Estimating the amount of cyan, magenta, yellow, and black inks in arbitrary colour pictures

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1 Neural Comput & Applic (2007) 16: DOI /s ORIGINAL ARTICLE Antanas Verikas Æ Marija Bacauskiene Carl-Magnus Nilsson Estimating the amount of cyan, magenta, yellow, and black inks in arbitrary colour pictures Received: 20 June 2005 / Accepted: 12 June 2006 / Published online: 18 July 2006 Ó Springer-Verlag London Limited 2006 Abstract This paper is concerned with the offset lithographic colour printing. To obtain high quality colour prints, given proportions of cyan (C), magenta (M), yellow (Y), and black (K) inks (four primary inks used in the printing process) should be accurately maintained in any area of the printed picture. To accomplish the task, the press operator needs to measure the printed result for assessing the proportions and use the measurement results to reduce the colour deviations. Specially designed colour bars are usually printed to enable the measurements. This paper presents an approach to estimate the proportions directly in colour pictures without using any dedicated areas. The proportions the average amount of C, M, Y, and K inks in the area of interest are estimated from the CCD colour camera RGB (Lab) values recorded from that area. The local kernel ridge regression and the support vector regression are combined for obtaining the desired mapping Lab Þ CMYK, which can be multi-valued. Keywords Neural networks Æ Kernel ridge regression Æ Support vector regression Æ Offset printing Æ Colour print quality 1 Introduction Offset lithographic printing is the most widely used commercial printing technique. In the offset printing, A. Verikas (&) Æ C.-M. Nilsson Intelligent Systems Laboratory, Halmstad University, P. O. Box 823, Halmstad, Sweden antanas.verikas@ide.hh.se Tel.: Fax: cmn@ide.hh.se M. Bacauskiene Æ A. Verikas Department of Applied Electronics, Kaunas University of Technology, Studentu 50, Kaunas, Lithuania marija.bacauskiene@ktu.lt colour pictures are represented by cyan (C), magenta (M), yellow (Y), and black (K) dots of varying sizes on thin metal plates. The plates are mounted on press cylinders. Since both the empty and areas to be printed are on the same plane, they are distinguished from each other by the ones being water receptive and the others ink receptive. During printing, a thin layer of water is applied to the plate followed by an application of the corresponding ink. The inked picture is transferred from a plate onto the blanket cylinder, and then onto the paper. Figure 1 presents a schematic illustration of the ink-path. Ink feed control along the printed page is accomplished in narrow, about 4 cm wide, ink zones. The amount of ink deposited on the paper in each ink zone is determined by the opening of the corresponding ink-key, see Fig. 1. Figure 2 (Left) provides an example of an image taken from an offset-printed picture. On the right-hand side of Fig. 2 an enlarged view of a small area of the picture is shown. The four-colour dots are clearly seen in this figure. An image comprised of such dots is usually called a halftone image. Since four colours are used in the printing process, four halftone images are created. Figure 3 illustrates the flowchart of the graphical process resulting into a newspaper page. A colour camera and a scanner are the main tools used to obtain colour images that are later used in offset colour printing. The images, called original in this paper, are usually recorded in the RGB colour space, see Fig. 3. Since C, M, Y, and K colours are used to print colour pictures, the so-called colour separation process, converting images from the RGB to the CMYK colour space, is applied. Next, by applying some half-toning procedure [1, 2], each of the obtained C, M, Y and K images are converted into the halftone counterpart. In Fig. 3, only a small part, the hand of the player, of the halftone image is shown. Printing plates are then easily obtained from the halftone images by applying the so-called computer-to-plate (CTP) technology. Throughout the job run, the press operator samples the prints to assess print quality. The samples are

2 188 Inking system Ink Ink-key Ink fountain roller Ink rollers Plate cylinder Fig. 1 A schematic illustration of the ink-path Blanket cylinder Paper path Blanket cylinder compared to the approved reference print. If deviations are detected, an instrument, e.g., a densitometer or spectrophotometer, is used to obtain a numerical assessment of the deviations. The adjustments that are required to compensate for the colour deviations are usually attributed to adjusting the proportions of each ink deposited on the corresponding plate. To maintain the same printing quality during a job run, it is not uncommon for a printing press operator to adjust the amount of ink by nearly 20% [3]. Each printing press operator performs the adjustments based on his/hers perception of the relationship between the proportions of the different inks and the full-colour printed picture. The perception is very subjective and so is the printed result. To measure the ink proportions, usually small test areas are printed. Figure 4 presents an example of two types of such areas. Usually, there are many ink zones along the width of the plate cylinder and ink feed control is performed separately for each ink zone. Thus, for each ink zone, a separate test area is printed along the page edge. Full tone test areas of cyan, magenta, yellow, and black colours, as those shown on the upper part of Fig. 4, are usually used for densitometer or spectrophotometer based ink density measurements. The estimated ink proportions the press operator has to relate to the appropriate adjustments of the amount of ink deposited on paper necessary to maintain print quality. Since each press responds differently to ink key adjustments, then it is the experience the printing press operator has gathered from utilizing the press that allows him/her to make relevant adjustments to maintain the desired print quality. Obviously, this is quite a difficult task. Fig. 2 Left: An image of a printed picture. Right: An enlarged view of a small area of the picture shown on the left Fig. 3 The flowchart of the graphical process

