Circular Analysis based Line Detection Filters for Watermark Extraction in X-ray images of Etchings

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1 Circular Analysis based Line Detection Filters for Watermark Extraction in X-ray images of Etchings M. van Staalduinen, J. C. A. van der Lubbe, E. Backer {M.vanStaalduinen, J.C.A.vanderLubbe, Dept. of Mediamatics, Information and Communication Theory group, Delft University of Technology, P.O. Box 53, 26 GA Delft Keywords: Line Detection, Shape Matching, oisy Images, Circular Analysis, Kuwahara Filtering, Template-Based Filtering, Watermark Analysis Abstract Watermarks and chain lines are paper features that are used to prove the authenticity of etchings. If an artist has printed etchings on paper with the same paper features, then he has used this paper probably in the same period. The aim of the Rembrandtproject is to find automatically paper with similar watermarks and chain lines in a large database. Watermarks and chain lines are made visible by means of X-ray technique. For matching the line patterns among others, they should be extracted from the noisy X-ray images. This paper investigates two line detection filters: an Extended Kuwahara Filter and a Template-Based Filter. These filters are based on a circular analysis for each pixel. To assess the quality of the filters a set of model images with artificial noise is used. Because of a better performance with tracings it is useful to extract the line patterns from X-ray images and to use these patterns for the matching procedure. The aim of the Rembrandt-project is to extract watermarks and chain lines and to search in a large database for papers with similar watermarks and chain lines. To extract these patterns, line detection methods are applied. Because of the absence of a ground truth watermark, synthetic line images are generated to evaluate the quality of the line detection filters automatically. This paper investigates two line detection filters: an Extended Kuwahara Filter and a Template-Based Filter. These filters determine for each pixel on the. Introduction The authenticity of etchings can be proved by concluding that two etchings have been printed on paper coming from the same sieve [3]. Both watermark and chain lines are unique sieve features that are used to derive this conclusion. Etchings on paper with similar watermark and chain lines used by the same artist have probably been printed in the same period. Reproductions of these line patterns are generated by X-ray images of the paper as visualized in Figure. The line patterns should be extracted from noisy X-ray images in order to make matching possible [4,5,6]. In [,2] retrieval results for two types of watermark databases are presented: one for tracings, which are just the line patterns of watermarks, and one for the X-ray images themselves. In general the retrieval performance is better for tracing images than for X- ray images, but is still not perfect as shown in [,2]. Figure a. Example of a sieve that is used for paper production, b. A X-ray image of a watermark, c. Part of an etching with a visible watermark.

2 Circle A Radius: 2 pixels Square A Length: 2 pixels Cross A Junction A Line end A Circle B Radius: 4 pixels Square B Length: 4 pixels Cross B Junction B Line end B Figure 2. Set of model images basis of its circular environment the most probable intensity value. In order to evaluate the filters, model images are distorted with additive Gaussian noise and with help of the filters the original images are reconstructed. This paper is organized as follows. The used approach is presented in Section 2. Section 3 explains the circular analysis. The Extended Kuwahara Filter and the Template-Based Filter that use features of the circular analysis are presented in Sections 4 and 5, respectively. Results of the filtering of distorted model images are presented in Section 6. Future work is considered in Section 7. Section 8 presents the conclusions. 2. Methodology Automatic evaluation of line detection filters applied to real X-ray images is very difficult, because a ground truth image is not available in general. To evaluate the filters automatically a set of ary model images is created. This set of ary images covers the most frequently occurring basic line features like: straight lines, curved lines, corners, crosses, junctions and end points. Figure 2 shows the set of model images. Within a watermark image it is reasonable that line patterns have a constant line width. These lines are in fact caused by metal wires in the sieve, which have a constant wire thickness. To assess the performance dependency on line width, the set of model images consists of line patterns with two different line widths, i.e. 2 and 4 pixels. The line detection filters are investigated as follows. To a ary model image I noise σ is added, the resulting image I σ is normalized to I and filtered by one of the two line detection filters F. The result is an enhanced image I e. This image is thresholded, which leads to ary image and evaluated by I e comparing it with the original model image. Figure 3 presents this approach schematically. The performance is expressed in terms of precision and recall. It takes into account the pixels that are classified as pattern, thus with intensity value. Precision (Pr) is defined as the number of correctly classified pixels in comparison with the total number of classified pixels. (Rc) is defined as the number of correctly classified pixels with respect to the total number of classified pixels in the ary source image. e = e e m,n m,n Pr[ II, ] Imn [, ] I [ mn, ] I [ mn, ], e Rc[ II, ] = Imn [, ] I [ mn, ] Imn [, ]. m,n e Where Imn [, ] and Ie [ m, n] are the intensity values of pixel [m,n]; i.e. or in this ary case. m,n

