Traditional printing relies primarily on subtractive color mixing techniques. In this case, optical color mixing is achieved by one of the established halftoning methods that use Cyan, Magenta, Yellow and Black (CMYK) primaries on a reflective white substrate. The reason behind the subtractive color mixing in printing is the high absorbance of available pigments used in inks. A new type of mica-based pigments that exhibit high reflectivity at Red, Green, Blue and White (RGBW) spectral bands was recently introduced by Merck (SpectravalTM). Printing with RGBW primaries on black background allows additive color mixing in prints. While offering excellent color depth, the reflected spectra of such pigments vary with the angles of incidence and observation. As a result, new approaches in modelling the appearance of prints as well as strategies for color separation and halftoning are needed. The prior optical characterization of the reflective inks is an essential first step. For this purpose, we have used SpectravalTM pigments to prepare acrylic based inks, which we applied on glass slides by screen printing. In this work, we measured the relative spectral bidirectional reflection distribution of Red, Green, Blue and White reflective inks. The measurements were conducted on an experimental set up consisting of a goniometer, spectrometer, and a xenon light source. Based on the measurements, we simulate the reflectance spectra under diffuse illumination and demonstrate ratios of red, green, and blue spectral components for different observation angles of individual inks and their combinations.

The appearance of 3D-printed objects is affected by numerous parameters. Specifically, the colour of each point on the surface is affected not only by the applied material, but also by the neighbouring segments as well as by the structure underneath it. Translucency of the 3D printing inks is the key property needed for reproduction of surfaces resembling natural materials. However, the prediction of colour appearance of translucent materials within the print is a complex task that is of great interest. In this work, a method is proposed for studying the appearance of translucent 3D materials in terms of the surface colour. It is shown how the thickness of the printed flat samples as well as the background underneath affect the colour. By studying diffuse reflectance and transmittance of layers of different thicknesses, apparent, spectral optical properties were obtained, i.e., extinction and scattering coefficients, in the case of commercially available polylactic acid (PLA) filaments for Fused Deposition Modelling (FDM) printers. The coefficients were obtained by fitting a simplistic model to the measured diffuse reflectance as a function of layer thickness. The results were verified by reconstructing reflected spectra with the obtained parameters and comparing the estimated colour to spectrophotometer measurements. The resulting colour differences in terms of the CIEDE2000 standard are all below 2.

Many image reproduction devices, such as printers, are limited to only a few numbers of printing inks. Halftoning, which is the process to convert a continuous-tone image into a binary one, is, therefore, an essential part of printing. An iterative halftoning method, called Iterative Halftoning Method Controlling the Dot Placement (IMCDP), which has already been studied by research scholars, generally results in halftones of good quality. In this paper, we propose a structure-based alternative to this algorithm that improves the halftone image quality in terms of sharpness, structural similarity, and tone preservation. By employing appropriate symmetrical and non-symmetrical Gaussian filters inside the proposed halftoning method, it is possible to adaptively change the degree of sharpening in different parts of the continuous-tone image. This is done by identifying a dominant line in the neighborhood of each pixel in the original image, utilizing the Hough Transform, and aligning the dots along the dominant line. The objective and subjective quality assessments verify that the proposed structure-based method not only results in sharper halftones, giving more three-dimensional impression, but also improves the structural similarity and tone preservation. The adaptive nature of the proposed halftoning method makes it an appropriate algorithm to be further developed to a 3D halftoning method, which could be adapted to different parts of a 3D object by exploiting both the structure of the images being mapped and the 3D geometrical structure of the underlying printed surface.

Managing the final appearance of 3D surfaces is an interesting and essential topic in 3D printing applications. Knowledge about the parameters which influence the 3D surface reproduction quality enables engineers to achieve the final appearance as accurately as designed. Many studies have been conducted to explore numerous parameters that affect the quality of 3D surface reproduction. This work contributes to verifying the role of halftoning in increasing the 3D surface visual quality and the control over the surface appearance of a 3D printed object. The results show that applying different halftones according to the geometrical characteristics of the 3D surface could emphasize or diminish the perceived 3D geometrical structures of a shape. The experimental results are in line with the simulated outputs reported in previous work. Our findings might introduce a new approach towards having more control over 3D appearance reproduction without changing the material or printer settings.

