Digitally reconstructing Van Gogh's Field with Irises near Arles. Part 1: Varnish

Varnish layers applied to paintings often discolor as they age, upsetting the original colour relationships intended by the artist. The removal of aged varnish layers using physical and chemical means is a highly skilled and often time‐consuming operation, which is not lightly undertaken. There are many aspects under consideration before embarking upon such treatment, including the visual result inferred by spot cleaning tests. In this article, we develop a technique for digital removal of discolored varnish that can help to envisage how a painting will look following cleaning treatment. The digital technique was applied to Vincent van Gogh's painting Field with Irises near Arles (May 1888), in parallel to the painting actually being cleaned, which allowed direct validation of the method developed. In the new method, we utilized not only hyperspectral data from parts of the painting with and without the varnish, but also experts' identification of spots on the painting where unmixed white pigment has been applied. The physical model that we use is based on Kubelka‐Munk two‐constant theory, commonly used to model the optical properties of paint. We show that with this model it is possible to determine the transmittance and reflectance of the varnish layer as function of wavelength. Results from previous studies confirm the calculated values. With the new method, we created a high‐resolution digital image of the painting, as it would look after varnish removal, at a moment when the actual varnish was still present on the painting. The new method may help conservators and others involved in decisions made regarding issues of varnish removal from paintings, or may help to visualize the colors of a painting without discolored varnish in cases where its physical removal cannot be safely accomplished and so is not an option.     

Digitally reconstructing Van Gogh's Field with Irises near Arles part 3: Determining the original colors

In earlier articles, we determined the spatial distributions and concentrations of all pigments used by Van Gogh in his painting Field with Irises near Arles. The colors of some pigments are expected to have changed over time, especially those of chrome yellow, cochineal, and eosin lake. For all pigments in this painting, we made physical paint reconstructions by following historical sources on raw materials and production processes, and we determined their optical properties. We combined this with pigment concentration maps to reconstruct the original colors of the painting digitally. When substituting the reconstruction paints into the calculations, we found that technical‐scientific data was not sufficient to resolve several issues. In those cases, discussions within the broad interdisciplinary team allowed us to make informed decisions. These issues refer to the representation of the sky area, and the original contributions of the red lake pigments to local colors. The digitally reconstructed colors of the painting show that due to discoloring of red lake pigments, the irises in the field have changed from a warm purple to purplish blue, and many pink spots in the field have turned to white. The range of yellows in the field has decreased and partly turned to dark brown. The digital reconstruction gives a better understanding of the color scheme used by Van Gogh when compared to remarks the artist made in letters when describing this painting. Also, the original color composition is seen to be aligned with color theories on which Van Gogh based his work.     

Color mixing and color separation of pigments with concentration prediction

In this study, we propose a color mixing and color separation method for opaque surface made of the pigments dispersed in filling materials. The method is based on Kubelka–Munk model. Eleven different pigments with seven different concentrations have been used as training sets. The amount of concentration of each pigment in the mixture is estimated from the training sets by using the least‐square pseudo‐inverse calculation. The result depends on the number and type of pigments selected for calculation. At most we can select all pigments. The combinations resulted with negative concentrations or unusual high concentrations are discarded from the list of candidate combination. The optimal pigment's set and its concentrations are estimated by minimizing the reflectance difference of given reflectance and predicted reflectance. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 461–469, 2008     

Color of pigmented plastics—Measurements and predictions

The effect of the concentration of a colorant (masterbatch) and the surface texture on the color of an opaque injection‐molded plaque is experimentally described by means of the spectral reflectance and the CIELAB coordinates. It was noted that the surface texture had a marked influence on the experimental results and on the perceived color. The relation between the color of these pigmented plastic plaques and intrinsic physical material properties, such as light absorption and scattering coefficients, is described by means of the Kubelka‐Munk equation for pigment/paste mixtures. The concentration dependence of this Kubelka‐Munk equation for different masterbatch‐polymer mixtures can be modeled in terms of the color of the individual constituents using a fitting parameter. Further experiments were carried out which indicated that the fitting parameter had a physical meaning. The effect of the surface texture on the optical appearance of the plaques can also be accounted for by this parameter.     

Spectral analysis of blacks

The spectral behavior of different black surfaces including papers and fabrics are investigated in this study. Several colored pigments are mixed with the blacks in different concentrations to prepare black surfaces with different shades while a series of black dyestuffs are applied on textile materials to increase the ranges of black objects. The principal component analysis technique is applied to determine the actual spectral size of the reflectance dataset. The technique simply extracts the principal directions of spectral data and organizes them in restricted spectral spaces. Three different spectral spaces, i.e., the reflectance spectra, the Kubelka‐Munk function of reflectance as well as the inverse of reflectance factor are selected to present the samples in the restricted spaces. Based on the results, it is found that, there are no significant differences between the employed spaces and far from the employed spectral domains, black surfaces could be adequately described in a three‐dimensional space. The three extracted statistical colorants are used for reconstruction of reflectance spectra of samples while the root mean square error percentage and the color difference values under the standard observing condition confirm the suitability of such virtual primaries. The work is extended to reconstruction of spectral data from colorimetric information and the adequacy of such three‐dimensional space is reconfirmed. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2012     