3 Binary Line Pattern I + Iσ ormalization I Filter F Ie T I e Evaluation Precision (Pr) oise σ (Rc) Figure 3. System description that presents the process of constructing the noisy line patterns, normalization process and Filtering position. a. σ = b. σ = 64 c. σ = 28 d. σ = 92 e. σ = Figure 4. Four different noise realizations that are added to model image Square B The performance of the filters is investigated for different noise levels. The ary model images have intensity values and 255, to which Gaussian noise is added with a standard deviation σ of, 64, 28, 92 and, which correspond to Signal-to-oise ratios (SR) [8] of, 2, 6, 3, db, respectively. Figure 4 shows five different noise realizations added to image Square B. Within a watermark image the mean intensity value of the background µ BG and of the pattern µ PAT are not constant. While for the final classification of each pixel, whether it belongs to the line pattern or background, a threshold should be applied. Because of the mean intensity variance the optimal threshold is image and position dependent. To avoid this problem each image is normalized to the domain where negative values represent the background and positive the line pattern, and with a zero threshold. A general normalization function that satisfies the requirements for each pixel [m,n] is the following: I I [ m, n] [, ] [, ] BG m n m n σ µ = () µ [ mn, ] µ [ mn, ] PAT BG For the X-ray images the values µ BG and µ PAT will not always be constant, so these should be estimated. For the model images their values are constant µ = and µ = 255 so equation () becomes: BG PAT I [ m, n] I[ m, n] = σ 255 The line detection is in fact a classification problem where each pixel should be classified as pattern or background. Within the normalized images pixels with positive intensity values belong to the pattern and negative values belong to the background. As a matter of fact some pixels are not classified correctly due to noise. The aim of the filters is enhancing the classification of these pixels to the right class. The final classification is performed by zero thresholding the enhanced image. The two investigated filters F are the Extended Kuwahara Filter F K and the Template-Based Filter F T. The Extended Kuwahara Filter enhances the noisy line pattern based on the most probable path that can be followed from a certain pixel. While the Template-Based Filter enhances the noisy line pattern based on best matching line pattern template. These filters are based on the Circular Analysis, which takes the circular environment of each pixel into account. 3. Circular Analysis The Circular Analysis can be considered as a context descriptor of a pixel; the context is described by a set of intensity paths with a certain length and under a certain angle from a central pixel. Figure 5 presents the Circular Analysis in a certain pixel. The Circular Analysis is formalized as follows: r : radius, θ : angle in radians, CA[ r, θ, m, n] = I[ m', n'], ( θ ) ( θ ) m' = m+ rcos, n' = n+ rsin, mn, and m', n' R.

4 m n m θ n r 3 3 Figure 5. Visualization of the Circular Analysis for R=7 and resolution 24 σ = σ = 64 σ = 28 σ = 92 σ = Pr = ; Rc = ; Pr = 9; Rc = 9; Pr = ; Rc = 9; Pr = ; Rc = 3; Pr =.4; Rc = 6; Figure 6. Five output examples of the Extended Kuwahara Filter for different noise levels. I[ m', n' ] is calculated by first order interpolation of the nearest neighbor pixels [8]. In the following CA [ r,θ ] in position [m,n] will be used as an CA r,θ, m, n. alternative notation for [ ] The filters enhance the noisy images based on the path sample mean and path sample standard deviation. R is the maximal radius and the path length of the Circular Analysis. R CA R, = CA[ r, ], R + r= µ θ θ R CA R, =, R + r= 2 ( CA r CA R, ). σ θ θ µ θ 4. Extended Kuwahara Filter Kuwahara filtering [7] is a non-linear filter that suppresses noise and preserves edges. In the present research line preserving noise suppression is required. A Kuwahara filter takes the mean of the quadrant with the lowest variance as a representation of the central pixel intensity. Here the mean of the path with the smallest variance is chosen as an intensity value for the central pixel value. This filter is called the Extended Kuwahara Filter. According to the Extended Kuwahara Filter for each pixel [m,n] the CA is computed. θmin = argmin σca R, θ, θ< 2π FK[ m, n] = µ CA R, θmin. Figure 6 presents some examples of the output of the Extended Kuwahara Filter. These examples show the line preserving property of the Extended Kuwahara Filter. The performance scores are calculated by applying the threshold to F K. 5. Template-Based Filter Template-Based filtering classifies each pixel based on the best matching template. A template consists of four perpendicular paths, which have a High or a Low mean value. Six templates are defined:

5 σ = σ = 64 σ = 28 σ = 92 σ = Pr = ; Rc = ; Pr = 9; Rc = ; Pr = ; Rc = 9 Pr =.36; Rc = 2; Pr =.7; Rc = ; Figure 7. Five model images with the five added noise levels (upper part) and the filter output (lower part) with performance scores for Template-Based Filtering. LLLL, HLLL, HHLL, HHHL, HLHL, HHHH. L represents a low path sample mean and H represents a high path sample mean. Each template has its own meaning, like HLHL represents a line and LLLL represents background. Application of this filter to a model image without noise should result in the model image itself. It is possible to have templates that match best, which usually results in the conclusion that a pixel belongs to the pattern. This usually occurs in the neighborhood of patterns. To classify correctly, the path standard deviation should be taken into account. If one of the templates HLLL, HHLL and HHHL matches best, the mean of the path with the lowest variance will be decisive for the central pixel. An overview of the meanings and classification of each template is presented in Table. Table. Meaning and possible Classes per Template Template Meaning Classification LLLL Background Background HLLL End pixel Background/Pattern HHLL Corner pixel Background/Pattern HHHL Junction pixel Background/Pattern HLHL Line pixel Pattern HHHH Cross pixel Pattern A template τ in the Template-Based Filter can be described as follows: L =, H =, τ { LLLLHLLLHHLLHHHLHLHLHHHH},,,,,, { } τ n L, H for n=,,2,3. The template match mean are computed as follows: max τ 3 n= θ< 2π max max τ = τ τ max µ τ µ [ ]*, n τ θ τ n µ CA R θ π = +, 2 θ = arg max µ τ θ, µ µ θ. and the angle max θ τ At this moment it is not clear how to compute a representative value for a central pixel out of this filter. Tentatively, a fixed value f v = is used. This value is chosen, because it represents in the positive case µ PAT and in the negative case µ BG. The final classification is done based on the best matching template τ B : max τ τ B = arg max µ, all τ {, } fv if τ B HHHH HLHL fv if τ B = LLLL FT [ m, n] = if τ B { HLLL, HHLL, HHHL} fv and τ B[ j] = H fv otherwise, with j = arg min σ CA R, θ iπ τ +. B 2 i=,,2,3 The output of this filter for five different noise levels added to five model images is presented in Figure 7. The performance scores are computed by applying the zero threshold to F T. ext section investigates the performance of the filters for different settings and various noise realizations.

6 6. Results Experiments are used to show the quality of the filters. The quality is considered to what degree the model images can be reconstructed by the line detection filters. If the precision and recall scores are equal to one, then the original image is perfectly reconstructed. The results are presented in precisionrecall plots, where each point represents the mean precision and recall score for different noise realizations. The precision and recall scores are assumed to be of equal importance. Table 2 shows all the different parameters and the options. Precision Circle - Kuwahara Circle - Template Square - Kuwahara Square - Template Cross - Kuwahara Cross - Template Junction - Kuwahara Junction - Template Line End - Kuwahara Line End - Template.3.3 Figure 9. Performance scores for all model images with σ = 28 and line width 2 Table 2. An overview of all parameters and options Parameter Options Images Figure oise levels, 64, 28, 92, Filter Kuwahara, Template Radius 6,8 First Square A with σ = 28 is considered. The performance scores for different configurations and for different radius R are shown in Figure 8. The dashed lines are the lines where the sum of precision and recall is constant. Precision Circle - Kuwahara Circle - Template Square - Kuwahara Square - Template Cross - Kuwahara Cross - Template Junction - Kuwahara Junction - Template Line End - Kuwahara Line End - Template.3.3 Figure. Performance scores for all model images with σ = 28 and line width 4 Precision Kuwahara R=6 Kuwahara R=8 Template R=6 Template R=8.3.3 Figures 9 and show best performance for the Template-Based Filter. Figure presents the performance of the filters for image Square A with all the noise levels. Figure 8. Performance scores for model image Square A with σ = 28 for the two filters at different radii. Figure 8 shows that the Template-Based Filter performs better than the Extended Kuwahara Filtering for both radii. Figures 9 and show the performance for all the model images again at a noise level of σ = 28.