Realistic appearance reproduction is of great importance in 3D printing’s applications. Halftoning as a necessary process in printing has a great impact on creating visually pleasant appearance. In this article, we study the aspects of adapting and applying Iterative Method Controlling Dot Placement (IMCDP) to halftone three-dimensional surfaces. Our main goal is to extend the 2D algorithm to a 3D halftoning approach with minor modifications. The results show high-quality reproduction for all gray tones. The 3D halftoning algorithm is not only free of undesirable artifacts, it also produces fully symmetric and wellformed halftone structures even in highlight and shadow regions.

The spatial resolution of 3D printing is finite. The necessary discretisation of an object before printing produces a step-like surface structure that influences the appearance of the printed objects. To study the effect of this discretisation on specular reflections, we print surfaces at various oblique angles. This enables us to observe the step-like struc- ture and its influence on reflected light. Based on the step-like surface structure, we develop a reflectance model describing the redistribution of the light scattered by the surface, and we study dispersion effects due to the wavelength dependency of the refractive index of the material. We include preliminary verification by comparing model predictions to photographs for different angles of observation.

To improve color reproduction, many printers today use extra colorants, in addition to the traditional four inks (Cyan, Magenta, Yellow and Black). Adding the complementary colorants (Red, Green and Blue) increases the gamut of reproducible colors, while lighter versions of the primary inks can be added to reduce graininess and dot visibility. Using more than three inks introduces colorimetric redundancy in the color separation process, because different ink combinations can reproduce the same target color. When additional inks are introduced, this redundancy rapidly increases, and it is thus crucial to introduce additional constraints in the color separation process, to improve determinacy and to optimize different aspects of print quality. This study focuses on an analysis of the redundancy in the color separation process for an 11-ink printer. It is investigated how the extensive colorimetric redundancy can be utilized to select optimal ink combinations to meet the, sometimes contradictory, criteria of color accuracy, graininess and ink consumption. Analysis of the results of applying different criteria in the color separation process shows that the result heavily depends on the selected criterion. For example, prioritizing graininess will improve print quality by reducing dot visibility, imposing the use of lighter inks, but it will also increase ink consumption.

Multi-channel printing employs additional inks to improve the perceived image quality by reducing the graininess and augmenting the printer gamut. It also requires a color separation that deals with the one-to-many mapping problem imposed when using more than three inks. The proposed separation model incorporates a multilevel halftoning algorithm, reducing the complexity of the print characterization by grouping inks of similar hues in the same channel. In addition, a cost function is proposed that weights selected factors influencing the print and perceived image quality, namely color accuracy, graininess and ink consumption. The graininess perception is qualitatively assessed using S-CIELAB, a spatial low-pass filtering mimicking the human visual system. By applying it to a large set of samples, a generalized prediction quantifying the perceived graininess is carried out and incorporated as a criterion in the color separation. The results of the proposed model are compared with the separation giving the best colorimetric match, showing improvements in the perceived image quality in terms of graininess at a small cost of color accuracy and ink consumption. (c) 2016 Wiley Periodicals, Inc.

Multichannel printing employs additional colorants to achieve higher quality reproduction, assuming their physical overlap restrictions are met. These restrictions are commonly overcome in the printing workflow by controlling the colorant choice at each point. Our multilevel halftoning algorithm bundles inks of same hues in one channel with no overlap, separating them into eight channels, consequentially benefitting of increased ink options at each point. In this article, implementation and analysis of the algorithm is carried out. Color separation is performed using the cellular Yule‐Nielsen modified spectral Neugebauer model. The channels are binarized with the multilevel halftoning algorithm. The workflow is evaluated with an eight-channel inkjet at 600 dpi resulting in mean and maximum ΔE ₉₄ color differences around 1 and 2, respectively. The halftoning algorithm is analyzed using S-CIELAB, thus involving the human visual system, in which multilevel halftoning showed improvement in terms of image quality compared to the conventional approach.