3 189 Fig. 4 Above: An example of the full tone test areas. Below: An example of the double grey-bar However, print quality of a printed picture depends on both ink densities and dot sizes [4]. Thus, to take both these factors into consideration, one needs to measure the ink proportions on halftone areas, for example, on the so-called double grey-bars, shown in the lower part of Fig. 4. One half of the double grey-bar is printed with cyan, magenta, and yellow inks while the other half is printed as a black halftone screen. The neural networks and image analysis based tool for estimating the ink proportions, CMYK values, on the double grey-bars has recently been developed [5]. It has also been demonstrated that using the CMYK signals estimated on the double grey-bars as well as a set of parameters characterizing the offset printing press, a sufficiently accurate neural network based model can be developed and used to control the amount of ink of each colour deposited on paper, the ink feed [6]. The technique developed for measuring the CMYK values on the double grey-bars [5] employs a CCD colour camera instead of a densitometer or spectrophotometer and is targeted for newspaper printing. In the graphic arts industry, however, traditionally, the densitometer or spectrophotometer have been the main measurement tools to obtain information for print quality evaluations and process control. Although CCD colour cameras are not designed for performing colourimetric measurements directly, colour cameras have been increasingly used as devices for colour measurements [7] and pressroom tools for colour print quality monitoring [4, 5, 8 10]. There are several advantages of using CCD colour cameras for colour printing quality control: 1. Possibility to measure multiple process and print quality parameters simultaneously. 2. Possibility to record an image, which can be further analyzed for obtaining various parameters characterizing the printing process. 3. Ability to detect measurement errors. 4. Possibility to accomplish comprehensive on-line monitoring of the printing process. Despite the aforementioned advantages, the relatively narrow dynamic range of the CCD colour cameras limits the range of ink densities that can be measured accurately. However, since this study is concerned with newspaper printing, where the densities used are such that the corresponding reflectances are within the range of 8-bit CCD colour cameras, we also resorted to using a CCD colour camera instead of the traditional instruments. Moreover, 10-bit and even 12-bit colour cameras are more and more common, nowadays. In this study, we go beyond printing special dedicated test areas, such as the double-grey bars. Instead, we present a novel technique for estimating the CMYK values from CCD colour camera measurements made directly on halftone four-colour pictures. Observe that, when using the double-grey bars, threeand one-colour images are utilized. Since a colour camera provides RGB (Lab) [11] values, measuring on four-colour pictures amount to discovering the mapping Lab Þ CMYK. This is a difficult task, since the same Lab can be obtained from different CMYK values. To solve the task, we resorted to the local kernel ridge regression and the support vector regression. Having Lab values measured on a fourcolour picture, the CMYK values of the corresponding area, available from the halftone C, M, Y, and K images, see Fig. 3, are exploited for determining the suitable local analysis region in the Lab space. The local analysis allows us from avoiding difficulties arising due to the aforementioned non one-to-one mapping Lab Þ CMYK. The technique proposed for estimating the mapping, thoroughly described in Sects. 3 and 4, constitutes the main contribution of the paper. To our knowledge, the technique is the only attempt to estimate the amount of cyan, magenta, yellow, and black inks in arbitrary fourcolour pictures. A work by Tominaga [12], briefly reviewed in Sect. 1, presents an approach to estimate the map Lab Þ CMYK. The aim of that work is to create a printer controller. Numerous other techniques for creating printer controllers exist [13 15]. However, for a non one-to-one mapping, the controller approach cannot answer the questions we are interested in, namely, which CMYK values have produced the Lab values in question. The remaining of the paper is organized as follows. Section 2 outlines the methods employed to solve the task. The mixture density networks and the local kernel regression are considered in this section. Results of the experimental investigations are given in Sect. 3. Finally, Sect. 4 presents conclusions of the work.

