, the resulting watermarked image will be distorted. This distortion reduces the image fidelity and watermark signal strength. As argued in [9], having exact inversion is not the necessary condition for the embedding function. Two approaches can be considered. One method is defining a set of invertible vectors and works only with those vectors during embedding procedure. Though the embedding space is reduced, exact inversion is possible. Another approach is to use a conversion function that maps the embedded watermark and the extracted vector. Our approach belongs to this category. At the detector, after estimation of watermark, this signal is mapped into the inserted watermark using the conversion function. VI. CONCLUSION We propose a new RST-invariant watermarking method based on algebraic invariants. Zernike moments are used for the invariant watermark. With the combination of normalization, we have achieved RST invariance. Novel watermark embedding

KIM AND LEE: INVARIANT IMAGE WATERMARK USING ZERNIKE MOMENTS 775 and detection algorithms which can reduce the implementation errors are proposed. The watermark is embedded by modifying the Zernike feature vector of the original image. The watermark is generated during embedding procedure after iterative validation procedure. We have shown a mathematical description about the invariance property and have also performed simulation. The results show that our method is robust against geometric distortion and compression, as intended. REFERENCES [1] I. J. Cox and M. L. Miller, Eletronic watermarking: the first 50 years, in Proc. IEEE Int. Workshop Multimedia Signal Processing, 2001, pp. 225 230. [2] F. Hartung and M. Kutter, Multimedia watermarking technique, Proc. IEEE, vol. 87, pp. 1079 1107, July 1999. [3] F. A. P. Petitcolas, R. J. Anderson, and M. G. Kuhn, Attacks on copyright marking systems, in Proc. 2nd Int. Workshop Information Hiding, 1998, pp. 218 238. [4] S. Pereira and T. Pun, Robust template matching for affine resistant image watermarksi, IEEE Trans. Image Processing, vol. 9, pp. 1123 1129, July 2000. [5] M. Kutter, Watermarking resisting to translation, rotation, and scaling, in Proc. SPIE Multimedia Systems Applications, 1998, pp. 423 431. [6] M. Kutter, S. K. Bhattacharjee, and T. Ebrahimi, Toward second generation watermarking schemes, in Proc. IEEE Int. Conf. Image Processing, 1999, pp. 320 323. [7] H. S. Kim, Y. Baek, and H. K. Lee, Rotation-, scale-, and translationinvariant image watermark using higher order spectra, Opt. Eng., vol. 42, no. 2, pp. 340 349, Feb. 2003. [8] J. J. K. O Ruanaidh and T. Pun, Rotation, scale, and translation invariant spread spectrum digital image watermarking, Signal Processing, vol. 66, pp. 303 317, 1998. [9] C. Y. Lin, M. Wu, J. A. Bloom, I. J. Cox, M. L. Miller, and Y. M. Lui, Rotation, scale, and translation resilient watermarking for images, IEEE Trans. Image Processing, vol. 10, pp. 767 782, May 2001. [10] B. A. Dudani, K. J. Breeding, and R. B. McGhee, Aircraft identification by moment invariants, IEEE Trans. Comput., vol. C-26, pp. 39 46, 1977. [11] S. S. Reddi, Radial and angular moment invariants for image identification, IEEE Trans. Pattern. Anal. Machine Intell., vol. PAMI-3, pp. 240 242, 1981. [12] Y. S. Abu-Mostafa and D. Psaltis, Image normalization by complex moments, IEEE Trans. Pattern. Anal. Machine Intell., vol. PAMI-7, pp. 46 55, 1985. [13] A. P. Reeves, R. J. Prokop, S. E. Andrews, and F. P. Kuhl, Three dimensional shape analysis using moment and Fourier descriptors, IEEE Trans. Pattern. Anal. Machine Intell., vol. 10, pp. 937 943, 1988. [14] J. Wood, Invariant pattern recognition: a review, Pattern Recognit., vol. 29, no. 1, pp. 1 17, 1996. [15] M. K. Hu, Visual pattern recognition by moment invariants, IEEE Trans. Inform. Theory, vol. 8, pp. 179 187, 1962. [16] M. Alghoniemy and A. H. Tewfik, Image watermarking by moment invariant, in Proc. IEEE Int. Conf. Image Processing, 2000, pp. 73 76. [17] C. H. Teh and R. T. Chin, On image analysis by the methods of moments, IEEE Trans. Pattern Anal. Machine Intell., vol. 10, pp. 496 513, Apr. 1988. [18] A. Khotanzad and Y. H. Hong, Invariant image recognition by