A multilevel halftoning algorithm can be used to overcome some of the challenges of multi-channel printing. In this algorithm, each channel is processed so that it can be printed using multiple inks of approximately the same hue, achieving a single ink layer. The computation of the threshold values required for ink separation and dot gain compensation pose an interesting challenge. Since the dot gain depends on the specific combination of ink, paper and print resolution, compensating the original image for multilevel halftoning means expressing the dot gain of multiple inks of same hue in terms of the coverage of a single ink. The applicability of the proposed multilevel halftoning workflow is demonstrated using chromatic inks while avoiding dot overlap and accounting for dot gain. The results indicate that the multilevel halftoned image is visually improved in terms of graininess when compared to bi-level halftoned images.

Color vision deficiency (CVD) is the inability, or limited ability, to recognize colors and discriminate between them. A person with this condition perceives a narrower range of colors compared to a person with normal color vision. In this study we concentrate on recoloring digital images in such a way that users with CVD, especially dichromats, perceive more details from the recolored images compared to the original ones. During this color transformation process, the goal is to keep the overall contrast of the image constant, while adjusting the colors that might cause confusion for the CVD user. In this method, RGB values at each pixel of the image are first converted into HSV values and, based on pre-defined rules, the problematic colors are adjusted into colors that are perceived better by the user. Comparing the simulation of the original image, as it would be perceived by a dichromat, with the same dichromatic simulation on the recolored image, clearly shows that our method can eliminate a lot of confusion for the user and convey more details. Moreover, an online questionnaire was created and a group of 39 CVD users confirmed that the transformed images allow them to perceive more information compared to the original images.

Printing using more than four ink channels visually improves the reproduction. Nevertheless, if the ink layer thickness at any given point exceeds a certain limit, ink bleeding and colour accuracy problems would occur. Halftoning algorithms that process channels dependently are one way of dealing with this shortcoming of multi-channel printing. A multilevel halftoning algorithm that processes a channel so that it is printed with multiple inks of same chromatic value was introduced in our research group. Here we implement this multilevel algorithm using three achromatic inks – photo grey, grey, black – in a real paper-ink setup. The challenges lay in determining the thresholds for ink separation and in dot gain compensation. Dot gain results in a darker reproduction and since it originates from the interaction between a specific ink and paper, compensating the original image for multilevel halftone means expressing dot gain of three inks in terms of the nominal coverage of a single ink. Results prove a successful multilevel halftone implementation workflow using multiple inks while avoiding dot-on-dot placement and accounting for dot gain. Results show the multilevel halftoned image is visually improved in terms of graininess and detail enhancement when compared to the bi-level halftoned image.

The tone value increase in halftone printing commonly referred to as dot gain actually encompasses two fundamentally different phenomena. Physical dot gain refers to the fact that the size of the printed halftone dots differs from their nominal size, and is related to the printing process. Optical dot gain originates from light scattering inside the substrate, causing light exchanges between different chromatic areas. Due to their different intrinsic nature, physical and optical dot gains need to be treated separately. In this study, we characterize and compare the dot gain properties for offset prints on coated and uncoated paper, using AM and first and second generation FM halftoning. Spectral measurements are used to compute the total dot gain. Microscopic images are used to separate the physical and optical dot gain, to study ink spreading and ink penetration, and to compute the Modulation Transfer Function (MTF) for the different substrates. The experimental results show that the physical dot gain depends on ink penetration and ink spreading properties. Microscopic images of the prints reveal that the ink penetrates into the pores and cavities of the uncoated paper, resulting in inhomogeneous dot shapes. For the coated paper, the ink spread on top of the surface, giving a more homogenous dot shape, but also covering a larger area, and hence larger physical dot gain. The experimental results further show that the total dot gain is larger for the uncoated paper, because of larger optical dot gain. The effect of optical dot gain depends on the lateral light scattering within the substrate, the size of the halftone dots, and on the halftone dot shape, especially the dot perimeter.