4 190 2 Methods 2.1 Inverting the CMYK Þ Lab mapping To discover the mapping Lab Þ CMYK, one can think of using the approach proposed by Tominaga [12]. The task pursued by Tominaga is to create a printer controller implementing the aforementioned mapping. The concatenation of two networks, as shown in Fig. 5, is employed to solve the task. First, the right-hand part of the network, dedicated to estimate the mapping CMYK Þ Lab, is trained and the parameters of the network are frozen. The left-hand part of the network is then trained to implement the mapping Lab Þ Lab in the concatenated structure. After the training, the left-hand part of the network is used to implement the mapping Lab Þ CMYK. In the printer controller case, the task is to know which CMYK values can produce the desired Lab values. In our case, however, the question is, which CMYK values have produced the Lab values in question. Since we are dealing with multi-modal conditional densities, the printer controller approach cannot be applied. 2.2 Mixture density networks Mixture density networks [16], as being capable of estimating conditional probability density functions, can be used to solve the problem. Using the mixture model approach, the conditional probability density function of target variables y conditioned on x is given by pðyjxþ ¼ XK j¼1 a j ðxþ/ j ðyjxþ ð1þ where K is the number of mixture components, a j (x) is the mixing coefficient, and / j (y x) represents the jth component of the conditional density of the target vector y. In our case, the target variables y are given by CMYK and x by Lab. Spherical Gaussians of the following form are usually used as mixture components L a b C K Fig. 5 Two neural networks concatenated to perform the mapping Lab Þ CMYK Þ Lab L a b ( 1 / j ðyjxþ ¼ exp ð2pþ c=2 r c jðxþ k y l ) jðxþ k2 2r 2 j ðxþ ð2þ where c is the dimensionality of the target y, l j ðxþ is the centre of the jth component, and r 2 j (x) is the common variance characterizing the width of the jth component. The mixture parameters a j (x), l j ðxþ; and r 2 j (x) can be estimated by using the mixture density network, as proposed in [16]. Our experience of using the mixture density networks for solving the problem is that the estimation result is too sensitive to the number of mixture components K chosen to model the density. Determination of the appropriate number of the components turned to be a difficult task and the results obtained were not accurate enough. Therefore, we resorted to approaches based on the local support vector and kernel ridge regression [17]. 2.3 Kernel regression used We can expect avoiding difficulties arising due to the non one-to-one mapping Lab Þ CMYK by employing local analysis instead of the global one. Kernel regression allows local analysis. To solve the task, we exploit two types of kernel regression, namely the local ridge regression and the local one-norm e-insensitive, support vector regression. First, we present the general regression equations and then explain how the local analysis is accomplished. Let us assume that we have N colour patches spread over the whole colour gamut in question with known Lab, x, and CMYK, y, values, the training set S ={(x 1, y 1 ),...,(x N, y N ) }. We collect the x vectors into the N 3 matrix X and the y vectors into the N 4 matrix Y. The N 4 matrix of the optimal kernel ridge regression parameters A is then given by A ¼ðK þ ki N Þ 1 X ð3þ where I N is the N N identity matrix, k > 0 is a parameter, and K is the N N kernel matrix with j(x i, x j ) being a kernel. In this study, we used polynomial j p (x i, x j ) and Gaussian j g (x i, x j ) kernels: j p ðx i ; x j Þ¼ð1þx T i x jþ d j g ðx i ; x j Þ¼expf jjx i x j jj 2 =rg ð4þ ð5þ with d being a parameter and r the standard deviation of the Gaussian. A vector of the predicted values by for a given measurement vector x is then given by by ¼ A T k ð6þ where k is the vector with entries j(x i, x), i = 1,...,N. All training data points are used to find the prediction based on the kernel ridge regression approach. Thus, for large data sets it could be rather time consuming to compute the prediction vector. Many practical

5 191 experiments have proven that by resorting to the e- insensitive, support vector regression [17] we not only reduce the number of data points exploited in the solution, but can also reduce the generalization error. In the support vector regression case, the iterative optimization procedure has to be used, however, to find the solution. In this application, we use the one-norm e-insensitive, support vector regression. Thus, the optimization problem is to find a maximizing [17] W ðaþ ¼ XN subject to X N i¼1 i¼1 a i y i e XN i¼1 ja i j 1 2 X N i;j¼1 a i a j jðx i ; x j Þ ð7þ a i ¼ 0; C a i C; i ¼ 1;...; N ð8þ where C > 0 is the regularization constant. Observe that a one-dimensional output is assumed in the above equations. The function f implementing the one-norm e-insensitive, support vector regression is then given by f ðxþ ¼ XN where j¼1 b ¼ e þ y i XN a j jðx j; xþþb j¼1 a j jðx i; x j Þ ð9þ ð10þ for i such that 0 < a i < C. We exploit both, the ridge and the support vector, regression