advertisement

Digital Restoration of Watermark Images Andrey Karnaukhov(*), Igor Aizenberg($), Alois Haidinger(-),Victor Karnaukhov(*) Nikolai Merzlyakov(*), Olga Milukova(*), and Emanuel Wenger(#) (*) Russian Academy of Sciences, Institute for Information Transmission Problems, Moscow, Russia E-mail: [email protected], [email protected], [email protected], [email protected] ($) Neural Network Technologies, Tel Aviv, Israel E-mail: [email protected] (-) Austr. Acad. of Sci., Comm.of Paleography a. Codicology of Medieval Manuscripts, Vienna, Austria E-mail: [email protected] (# ) Austrian Academy of Sciences, Commission of Scientific Visualization, Vienna, Austria E-mail: [email protected] Abstract Can traditional methods of image restoration be applied for restoration of watermark images? This paper deals with beta-radiographic hardcopies of watermark images taken from the old books and documents. The fast Fourier transform techniques used for restoration of watermark images. Software tools were implemented in the frame of an integrated system for digital processing, identification of watermark images and database management. The watermark images restored by using the Tikhonov’s regularization filter are presented. 1. Introduction Watermarks are widely used for chronological identification and classification of historical documents and corresponding historical events since more than 100 years. To identify a given watermark, incunabulists, medievalists, historians, and other researchers use catalogues of watermarks published in tens of volumes all over the world [1,2]. The images in these catalogues represent graphic copies of watermarks were received by hand-draw sketching from pages of historical documents, medieval handwritten books, and incunabula. The identity of a watermark with one in the standard catalogues is a good indicator for the age of the watermark, the paper, and the document in question. So, chronological identification and classification of historical documents and corresponding historical events at such approach is carried out by simple search of an identical or a similar watermark in catalogues and performance of some measurements with the help of a ruler. A low efficiency of such identification by using these methods is obvious. Until the 19th century all paper was made by using a special paper-producing mold: a rectangular sieve consisting of a frame and a bottom made of a wire mesh. From the thirteenth century on nearly all European papermakers characterized their production by means of watermarks. These watermarks were caused by wire figures, which were fixed on the wire mesh. The molds were dipped into vats of liquid pulp. When lifting them out, the liquid drained out through the wire mesh and the fibers became interwoven to a sheet of paper. The pattern of the mesh with the watermark wire-figure attached on it was imprinted in the paper. Due to some natural technological restrictions the longevity of paper producing molds was short. Molds, and more particularly, meshes and wire-figures were in use only for one or two years or even a few months. So, undated manuscripts can be accurate dated when identical watermarks are found in dated ones. As a matter of fact, watermarks performed the function of legal trademarks of the paper producers. A particular paper producer after breakage of the paper-producing mold to save his/her trademark had to repair or usually recreate mold with the same watermark. Such repaired or recreated meshes and/or watermarks slightly or noticeably differed from their predecessor. For correct dating of such slightly deviated watermarks the full mesh structure of the paper-producing mold has to be analyzed too. 2. Image Restoration Techniques Watermarks and wire meshes of paper-producing molds are imprinted in the paper as small deviations in the thickness of paper. These thickness deviations can be revealed, displayed, and hardcopied by several methods. The electron radiography or betaradiography seem to be the best in present time among the methods for a unique recording of watermarks because of their good quality. Small deviations in the density of the paper are recorded sufficiently well with these procedures. A typical watermark image scanned from a beta-radiographic hardcopy is presented in Figure 1. The imprinted watermark (c) and mesh structure (laid lines (b, and chain lines (c)) are recorded as inhomogeneous structure of low contrast smoothed lines corrupted by a noise: contrast and smoothed black and white spots of different forms and sizes. Figure 1 A typical watermark image scanned from a beta-radiographic hardcopy. Generally speaking, we can consider these smoothed images of watermarks, laid and chain lines as blurred images of the original “ideal” images of these objects. From this point of view, we can re-formulate our task to the task of digital restoration of watermarks, laid and chain line images from their electron radiography or betaradiography hardcopies. Image restoration is often defined as a process of recovering an original image from its blurred degraded version [3]. The image restoration problem is usually formulated in the following way: given a degraded image u~x, y , it is required to estimate an original non-degraded image zx, y from the following equation: u~ ( x, y ) u ( x, y ) n( x, y ), (1) x, y , or in the matrix form: u~ Az n, (2) where A is a linear imaging operator, ux, y is the blurred image, nx, y is the noise, u~x, y is the output blurred image degraded by noise. There are a lot of different approaches in solving this problem. The most universal techniques are given by the