Ever since its origin in the late 19th century, a color reproduction technology has relied on a trichromatic color reproduction approach. This has been a very successful method and also fundamental for the development of color reproduction devices. Trichromatic color reproduction is sufficient to approximate the range of colors perceived by the human visual system. However, tricromatic systems only have the ability to match colors when the viewing illumination for the reproduction matches that of the original. Furthermore, the advancement of digital printing technology has introduced printing systems with additional color channels. These additional color channels are used to extend the tonal range capabilities in light and dark regions and to increase color gamut. By an alternative approach the addition color channels can also be used to reproduce the spectral information of the original color. A reproduced spectral match will always correspond to original independent of lighting situation. On the other hand, spectral color reproductions also introduce a more complex color processing by spectral color transfer functions and spectral gamut mapping algorithms. In that perspective, spectral vector error diffusion (sVED) look like a tempting approach with a simple workflow where the inverse color transfer function and halftoning is performed simultaneously in one single operation. Essential for the sVED method are the available color primaries, created by mixing process colors. Increased numbers of as well as optimal spectral characteristics of color primaries are expected to significantly improve the color accuracy of the spectral reproduction. In this study, sVED in combination with multilevel halftoning has been applied on a ten channel inkjet system. The print resolution has been reduced and the underlying physical high resolution of the printer has been used to mix additional primaries. With ten ink channels and halfton cells built-up by 2x2 micro dots where each micro dot can be a combination of all ten inks the number of possible ink combinations gets huge. Therefore, the initial study has been focused on including lighter colors to the intrinsic primary set. Results from this study shows that by this approach the color reproduction accuracy increases significantly. The RMS spectral difference to target color for multilevel halftoning is less than 1/6 of the difference achieved by binary halftoning. © (2013) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Abstract: Spectral Vector Error Diffusion, sVED, is an interesting approach to achieve spectral color reproduction, i.e. reproducing the spectral reflectance of an original, creating a reproduction that will match under any illumination. For each pixel in the spectral image, the colorant combination producing the spectrum closest to the target spectrum is selected, and the spectral error is diffused to surrounding pixels using an error distribution filter. However, since the colorant separation and halftoning is performed in a single step in sVED, compensation for dot gain cannot be made for each color channel independently, as in a conventional workflow where the colorant separation and halftoning is performed sequentially. In this study, we modify the sVED routine to compensate for the dot gain, applying the Yule-Nielsen n-factor to modify the target spectra, i.e. performing the computations in (1/n)-space. A global n-factor, optimal for each print resolution, reduces the spectral reproduction errors by approximately a factor of 4, while an n-factor that is individually optimized for each target spectrum reduces the spectral reproduction error to 7% of that for the unmodified prints. However, the improvements when using global n-values are still not sufficient for the method to be of any real use in practice, and to individually optimize the n-values for each target is not feasible in a real workflow. The results illustrate the necessity to properly account for the dot gain in the printing process, and that further developments is needed in order to make Spectral Vector Error Diffusion a realistic alternative for spectral color reproduction.

Multi-channel printing with more than the conventional four colorants brings numerous advantages, but also challenges, like implementation of halftone algorithms. This paper concentrates on amplitude modulated (AM) halftoning for multi-channel printing. One difficulty is the correct channel rotation to avoid the moiré effect and to achieve colour fidelity in case of misregistration. 20 test patches were converted to seven-channel images and AM halftoning was applied using two different approaches in order to obtain a moiré-free impression. One method was to use orthogonal screens and adjust the channels by overlapping the pairs of complimentary colours, while the second was to implement non-orthogonal halftone screens (ellipses). By doing so, a wider angle range is available to accommodate a seven-channel impression. The performance was evaluated by simulating misregistration in both position and angle for a total of 1600 different scenarions. ΔE values were calculated between the misregistered patches and the correct ones, for both orthogonal and non-orthogonal screens. Results show no visible morié and improvement in colour fidelity when using non-orthogonal screens for seven-channel printing, producing smaller colour differences in case of misregistration.

The interest for spectral color reproduction has increased with the growing field of multispectral imaging and the increasing use of multi-colorant printing systems. Spectral color reproduction, i.e. aiming at reproducing the spectral reflectance of an original, first requires a colorant separation for a multi-colorant printing system, followed by halftoning of each the color channels. Spectral vector error diffusion, sVED, has previously been introduced as a tempting alternative for spectral color reproduction, since the method combines the colorant separation and the halftoning in a single step. Only the spectral properties of the Neugebauer primaries are needed as input, and there is no need to invert a complex printer model for the colorant separation. Previously, spectral vector error diffusion has been positively evaluated for simulated prints, assuming a perfect printer and no dot gain. In this study, we evaluate the performance of sVED in practice, for real prints.Spectral vector error diffusion has been used to reproduce 1000 spectral targets, all within the spectral gamut of the printing system. The resulting color patches have been printed in various print resolutions, using a 10-colorant inkjet printing system. The experimental results reveal a remarkably large difference between the reproduction errors for the printed samples compared to the simulated spectra from the digital halftones. The results show a strong relation between the print resolution and the magnitude of the reproduction error, with lower resolutions giving smaller errors, due to the effect of dot gain in the printing process. The experimental results imply that in its current form, without compensation for physical and optical dot gain, spectral vector error diffusion produces unacceptable spectral and colorimetric reproduction errors, for any print resolutions used in practice.The results further show that the sVED method in many cases produces color patches that appear noisy and visually unpleasant. By replacing the spectral RMS difference with the ΔE₉₄ color difference as criterion in the sVED algorithm, the graininess as well as the resulting color difference was decreased. However, the improvements in colorimetric performance and more visually pleasant reproductions, comes at the cost of an increase in spectral reproduction errors.

