Memory-based neuro-fuzzy system for interpolation of reflection coefficients of printing inks
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CYBERNETICS MEMORY-BASED NEURO-FUZZY SYSTEM FOR INTERPOLATION OF REFLECTION COEFFICIENTS OF PRINTING INKS Ye. V. Bodyanskiya† and N. Ye. Kulishovaa‡
UDC 519.7:004.8
The problem of interpolation of a two-dimensional function on a nonuniform axial rectangular grid is considered. To solve the problem, a memory-based neuro-fuzzy system is proposed. This system is computationally simple and provides a high-quality interpolation. Keywords: computational intelligence, neuro-fuzzy system, interpolation. INTRODUCTION Modern color image reproducing devices use color control systems realizing multistage processes of processing color data by applying profiles. However, in polygraphic practice, this approach is not always efficient since it requires the presence of a great many profiles for each printing machine with allowance made for concrete paper and ink grades. Moreover, in a printing machine, different ink sections can have different characteristics and can unstably form the same color within a printers sheet. To faithfully reproduce topical colors, the duplicate method is often used in which relationships between basic ink colors of polygraphic synthesis are fixed that give colors close to prescribed ones. This approach requires the presence of detailed information expressed in analytical form on the chromatogenic properties of the system “machine–ink–paper.” It is this case when the best solution of the color reproduction problem is obtained. However, this information is available only in the form of a collection of experimental data on spectral characteristics of the ink film applied to a paper sheet. It is usually obtained during spectrophotometric measurements of proofing bars printed by concrete printing machines. To optimally choose combinations of basic ink colors being synthesized, the dependence of the reflection coefficient of an ink film on the ink concentration and wavelength should be analytically represented, which is a sufficiently complicated problem. From the mathematical viewpoint, this problem is reduced to the interpolation of a sufficiently sophisticated two-dimensional nonlinear function specified over a set of points whose number can be very large. In the general case, to solve such problems, artificial neural networks can be used that possess universal approximating capabilities, in particular, radial basis neural networks [1–3] that are also well-adapted to the solution of problems of interpolation of multidimensional nonlinear functions [4, 5]. An important property of these networks is a linear dependence of the output signal on the parameters being tuned, which allows one to use the conventional least squares method (in the approximation problem) or standard methods of solving systems of linear equations (in the interpolation problem) to train them. However, as experience has shown [6], a usual radial basis neural network providing a highly accurate interpolation can generate significant oscillations between points, which makes its practically unacceptable. This is explained by the uncertain
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