approaches in this study. However, given an input vector x, anlab vector, the prediction vector y is calculated based on the information extracted from only a small local region of the colour space. The centre point of the region is determined in advance by the known nominal CMYK values, as it is explained in the next subsection. The nominal CMYK values are available from the halftone C, M, Y, and K images. Since the support vector regression requires an iterative optimization, the set of regression parameters a 1 ; b 1 ;...; a M ; b M ; where M is the number of the regression regions computed in advance. Thus, the space partitioning for the local support vector regression is performed in advance and, therefore, is hard. In contrast, we use the soft space partitioning for the local ridge regression which is governed by the given nominal CMYK values and the Lab values. The matrix of the optimal ridge regression parameters A is computed on-line having the specific Lab and CMYK values. The output values obtained from the two regression approaches are aggregated via weighted averaging. Why do we use two kernel regression techniques? The support vector regression usually provides a lower generalization error than the kernel ridge regression. However, since in the case of support vector regression, we use the hard, in advance pre-computed, space partitioning, the analysis region may not be optimal for the data point at hand. In such a situation, a higher accuracy may be obtained from the local kernel ridge regression, which chooses the analysis region on-line by looking at the nearest neighbours of the data point being analyzed. In general, kernel approaches imply local analysis. In our case, the locality is defined in the Lab space. However, when using the C, M, Y, and K printing inks, very similar Lab values can be obtained from quite different CMYK values. Therefore, nonetheless the locality implied by the kernel approaches, we also enforce another type of locality defined in the CMYK space and governed by the nominal CMYK values. 2.4 Local kernel regression To make a prediction of the actual CMYK d values from the average Lab values measured by a CCD camera in a small area of a printed picture, we exploit information available from the halftone C, M, Y, and K images, the nominal CMYK values. The automated system for an on-line registration of C, M, Y, and K printing plates allows finding the nominal CMYK values related to the measured Lab counterparts. Since we know the nominal CMYK values, the regression region can be restricted around these nominal values. The local regression region is found in two steps. First, the local region is roughly determined based on the nominal CMYK values. The size of the region is given by the N 1 closest data points in the training set to the colour in question. The distance is measured in the CMYK space using the Euclidean distance measure d CMYK qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ðc x C i Þ 2 þðm x M i Þ 2 þðy x Y i Þ 2 þðk x K i Þ 2 where C, M, Y, and K range from 0 to 100 (the percentage of the area covered by the corresponding ink), x refers to the data point in question and the index i addresses a data point from the training set S. The number of data points N 1 selected is low enough to assure that non of the two different CMYK vectors produce very similar Lab vectors. In the next step, N 2 < N 1 closest data points to the one being analyzed are selected amongst the N 1 candidates chosen in the first step. The selection is performed in the input, Lab, space. To find the N 2 data points, we use the following, modified DE colour difference [11] formula: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ME ¼ w L ðml Þ 2 þ w a ðma Þ 2 þ w b ðmb Þ 2 ð11þ with the weighting factor w L being selected experimentally and

6 192 w a ¼ð1þ0:05ja Ref jþ 1 w b ¼ð1þ0:05jb Ref jþ 1 ð12þ ð13þ where the weighting factors w a and w b are calculated from the a and b values, respectively, of the reference colour of the two colours compared and, therefore, are data dependent. Thus, to make the local regression based prediction of CMYK d values from known camera RGB values, they are first transformed to the Lab triplet and N 2 data points, closest to the triplet are found in the two-step process. The Lab values of the N 2 selected data points are then utilized to calculate the regression parameters in the way described in the previous subsection. To aggregate prediction results obtained from the two regression approaches, the weighted averaging technique is employed [18]. The aggregation weights v i (x), i = 1, 2 are data dependent and are given by expf bd i ðxþg v i ðxþ ¼ ð14þ expf bd 1 ðxþg þ expf bd 2 ðxþg where b is a parameter and d i (x) stands for the distance measured in the Lab colour space between the data point x and the centre point of the corresponding regression region. Equation (11) is utilized to measure the distance d i (x). 