This paper describes a method for 3-D surface estimation based on reflection measurements in different orientationsof the light source and the paper. To facilitate the estimation, surface facets that probably support specular reflection weremarked and isolated, so as to enable the application of sample Lambertian reflectance model over those non-specular reflectionpoints. A computer controlled imaging device was used to capture images in a large number of orientations. The image capturewas performed using several different exposures in order to present larger dynamic irradiance range. Images together with theircounterpoints under antithetical illuminations were used to deal with the possible situation that light failed illumination arrivalson some points locate behind bulges.Iteration using difference approximation as well as enforcing integrability algorithm wereused to calculate the surface height based on Shaping from Shading algorithm.

By separating the optical dot gain from the physical dot gain, it is possible to study different behaviors of color inks on different papers. In this study we are investigating the dependency of dot gain and wavelength in color print. Microscopic images have been used to separate optical and physical dot gain from each other. The optical behavior of primary color inks in different absorbing wavelength bands has been studied. It has been illustrated that the light scattering in the paper is wavelength independent, and therefore the Point Spread Function which indicates the probability of light scattering of the paper does not change in visible wavelengths (380 nm -700 nm). We have shown that it is possible to separate two printed color inks on one specific wavelength, due to the filtering behavior of the color inks. By considering the fact that light scattering in the paper is wavelength independent, it was possible to separately analyze the dot gain of each color.

In commercial prints the halftone dots are seldom placed exactly at their corresponding positions in the digital bitmap, mostly due to the imprecise transportation of the printing substrate. In this study, we firstly present an image processing model to measure the displacement of the dots in different color separations by using a high resolution camera. By using a filter wheel equipped with a set of interference filters and sending light in different wavelength bands, it is possible to separate the different color inks. For example, for the combination of cyan and magenta inks, only cyan will be visible in the captured image if the wavelength band of the incoming light is concentrated around 700 nm. On the other hand, for the wavelength band concentrated around 500 nm only magenta will be visible. By comparing the positions of the dots in the captured images with those in the original bitmap we can measure register shift. Secondly in this study, we investigate how miss-registration affects the color appearance of the final print for different halftoning techniques. We use AM, FM first generation and FM 2nd generation halftoning methods and investigate and compare their sensitivity to register shift.

In the present work we measure the register shift for color patches printed in offset by the proposed image processing model. In order to study the effect of miss-registration on the resulting color appearance we first simulate the miss-registration in the digital bitmap. Then we print the simulated bitmap using an office laser printer. Since the miss-registration is usually negligible for digital prints, especially in lower resolution, we can examine the accuracy of our model for measuring dot displacement by comparing the simulated displacement with the measured one. Finally, by using a spectrophotometer to measure color coordinates, we can study the effect of miss-registration on the resulting color appearance for different halftoning methods by calculating the ΔElab color difference.

Modeling color reproduction in halftone prints is difficult, mainly because of light scattering in the substrate, causing optical dot gain. Most available models are limited to macroscopic color measurements, averaging the reflectance over an area that is large relative the halftone dot size. The reflectance values for the full tone ink and the unprinted paper are used as input, and these values are assumed to be constant. An experimental imaging system, combining the accuracy of color measurement instruments with a high spatial resolution, allows us to measure the individual halftone dots, as well as the paper between them. Microscopic reflectance  measurements reveal that the micro-reflectance of the printed dots and the paper between them is not constant, but varies with the dot area coverage. By incorporating the varying micro-reflectance values of the ink and paper in an expanded Murray-Davies model, we have previously shown that the resulting prediction errors are smaller than for the famous Yule-Nielsen model. Moreover, unlike Yule-Nielsen, the expanded Murray-Davies model takes into account the varying micro-reflectance for the printed dots and the paper, thus providing a better physical description of optical dot gain in halftone reproduction.

