Basic mathematics of color space invariants

Color management in printing processes has been traditionally based on an analysis of the behavior of tone reproduction curves (TRC) calculated for the initial color channels. The tone curves, as well as, the color channels, are considered separately. This approach does not take into account the mutual influence of colorants when they overlap. We propose replacing two-dimensional tone reproduction curves with three-dimensional gradation trajectories in the CIE Lab metric space. When two colors overlap, one considers the space between two gradation trajectories that forms a gradation surface. These objects are described using the apparatus of differential geometry of spatial curves and surfaces, respectively, and are also invariants of color spaces. In this paper, we offer their analytical description. © 2020 World Scientific and Engineering Academy and Society. All rights reserved

Linearization of inkjet plotter using tonal trajectory

Демонстрируются возможности градационных траекторий применительно к задачам линеаризации струйных цифровых печатных систем с использованием математического аппарата дифференциальной геометрии пространственных кривых. В настоящей работе вводится понятие градационной траектории, предлагается два критерия для их получения и алгоритм, основанный на этих критериях, рассматривается практическое применение градационных траекторий как таковых.The possibilities of gradation trajectories are applied to the problems of inkjet digital printing systems linearization using the mathematical methods.In this article the concept of gradation trajectory is introduced. Two criteria for the preparation of gradation trajectories and algorithm based on those criteria are proposed.The practical application of gradation trajectories as a method of linearization is considere

The Melt Heat Treatment and the Structural Changes in ZhS6U and Inconel 718

One of the most curious phenomena observed in metal melts is the temperature-induced liquid-liquid structural changes. As a result of the thermal treatment lead to LLT, a more equilibrium and micro-uniform melt consisting of atomic associations is formed. In nickel alloy melts, the changes that have occurred are irreversible and have a significant effect on the formation of the final structure and the mechanical properties of the metal in the solid state after its crystallization. In addition, they are the starting point for the scientific substantiation of new technological modes of smelting and heat treatment of alloys, which further improve their operational properties, as well as reduce metallurgical defects and production waste, and rational use of expensive ligands. All this in general will lead to a significant increase in the performance of melts and metal products. Our work is devoted to the experimental confirmation of the LLT transition in two common nickel-based alloys by a non-invasive electromagnetic method. © Published under licence by IOP Publishing Ltd

The forward problem of spectral reflection prediction: Mutual match between framework selection and the training set volume

Novel technology of the color reproduction is closely related to a variety of color prediction techniques. Along with the deterministic models, those based on the use of artificial neural networks have recently begun to appear. An important problem in the application of a neural network approach is the choice of the training set and network training algorithms. In our work, we describe the results of a computational experiment where various configurations of the artificial neural networks along the different volumes of training subsamples were simultaneously determined providing a satisfactory accuracy of the spectral reflection prediction. The results show that each subsample might be mapped to a particular network configuration. © 2020 American Institute of Physics Inc.. All rights reserved

The inverse problem of spectral reflection prediction: Problems of framework selection

Digital image processing requires substantial computations for characterization. It is since the reliable color reproduction can be achieved by establishing the correspondence between the spectral reflectance of the printed surface and the amounts of deposited inks. The processing is implemented by using different mathematical models. Most of the color prediction models engage some mathematical techniques to predict spectral reflectance for a mixture of colorants that are characterized by absorption and scattering during the light propagation. However, few attempts were made to make a model for prediction the colorants values based on an observing spectrum. This work is devoted to application of artificial neural network approach for solving the inverse problem of spectral reflection prediction. This task has been considered unsolvable as it involves solving a system of the linear differential equations, in which the number of unknowns exceeds the number of equations. Our attempt is based on the assumption that the prediction of the initial colorants from spectral data is possible by analogy with the work of the color perception system in humans. The aim of our study is to offer an approach to the framework selection. The model is built in Matlab and shows satisfactory prediction accuracy. © 2020 American Institute of Physics Inc.. All rights reserved

A field expansions method for scattering by periodic multilayered media

The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein described is a boundary perturbation method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than finite difference and finite element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. The approach is a generalization to multiple layers of Bruno and Reitich’s “Method of Field Expansions” for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original field expansions method, this approach is extremely efficient and spectrally accurate

Determining the ideal initial printing colorants in electrophotography by the discrete gradation trajectories

The accuracy and repeatability of the color reproduction in print is determined by the fine-tuning of the tone reproduction curves of the basic printing colorants (most often this is CMYK). However, the diversity of manufacturers of printing equipment and dyes introduces an element of significant uncertainty about color uniformity. In addition, the traditional approach does not take into account the effect of hue change when applying the original dyes, as well as the nonlinearity of the hue rise in high- and low-density areas. Determining the color of base colorants that produces the most uniform tone change is an important engineering challenge. Previously, there was no scientific basis for such calculations. We recently proposed an alternative color correction model based on gradation trajectories as an analogue of gradation curves in the CIE Lab space. We have also described the extension of the approach to double color overlay (gradation surfaces) and its analytical and discrete implications. The trajectories are the geodetic lines on gradation surfaces. In this paper, we propose using the gradation trajectories to determine “ideal” or “true” initial printing dyes for electrophotography. To simplify calculations, natural color discretization in digital printing is used. © 2022 John Wiley & Sons, Ltd.Wake Forest University, WFUSupport for this research was provided by the Babcock Graduate School of Management, Wake Forest University; Rutgers Business School – Newark and New Brunswick, Rutgers University; and the Jones Graduate School of Management, Rice University. Helpful comments on earlier versions of this chapter were provided by Jack Brittain, Margaret Duval, Reuben McDaniel, Tim Ruefli, John Slocum, Kathie Sutcliffe, and Doug Wholey