3 Experimental tests The experimental tests performed concern an offset newspaper printing process. An on-line printing process monitoring system, installed in the pressroom for monitoring the offset newspaper printing press, has been used to capture images of printed colour areas used in the experimental tests. The system is equipped with a CCD colour camera of 1,600 1,200 pixels. The camera can be positioned with high accuracy at any point across the newspaper page and is able to record high quality well-focused colour images from a web running at up to 15 m/s speed. To test the ability of the regression approaches to estimate the mapping Lab Þ CMYK, a set of test colour patches were printed keeping the same ink density. For each cyan, magenta, and yellow inks, the average nominal ink coverage of a patch area, the dot size, was varied in 20% steps, namely 0, 20, 40, 60, 80, and 100%. The average ink coverage for the black ink was varied in 5% steps from 0 to 40%. An example of 216 such paths, with C, M, and Y varying from 0 to 100% and K set to 0, is shown in Fig. 6. To have a more dense representation of the four primary colours, series of halftones of pure C, M, Y, and K colours ranging from 0 to 100% in 3% steps were also printed. In total, 1,728 test colour patches were designed. Data from five of such prints, each containing 1,728 test areas, were automatically recorded using the on-line system. One set of the data has been used to estimate the Fig. 6 An image taken from 216 colour patches regression parameters, while the other four sets were allocated for testing. To estimate the regression parameters, the target values, the actual CMYK values, are to be known. Though the nominal CMYK values used to print the test patches are known, the actual values remain unknown, since halftone dots grow during the printing process. We estimated these values from the RGB values of the halftone series of the pure colours. The actual values of the nominal counterparts, not presented in the series, were obtained by linear interpolation. Other approaches, for example, based on the Neugebauer model [19], can be used [20]. 3.1 Choice of parameters There are several parameters to choose. The value of the ridge regression constant k = worked well in all the test performed. The optimal values of the ridge regression kernel parameters were found to be d =2 and r = 0.1. The suitable parameter values of the twostep procedure for determining the local regression region were: N 1 = 15, N 2 =8,andw L = 0.5. In the case of the support vector regression, the Gaussian kernel was utilized. The width of the kernel r = 0.2 turned to be a good choice. The value of the regression insensitivity parameter e was chosen based on the process knowledge and was set to e = The suitable value of the regularization constant C was found by crossvalidation and was equal to C = 50. The parameter b, used in the equation for calculating the aggregation weights, was set to unity in this study. 3.2 Results of the tests The main parameter characterizing the relevance of the approach is the estimation accuracy of the actual CMYK values from the measured Lab. Table 1 presents the average absolute estimation error of the

7 193 Table 1 The average estimation error of the CMYK values Kernel C M Y K Gaussian (1.205) (1.165) (1.474) (0.879) Polynom (1.227) (1.195) (1.636) (0.970) actual CMYK values. In the parentheses, the standard deviation of the error is provided. In the table, Kernel stands for the kernel type used in the local ridge regression. Observe that CMYK values range from 0 to 100. Figure 7 presents histograms of the estimation error of the actual M and K values. The estimation errors of the C and Y values were in the same range. Offset lithographic newspaper printing is the application area of this study. To the best of our knowledge, in offset printing there have been no attempts to estimate the mapping Lab Þ CMYK using colour measurements made directly on four-colour pictures. In [5], a system to estimate the mapping using colour measurements obtained from the double-grey bars was presented. The estimation accuracy of CMYK values obtained in the current work is very similar to that achieved in [5]. We remind that in the case of using the double-grey bars, the problem is much easier to solve. The experience acquired from the use of the double-grey bar measurements based system [5] shows that the estimation accuracy obtained in the current work is high enough for the approach to be used in practical applications. It is worth noting that evaluation of the estimation error is not an easy task, since the ground truth is not known. The actual CMYK values used to estimate the regression parameters were evaluated using patches of single colours only (no overprints). Let us assume that, for example, the actual value of C = 28 has been evaluated for the nominal C = 20. It was then assumed that for all the overprints printed using the nominal value of C = 20, the actual value of C is always 28, irrespective of the proportions of the other three inks. It is clear that the assumption does not always hold in practice. Thus we can expect that the estimation errors are even smaller, as the experience shows, than those observed in Fig. 7. The purpose of the next experiment was to show that if the nominal CMYK values remain constant, but ink density varies, the pattern of ink density