In this study, we further extend the methodology to handle color prints, predicting tristimulus values for prints with  multiple and overlapping colorants. After converting the microscopic images of halftone prints into CIEXYZ color space, 3D histograms are computed. In the 3D histograms, the paper and the inks appear as clusters, with the transitions between the clusters corresponding to the edges of halftone dots. The tristimulus values for the paper and the different combinations of ink are computed as the centers of gravity for the clusters in the 3D histogram. From the microscopic images we can also compute the physical dot area coverage for each of the Neugebauer primaries, which typically differ from the nominal one, due to physical dot gain. The result is an expanded Neugebauer model, employing the varying tristimulus values of the paper and primary inks, as well as for  overlapping, secondary colors. Experimental results confirm the accuracy of the proposed methodology, whencompared to measurements using a spectrophotometer. Further, the results have shown that the variation of the micro-reflectance of the Neugebauer primaries is large, and depends strongly on the total dot area coverage.

Modeling halftone print reproduction is difficult, mainlybecause of light scattering, causing optical dot gain. Mostavailable models are based on macroscopic color measurements,integrating the reflectance over an area that is large relative thehalftone dot size. The reflectance values for the full tone and theunprinted paper are used as input, and these values are assumedto be constant. An experimental imaging system, combining theaccuracy of color measurement instruments with a high spatialresolution, allows us to measure the individual halftone dots, aswell as the paper between them. Microscopic color measurementsreveal that the micro-reflectance of the printed dots and the paperis not constant, but varies with the dot area fraction. Byincorporating the varying reflectance of the ink and paper in anexpanded Murray-Davies model, the resulting prediction errorsare smaller than for the Yule-Nielsen model. However, unlikeYule-Nielsen, the expanded Murray-Davies model preserves thelinear additivity of reflectance, thus providing a better physicaldescription of optical dot gain. The microscopic colormeasurements further show that the color shift of the ink andpaper depends on the halftone geometry and the print resolution.In this study, we measure and characterize the varying microreflectanceof ink and paper with respect to properties of thehalftones, using AM and FM prints of various print resolutions.

To reproduce color images in print, the continuous tone image is first transformed into a binary halftone image, producing various colors by discrete dots with varying area coverage. In halftone prints on paper, physical and optical dot gains generally occur, making the print look darker than expected, and making the modeling of halftone color reproduction a challenge. Most available models are based on macroscopic color measurements, averaging the reflectance over an area that is large in relation to the halftone dots. The aim of this study is to go beyond the macroscopic approach, and study halftone color reproduction on a micro-scale level, using high resolution images of halftone prints. An experimental imaging system, combining the accuracy of color measurement instruments with a high spatial resolution, opens up new possibilities to study and analyze halftone color prints.

The experimental image acquisition offers a great flexibility in the image acquisition setup. Besides trichromatic RGB filters, the system is also equipped with a set of 7 narrowband filters, for multi-channel images. A thorough calibration and characterization of all the components in the imaging system is described. The spectral sensitivity of the CCD camera, which can not be derived by direct measurements, is estimated using least squares regression. To reconstruct spectral reflectance and colorimetric values from the device response, two conceptually different approaches are used. In the model-based characterization, the physical model describing the image acquisition process is inverted, to reconstruct spectral reflectance from the recorded device response. In the empirical characterization, the characteristics of the individual components are ignored, and the functions are derived by relating the device response for a set of test colors to the corresponding colorimetric and spectral measurements, using linear and polynomial least squares regression techniques.

Micro-scale images, referring to images whose resolution is high in relation to the resolution of the halftone, allow for measurements of the individual halftone dots, as well as the paper between them. To capture the characteristics of large populations of halftone dots, reflectance histograms are computed as well as 3D histograms in CIEXYZ color space. The micro-scale measurements reveal that the reflectance for the halftone dots, as well as the paper between the dots, is not constant, but varies with the dot area coverage. By incorporating the varying micro-reflectance in an expanded Murray-Davies model, the nonlinearity caused by optical dot gain can be accounted for without applying the nonphysical exponentiation of the reflectance values, as in the commonly used Yule-Nielsen model.