Zernike moments, IEEE Trans. Pattern Anal. Machine Intell., vol. 12, pp. 489 497, May 1990. [19] M. Farzam and S.Shahram Shirani, A robust multimedia watermarking technique using Zernike transform, in Proc. IEEE Int. Workshop Multimedia Signal Processing, 2001, pp. 529 534. [20] J. Leu, Shape normalization through compacting, Pattern Recognit. Lett., vol. 10, pp. 243 250, 1989. [21] M. Alghoniemy and A. H. Tewfik, Geometric distortion correction through image normalization, in Proc. IEEE Int. Conf. Multimedia and Expo, 2000, pp. 1291 1294. [22] P. Dong and N. P. Galatsanos, Affine transform resistant watermarking based on image normalization, in Proc. IEEE Int. Conf. Image Processing, 2002, pp. 489 492. [23] S. J. Perantonis and P. J. G. Lisboa, Translation, rotation, and scale invariant pattern recognition by high-order neural networks and moment classifiers, IEEE Trans. Neural Networks, vol. 3, pp. 241 251, 1992. [24] A. Khotanzad and J. H. Lu, Classification of invariant image representations using a neural network, IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1028 1038, 1990. [25] F. Zernike, Beugungstheorie des schneidenverfahrens und seiner verbesserten form, der phasenkontrastmethode, Physica, vol. 1, pp. 689 704, 1934. [26] S. X. Liao and M. Pawlak, On the accuracy of Zernike moments for image analysis, IEEE Trans. Pattern Anal. Machine Intell., vol. 20, pp. 1358 1364, Dec. 1998. [27] Corel Corporation, Corel Stock Photo Library 3. [28] J. Altmann, On the digital implementation of the rotation-invariant Fourier-Mellin transform, J. Inform. Process. Cybern., vol. EIK 28, no. 1, pp. 13 36, 1987. [29] M. L. Miller, Watermarking with dirty-paper codes, in Proc. IEEE Int. Conf. Image Processing, 1999, pp. 538 541. Hyung Shin Kim received the B.S. and Ph. D. degrees in computer science from Korea Advanced Institute of Science and Technology (KAIST), Daejon, in 1990 and 2003, respectively, and the M.S. degree in satellite communication engineering from the University of Surrey, Guildford, U.K., in 1990. From 1992 to 2001, he was with the Satellite Technology Research Center (SaTReC), KAIST, as a Senior Researcher. At SaTReC, he worked on real-time operating system and on-board computer systems. From 1998 to 2000, he was the Project Manager for the development of a small satellite, KAISTSAT-1. Since joining the Real-Time Computing Laboratory at KAIST in 1994, his research has shifted to problems in multimedia signal processing and digital contents right management. His research interests include information hiding, multimedia security, and pattern recognition. Heung-Kyu Lee received the B.S. degree in electronics engineering from the Seoul National University, Seoul, Korea, in 1978, and the M.S. and Ph.D. degrees in computer science from the Korea Advanced Institute of Science and Technology (KAIST), Daejon, in 1981 and 1984, respectively. From 1984 to 1985, he served as a Research Scientist at the University of Michigan, Ann Arbor. Since 1986, he has been a Professor with the Department of Computer Science, KAIST. He is currently also a Director of the Digital Right Management (DRM) forum in Korea, a Committee Chairman of the Secure Digital Contents Association (SEDICA) in Korea, and Vice Director of the AITRC center in KAIST. He was a Director of the Korean Society of Remote Sensing. His major interests are digital watermarking, real-time processing, and image processing. He is an author/coauthor of more than 120 journal and conference proceedings papers in his research areas. Dr. Lee has been a reviewer of many international journals, including the Journal of Electronic Imaging, Journal of Real-Time Imaging, and the ACM Multimedia System-Journal. He was a Program Chairman of IEEE Real-Time Computing Systems and Applications Conference in 1999 and 2000, respectively. He received the Order of Civil Merit, SukRyu Medal 5066 from the Republic of Korea in October 1992. He obtained a Best Paper Award from the Korean Information Science Society in 1992. He His biography has been selected by Marquis Who s Who for inclusion in Who s Who in Science and Engineering, Who s Who in America, and Who s Who in the World since 1996.