Colour in ceramic glazes: Efficiency of the Kubelka–Munk model in glazes with a black pigment and opacifier

In this study the efficiency of the Kubelka–Munk model (already known and consolidated in other industrial sectors) was evaluated in the prediction of the colour of an opaque ceramic glaze obtained by a mixture of black pigment (spinel Ni–Fe–Cr) and zircon opacifier (ZrSiO₄). Glazes with different percentages of black pigment and opacifier were prepared to determine the absorption and scattering optical constants from the reflectance curves measured with a spectrophotometer. After the physical and chemical characterization of the glaze components (frit, pigment and opacifier), suggestions for the adaptation of the Kubelka–Munk model were made to facilitate the experimental procedure of analysis. The result obtained with the adapted Kubelka–Munk model was in good agreement with the experimental reflectance curves. The reproduction of the desired colour was possible with a reduced number of experiments and the model made it possible to correlate the colour with the added pigments concentration facilitating the formulation step.     

The effect of nano‐ and micro‐TiO2 particles on reflective behavior of printed cotton/nylon fabrics in vis/NIR regions

To match the reflectance profile of desert colors including brown, olive green, and khaki in the Vis/near IR (NIR) bands, several pigments were used to print cotton/nylon fabrics. The reflectances of printed fabrics were measured by using spectrophotometric technique. TiO₂ microparticle and nanoparticle powders were also added to the printing pastes to evaluate their effect of reflectance, light, rubbing, washing fastnesses, and colorimetric values of each sample. Tuning the reflectance behavior of each color was successfully managed using specific pigments along with TiO₂ particles. NIR reflectance of brown, khaki, and olive green printed fabrics was enhanced by presence of TiO₂ in printing formulations, which is in complete agreement with the Kubelka–Munk theory. NIR enhancing effect of TiO₂ particles was fast against rubbing, washing, and light exposures while it could significantly change the visible appearance of the printed patterns even at concentrations as low as 0.25 g/kg. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2012     

Comparison of methods of parameric correction for evaluating metamerism

In practice, most metameric pairs do not achieve colorimetric equality for a set of reference conditions. These parameric pairs are composed of a residual color difference and a metameric difference. Three techniques have been used to correct this residual color difference: an additive correction in L*a*b*, a multiplicative correction in XYZ (recommended by the CIE), and parameric decomposition where the batch's spectrum is adjusted. Parameric decomposition can be viewed as batch correction using three “colorants” (process primaries) where the color‐mixing model is linear in reflectance. Most often, Cohen and Kappauf's Matrix R technique is used where the primaries are color matching functions. Alternative primaries were derived from a Munsell Book of Color and an automotive paint system using principal component analysis (PCA) and independent component analysis (ICA). 1,152 parameric pairs about 24 color centers were synthesized using the paint system and Kubelka–Munk turbid‐media theory. Each parameric pair was corrected to a metameric pair using these methods. Spectral accuracy was evaluated by comparing the corrected spectra to metameric reference spectra calculated using Kubelka–Munk batch correction. The Matrix R technique had the worst spectral accuracy under the reference conditions while both PCA and ICA had similar and reasonable accuracy. The special index of metamerism, change in illuminant, was calculated for each parameric pair using these various correction techniques to achieve colorimetric equality. The Matrix R and CIE‐recommended multiplicative techniques were statistically significantly worse than parameric decomposition using Munsell Book of Color PCA and ICA and automotive ICA process primaries. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 293–303, 2007     

Handling translucent specimens in an opaque Kubelka–Munk Environment

Computer‐color matching usually employs a subset of Kubelka–Munk equations which require that each specimen analyzed be at complete hiding. This set of equations is preferred because they are simpler than their counterpart equations that operate at incomplete hiding. On the other hand, in coatings and plastics very often colorant specimens must be utilized that, either because of their nature or concentration, fail to qualify as being at complete hiding. This communication examines techniques for handling such cases and makes recommendations for obtaining the theoretical opaque reflectance of the specimens from measurements over both black and white. In addition, the article recommends a new relationship that more aptly characterizes the contrast ratios required than previous methods have done.     