variations is observed in the variations of the actual CMYK values. To demonstrate this important behaviour, a series of test-prints was produced where the cyan ink density was systematically varied, while densities of the other inks were kept constant. No black ink has been used in these prints. Figure 8 illustrates one of the pictures from this series. The density of cyan, magenta, and yellow inks used to print each sample from the series was measured by a MacBeth densitometer on colour bars, which are not shown in Fig. 8. The actual CMYK values were computed, according to the approach proposed, from the RGB measurements made in the point marked by the white circle in Fig. 8. Both series of the measurements Fig. 7 Histograms of the estimation error of the actual M and K values: (top) M value, (bottom) K value Fig. 8 A picture from the series of prints, along with the measuring point marked by a white circle

8 194 Ink density CMY values Test print number Test print number Fig. 9 Left: Densitometer measurements for the series of testprints. Right: CMY values estimated in the marked point shown in Fig. 8 are plotted in Fig. 9. As expected, Fig. 9 reveals the same pattern of variations of both the ink densities and the actual CMYK values. Thus, the actual CMYK values respond to variations of both, ink densities and dot sizes, percentages of the area covered by cyan, magenta, yellow, and black inks. Since ink densities are measured on the specially designed colour bars, while actual CMYK values directly in the halftone images, some disagreement between fluctuations of the ink densities and CMYK values is expected. The actual CMYK values can be regarded as the average amount of cyan, magenta, yellow, and black inks estimated in the area of interest. Both, ink densities and dot sizes contribute to the actual CMYK values. The actual CMYK values plotted in Fig. 9 directly reveal that the amount of cyan ink is small in the measuring area. This information is not available, if one has the disposition of the ink density values only. If ink densities remain constant, but dot sizes change due to some reason, the change manifests itself in aberrant actual CMYK values. However, when using ink density to monitor the printing process, the change goes undetected. It all goes to show that regarding offset printing process monitoring, the actual CMYK values are superior to ink densities. C M Y C M Y 4 Conclusions An approach to estimate the actual amount of cyan (C), magenta (M), yellow (Y), and black (K) inks in a small area of an arbitrary colour picture was presented in this paper. The local kernel ridge regression and the support vector regression were combined for obtaining the estimate, which is based on the Lab values recorded from the area of interest and the nominal CMYK values of the area. The nominal values are available from the halftone C, M, Y, and K images. Since both ink densities and dot sizes contribute to the actual CMYK values, the values respond to variations of both ink densities and dot sizes, percentages of the area covered by cyan, magenta, yellow and black inks. In contrast, when using ink density to monitor the printing process, dot size changes go undetected, if ink densities remain constant. Therefore, concerning offset printing process monitoring the actual CMYK values are superior to ink densities. The attempt to solve the task by using the mixture density networks was not successful. The results were too sensitive to the number of mixture components chosen to model the density. Determination of the appropriate number of the components turned to be a difficult task and the results obtained were not accurate enough. The experimental investigations performed have shown that the obtained estimation accuracy is very similar to that achieved in the double-grey bar measurements based system. The obtained accuracy is high enough for the approach to be used in practice. The use of both the Gaussian and the polynomial kernels in the local kernel ridge regression provided approximately the same performance. References 1. Papas TN (1997) Model-based halftoning of color images. IEEE Trans Image Process 6: Baqai FA, Allebach JP (2002) Computer-aided design of clustered-dot color screens based on a human visual system model. Proc IEEE 90: Almutawa S, Moon Y (1993) Process drift control in lithographic printing: issues and connectionist expert system approach. Comput Ind 21: Verikas A, Malmqvist K, Malmqvist L, Bergman L (1999) A new method for colour measurements in graphic arts. Color Res Appl 24: Verikas A, Malmqvist K, Bergman L (2000) Neural networks based colour measuring for process monitoring and control in multicoloured newspaper printing. Neural Comput Appl 9: Verikas A, Bergman L, Malmqvist K, Bacauskiene M (2003) Neural modelling and control of the offset printing process. In: Proceedings of the IASTED International Conference Neural Networks and Computational Intelligence. IASTED, Cancun, pp Hong G, Luo MR, Rhodes PA (2001) A study of digital camera colorimetric characterization based on polynomial modeling. Color Res Appl 26:76 84

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