regularization and statistical estimation approaches [3-5]. In both cases, the solution of the restoration problem are transformed to estimation of either the conditional, or the unconditional extremum of a functional. Unfortunately, a direct implementation of the minimization task is difficult in the general twodimensional case. A simplification of the minimization task is usually based on usage of specific features of the integral operator A (see equation (2)). For example, if the imaging system can be described by a homogeneous operator A and the degraded image u~x, y is defined on the whole of plane x, y , the equation (1) comes to the convolution type. In such case, the blurred image is defined by the following equation: u~ ( x, y ) h( x , y ) z ( , )dd n( x, y ) (3) where u~ ( x, y ) is the blurred image, h( x , y ) is the blurring function, n( x, y ) is the noise, and z ( , ) is the desired, original image. This equation can be solved by using the fast Fourier transform technique [3]. We should specially emphasize that the degraded image u~x, y is usually defined on a bounded domain. It does not permit to apply Fourier transform directly to the equation (3). To overcome this restriction an additional procedure is required to extend the definition of the degraded image onto the whole plane x, y , [6]. The convolution nature of the above equation implies that its equivalent Fourier representation is ~ U ( f x , f y ) Z ( f x , f y ) H ( f x , f y ) N ( f x , f y ), ~ where U ( f x , f y ), Z ( f x , f y ), and N ( f x , f y ) are the Fourier spectra of the blurred image, original image, and noise, respectively, and H ( f x , f y ) is the blurring transfer function. It is known that the general linear solution of the equation (3) can be written as zˆ ( , ) K ( s, t )u~ (s, t )dsdt , where the kernel of the inversion has the following form: K ( s, t ) 1 4 2 R( f x , f y )e i ( sf x tf y ) df x df y 1 4 2 H * ( f x , f y )e i ( sf x tf y ) 2 H ( f x , f y ) ( f x , f y ) df x df y and R( f x , f y ) is the restoration filter, and ( f x , f y ) is a given function. In the presence of noise the optimal restoration filter (in the MSE criteria) is the least squares filter or the Wiener filter [3] H *( fx, fy ) R( f x , f y ) , S nn ( f x , f y ) 2 H( fx, fy ) S zz ( f x , f y ) (4) where H ( f x , f y ) is like above, S nn ( f x , f y ) and S zz ( f x , f y ) are the noise and the object power spectra, which are assumed to be known. It is also assumed that the noise added is white noise, i.e., its spectral density is constant, and the picture and the noise are uncorrelated. This method works well for images with a high signal to noise ratio (SNR), which is defined to be the ratio between the variance of the picture and the variance of the noise, and performs poorly for images with low SNRs. 3. Software implementation and experimental results For the experimental implementation of this approach we selected the linear model of image degradation (3) and used Fourier transform techniques for restoration of watermark images. For restoration of watermark images we used the Wiener filter (4) and a particular realization of the Tikhonov’s regularization filter. The second filter had the following transfer function: R( f x , f y ) H *( fx, fy ) 2 H ( f x , f y ) (1 ( f x2 f y2 )) , (5) where H ( f x , f y ) is like above, and are non-negative regularization parameters. Experimental results are given in Figure 2 and Figure 3, where Figure 2(a) the initial blurred watermark image; Figure 2(b) the watermark image restored by using the Wiener regularization filter (5), Figure 3(a) the initial blurred watermark image; Figure 3(b) the watermark image restored by using the regularization filter (5). All required software tools were implemented in the frame of an integrated system for digital processing, identification of watermark images and database management. Its detailed description is given in [7]. User interaction with this system is realized through a graphical user interface containing a set of graphical forms, menus, buttons, and other controlling objects. This graphical user interface is designed in the Windows-style. The integrated system is implemented on a PC-based platform and runs under Windows 9*/NT/2000 or higher operating system. Acknowledgements This work is supported partially by the Russian Foundation for Basic Research under the project numbers 99-07-90017 and 01-07-90354. References 1. Briquet Ch. M., Les Filigranes. Dictionnaire historique des marques du papier dés leur apparition vers 1282 jusqu’en 1600. Paris 1907. 2. Piccard G., Die Wasserzeichenkartei Piccard im Hauptstaatsarchiv Stuttgart. Findbuch I-XV, W. Kohlhammer, Stuttgart, 1966-1987. 3. Pratt W.K. Digital Image Processing. John Wiley and Sons, New York, 2nd edition, 1991. 4. Tikhonov A.N. and Arsenin V.J. Methods of solving of ill-posed tasks. Moscow, Nauka, 1983 (in Russian). 5. Tikhonov A.N., Goncharsky A.V., Stepanov V.V., and Yagola A.G. Numerical methods for the solution of ill-posed problems. Nauka, Moscow, 1990 (in Russian). 6. Milukova O.P. Fourier transform in restoration problem. Proc.SPIE, Vol.2363, 1995, pp.98-103. 7. V.N.Karnaukhov, E.Wenger, A.Haidinger, N.S.Merzlyakov, Y.J. Zhang. An Integrated System for Digital Processing and Identification of Watermark Images. First International Conference on Image and Graphics, August 16-18, Tianjin, China, 2000, p.119-122. а b Figure 2 An experimental result: (a) blurred image; (b) restored image by using the Wiener filter (4) а b Figure 3 An experimental result: (a) blurred image; (b) restored image by using a regularization filter (5)