7 Precision.3.2 Kuwahara R=6 Kuwahara R=8 Template R=6 Template R= Figure. Performance for Square A for various noise levels. Figure shows that the Template-Based Filtering outperforms Extended Kuwahara Filtering for all the noise levels. It also shows that for a larger radius of the Circular Analysis the precision scores better, while for a smaller radius it results in better recall scores. Finally, Figure 2 shows the Template-Based Filter performance for all the model images and the various noise levels. Precision.3.2. Circle W=2 R=2 Circle W=4 R=4 Square W=2 L=2 Square W=4 L=4 Cross W=2 Cross W=4 Junction W=2 Junction W=4 Line End W=2 Line End W= Figure 2 Performance for two different settings and all the images Template-Based Filter is a filter with perspective. In this paper the fact that the line width is constant has not been taken into account, which can lead possibly to better results. The final classification of a pixel to pattern or background is based on the smallest variance or the best matching template by using the Circular Analysis. In these cases respectively one or four paths of the total set are considered. However, the order of pixels in a path has not been considered. Methods will be investigated that take more information into account, like all the paths and information within a path. The aim of the Rembrandt-project is to find matches of similar line patterns. For this purpose the Template-Based Filtering could provide extra information like corner points, which can be useful for matching. Matching will be a computationally complex task, thus a pattern should be represented in such a way that search space reduction methods could be applied to find the matches within reasonable time. Before these methods can be applied to X-ray images the created model should be extended for example to correlated backgrounds. The normalization function should be investigated before it can be applied to real X-ray images. The function should be adaptive to artifacts in the images, like contrast flow and correlated noise elements caused for example by paper pulp and holes in the paper. 8. Conclusions For line patterns the Template-Based Filter performs best. For both filters a larger radius of the Circular Analysis results in a larger precision and a smaller radius results in a larger recall. Taking into account additional knowledge about the images, like the constant line width, will possibly result in better quality scores. It can be concluded from Figure 2 that the Template-Based Filtering performs best for all images with some exceptions. The latter is due to properties of the line patterns and possibly to the chosen quality measure. 7. Future work The previous section presented the performance results of the investigated filters and showed that the Acknowledgements The Rembrandt-project is carried out within the framework of the ToKe2 project, which focuses on the application of both informatics and cognitive sciences to cultural heritage, medical care and field of justice.

8 References [] K. J. Riley, and J. P. Eakins, Content-Based Retrieval of Historical Watermark Images: I Tracings, Proceedings of CIVR22, , London, July 22. [2] K. J. Riley, J. D. Edwards, J. P. Eakins, Content- Based Retrieval of Historical Watermark Images: II - Electron Radiographs, Proceedings of CIVR23, 3-4, July 23. [3] J. C. A. van der Lubbe, E. P. van Someren and M. J. T. Reinders, Dating and Authentication of Rembrandt's Etchings with the Help of Computational Intelligence, ICHIM (), , September 2. [4] R. C. Veltkamp, Shape Matching: Similarity Measures and Algorithms, invited talk, Proc. Int'l Conf. on Shape Modeling and Applications 2, pp , Genova, Italy, May 2. [5] S. Belongie, J. Malik, and J. Puzicha, "Matching Shapes," Proc. Eighth Int'l. Conf. Computer Vision, pp , July 2 [6] G. Mori, and J. Malik, Recognizing objects in adversarial clutter breaking a visual captcha, In Proc. Conf. Computer Vision and Pattern Recognition, Madison, USA, June 23 [7] Kuwahara, M., K. Hachimura, S. Eiho, and M. Kinoshita, Processing of RI-angiocardiographic image, in K. Preston, Jr. and M. Onoe, eds., Digital Processing of Biomedical Images, ew York: Plenum, pp , 976 [8] I.T. Young, J.J. Gerbrands, and L.J. Van Vliet, Fundamentals of Image Processing, Delft University of Technology, etherlands, 995.