Due to their different intrinsic nature, physical and optical dot gains need to be treated separately when modeling the outcome of halftone prints. However, in measurements of reflection colors, physical and optical dot gains always co-exist, making the separation a difficult task. Different methods to separate the physical and optical dot gain are evaluated, using spectral reflectance measurements, transmission scans and micro-scale images. Further, the relation between the physical dot gain and the halftone dot size is investigated, demonstrated with FM halftones of various print resolutions. The physical dot gain exhibits a clear correlation with the dot size and the dot gain increase is proportional to the increase in print resolution. The experimental observations are followed by discussions and a theoretical explanation.

Modeling the color reproduction of halftone prints is difficult, because of light scattering, causing optical dot gain. Most available models are limited to macroscopic color measurements, averaging the reflectance over an area that is large relative the dot size. The aim of this study is to go beyond the macroscopic approach and study optical dot gain on a micro-scale level, using colorimetric images of printed halftones. An experimental imaging system, combining the accuracy of color measurement instruments with a high spatial resolution, opens up possibilities to better study the color reproduction in halftone color prints. The main focus is to study how the reflectance values of the printed dots and the paper between the dots, Ri(Fi) and Rp(Fi), vary with the dot area fraction. Micro-scale images, i.e. when the resolution of the images is high in relation to the resolution of the halftone, allow for measurements of the individual halftone dots, as well as the paper between them. To capture the characteristics of large populations of halftone dots, histograms are computed. From the histogram data it is possible to derive the mean reflectance, R, the reflectance for the dots, Ri(Fi), and the paper between the dots, Rp(Fi). The true dot area coverage, including the physical dot gain, is computed using histogram data, as well as using line scans in the micro-scale images. A previously proposed extension of the Murray-Davies equation, incorporating Ri(Fi) and Rp(Fi), is evaluated. The model is further extended to handle color prints, predicting tristimulus values, by using 3D histograms in CIEXYZ color space. To reduce the complexity, projection from XYZ coordinates into one dimensional color distributions are used. The prediction errors of the model were found to be equivalent, or better, to that of the Yule-Nielsen model using an optimal n-factor. However, unlike Yule-Nielsen, the extended Murray-Davies model preserves the linear additivity of reflectance, thus providing a better physical description of optical dot gain in halftone color prints.

Modeling color print reproduction is difficult, mainly because of light scattering, causing optical dot gain. Most available models are based on macroscopic color measurements, the average value over an area that is large relative to the halftone dot size. The aim of this study is to go beyond the macroscopic approach, to study color print reproduction on a micro-scale level. An experimental imaging system, combining the accuracy of color measurement instruments with a high spatial resolution, opens up new possibilities to study and model color print reproduction. The main focus is to study how the reflectance values of the printed dots and the paper between them vary with the dot area fraction. A previously proposed expansion of the Murray-Davies model is further developed to handle color prints, predicting tristimulus values. The color of the halftone dots and the paper between them is derived from 3D color histograms in CIEXYZ color space. The prediction errors of the model were found to be equivalent, or better, to that of the Yule-Nielsen model using an optimal n-factor. However, unlike Yule-Nielsen, the expanded Murray-Davies model takes into account the varying reflectance of the ink and paper, and preserves the linear additivity of reflectance, thus providing a better physical description of optical dot gain in color reproduction.

The focus of the study is high quality image acquisition in colorimetric and multispectral formats. The aim is to combine the spatial resolution of digital images with the spectral resolution of color measurement instruments, to allow for accurate colorimetric and spectral measurements in each pixel of the acquired images. An experimental image acquisition system is used, which besides trichromatic RGB filters also provides the possibility of acquiring multi-channel images, using a set of narrowband filters. To derive mappings to colorimetric and multispectral representations, two conceptually different approaches are used. In the model-based characterization, the physical model describing the image acquisition process is inverted, to reconstruct spectral reflectance from the recorded device response. In the empirical characterization, the characteristics of the individual components are ignored, and the functions are derived by relating the device response for a set of test colors to the corresponding colorimetric and spectral measurements, using linear and polynomial least squares regression. The results indicate that for trichromatic imaging, accurate colorimetric mappings can be derived by the empirical approach, using polynomial regression to CIEXYZ and CIELAB. However, accurate spectral reconstructions requires for multi-channel imaging, with the best results obtained using the model-based approach.

The aim of the study is to reconstruct spectral and colorimetric data, using trichromatic and multi-channel imaging. An experimental image acquisition system is used, which besides trichromatic RGB filters also provides the possibility of acquiring multi-channel images, using 7 narrowband filters. To derive mappings to colorimetric and multispectral representations, two conceptually different approaches are used. In the model-based approach, the physical model describing the image acquisition process is inverted, to reconstruct spectral reflectance from the recorded device response. A priori knowledge on the smooth nature of spectral reflectances is utilized, by representing the reconstructed spectra as linear combinations of basis functions, using Fourier basis and a database of real reflectance spectra. In the empirical approach, the characteristics of the individual components are ignored, and the functions are derived by relating the device response for a set of training colors to the corresponding colorimetric and spectral measurements. Beside colorimetric regression, mapping device values directly to CIEXYZ and CIELAB, experiments are also made on reconstructing spectral reflectance, using least squares regression techniques.

The results indicate that for trichromatic imaging, accurate colorimetric mappings can be derived by the empirical approach, using polynomial regression to CIEXYZ and CIELAB. Because of the media-dependency, the characterization functions must be derived for each combination of media and colorants. However, accurate spectral reconstructions require for multi-channel imaging, using model-based device characterization. Moreover, the model-based approach is general, since it is based on the spectral characteristics of the image acquisition system, rather than the characteristics of a set of color samples.

The trichromatic principle of representing color has for a long time been dominating in color imaging. The reason is the trichromatic nature of human color vision, but as the characteristics of typical color imaging devices are different from those of human eyes, there is a need to go beyond the trichromatic approach. The interest for multi-channel imaging, i.e. increasing the number of color channels, has made it an active research topic with a substantial potential of application.

To achieve consistent color imaging, one needs to map the imaging-device data to the device-independent colorimetric representations CIEXYZ or CIELAB, the key concept of color management. As the color coordinates depend not only on the reflective spectrum of the object but also on the spectral properties of the illuminant, the colorimetric representation suffers from metamerism, i.e. objects of the same color under a specific illumination may appear different when they are illuminated by other light sources. Furthermore, when the sensitivities of the imaging device differ from the CIE color matching functions, two spectra that appear different for human observers may result in identical device response. On contrary, in multispectral imaging, color is represented by the object’s physical characteristics namely the spectrum which is illuminant independent. With multispectral imaging, different spectra are readily distinguishable, no matter they are metameric or not. The spectrum can then be transformed to any color space and be rendered under any illumination.

The focus of the thesis is high quality image-acquisition in colorimetric and multispectral formats. The image acquisition system used is an experimental system with great flexibility in illumination and image acquisition setup. Besides the conventional trichromatic RGB filters, the system also provides the possibility of acquiring multi-channel images, using 7 narrowband filters. A thorough calibration and characterization of all the components involved in the image acquisition system is carried out. The spectral sensitivity of the CCD camera, which can not be derived by direct measurements, is estimated using least squares regression, optimizing the camera response to measured spectral reflectance of carefully selected color samples.

To derive mappings to colorimetric and multispectral representations, two conceptually different approaches are used. In the model-based approach, the physical model describing the image acquisition process is inverted, to reconstruct spectral reflectance from the recorded device response. In the empirical approach, the characteristics of the individual components are ignored, and the functions are derived by relating the device response for a set of test colors to the corresponding colorimetric and spectral measurements, using linear and polynomial least squares regression.

The results indicate that for trichromatic imaging, accurate colorimetric mappings can be derived by the empirical approach, using polynomial regression to CIEXYZ and CIELAB. Because of the media-dependency, the characterization functions should be derived for each combination of media and colorants. However, accurate spectral data reconstruction requires for multi-channel imaging, using the model-based approach. Moreover, the model-based approach is general, since it is based on the spectral characteristics of the image acquisition system, rather than the characteristics of a set of color samples.