Towards automation of color/weave selection in Jacquard design: Model verification

Jacquard woven fabrics are made from colored yarns and different weaves for designing complex pictorial and other patterning effects. The final visualized color effect is the result of assigning weave designs to different areas of the pattern to be created. The current practice in creating Jacquard woven fabric designs is to produce many samples in a trial‐and‐error attempt to match artwork colors. An ability to simulate accurately the appearance of a design prior to manufacture is highly desirable to reduce trial‐and‐error sample production. No automated accurate digital color methodology is yet available to assist designers in matching the patterned woven fabric to the desired artwork. To achieve this, we developed a geometrical model to predict the color contribution of each yarn on the face of the fabric. The geometrical model combined with a Kubelka‐Munk based color mixing model allowed the prediction of the reflectance properties of the final color for a given design. We compared the predicted and experimental values of the reflectance properties for a range of fabrics using the same geometric model with three separate color mixing models. The geometrical model combined with a log‐based color mixing model produced reasonable agreement between predicted and measured ΔE_ab, with an average ΔE_ab of approximately five. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 225–232, 2009     

Predicting the spectral reflectance factor of translucent paints using Kubelka‐Munk turbid media theory: Review and evaluation

The use of Kubelka‐Munk (K‐M) turbid media theory in predicting the spectral reflectance factor of an opaque specimen from the specimen's constituent optical constants is well established in practice and well described in the literature. For translucent samples, there is a paucity of published results and the approaches are disparate. Accordingly, a review of K‐M theory and its application for predicting the spectral reflectance factor of translucent samples is presented and tested. Four methods for determining the absorption and scattering coefficients with respect to a certain film thickness are described: the black‐white method, the infinite method, the masstone‐tint method, and the two‐region method. The black‐white and infinite methods use the general form of the K‐M equation. The masstone‐tint method can be used for both the general form and the opaque simplification. The two‐region method, combining opaque and translucent approaches, was enhanced in this research and included an opacity calculation to automatically differentiate opaque and translucent spectral regions and a smoothing technique to combine both spectral regions. The two‐region method was tested using a set of acrylic‐emulsion artist paints and glazes spanning a range of opacities from opaque to nearly transparent. The results were reasonable and provided statistically significant improvement compared with the opaque simplification, commonly used in art conservation science and industrial color matching. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 417–431, 2009     

Digital color reconstructions of cultural heritage using color‐managed imaging and small‐aperture spectrophotometry

There are many examples of cultural heritage having optical properties that have changed with the passage of time. Examples include the yellowing, darkening, and fading of paints and varnishes caused by light exposure and atmospheric pollution. When it is infeasible to treat an object, an image simulation can provide a view to the past, known as a color reconstruction. A technique is described that relies on a color‐managed image, spectral reflectance factor measurements of the object, an optical model of colorant mixing, an optical database of artist materials, spreadsheet software, and image editing software. Spectral calculations are used to create adjustment curves where segmented portions of an object's image are translated in color. This approach has been used to produce color reconstructions of paintings by Vincent van Gogh and Georges Seurat. This colorimetric translation methodology is described and an example shown for the Chicago version of Vincent van Gogh's Bedroom. The methodology is compared with pixel‐based processing.     

A fluorescent extension to the Kubelka–Munk model

Traditionally, single constant Kubelka–Munk‐type colorant formulation algorithms have been used for color control in the paper industry. One of the limitations of the Kubelka–Munk approaches is that they neglect fluorescence phenomena and the interdependence of absorption and scattering. In this article, an extended phenomenologic model is derived, incorporating fluorescence and interdependence of absorption and scattering. This model predicts illuminator‐independent radiance transfer factors based on dye‐on‐fiber, from which the total radiance factor responses under arbitrary illumination can be computed. Illuminator‐independent responses to changes in colorant concentration can also be modeled, allowing control of illuminator metamerism in coloring processes with fluorescent colorants. This method requires spectrofluorimetric (two‐monochromator method) measurements to characterize the coloring process. © 2002 Wiley Periodicals, Inc. Col Res Appl, 28, 4–14, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.     

A general framework to study the price‐color relationship in paintings with an application to Mark Rothko rectangular series

We propose a general framework to study the relationship between the price of a painting and its color‐related attributes. To this end we focus on four key aspects: dominant colors, features of the color palette, color harmony, and color emotions. We demonstrate the usefulness of this approach with an example based on Mark Rothko's post‐1950 paintings (the “rectangular” series), and auction data from the 1994 to 2018 period. We identify two distinct price‐color regimes in Rothko's market: (a) [1994‐2005], a period in which prices are explained mainly by the growing popularity of the artist regardless of the color attributes of the paintings sold; and (b) [2006‐2018], a period in which color‐related attributes explain most of the prices. Furthermore, we find that in this second period, the dominant colors and the diversity of the color palette, are by far the most relevant attributes that influence the price; color harmony and color emotions hold almost no explanatory power during this period. Finally, we propose a new metric based on the Herfindahl Index to describe color diversity; this metric seems to be promising at characterizing the effect of the color palette on the price of a painting.     

Chromaticity changes of inorganic pigments in Chinese traditional paintings due to the illumination of frequently‐used light sources in museum

Optical radiation can cause permanent damage to the color of Chinese traditional paintings, which have extremely high responsivity in the museum illumination. In order to obtain quantitative influence laws of artificial illumination on inorganic pigments in Chinese traditional paintings and provide basis for choosing light sources, a long periodic illumination experiment was carried out to examine how prolonged exposure of three light sources (tungsten halogen, metal halide and white light emitting diodes), frequently‐used in museums, affect the chromaticity of five inorganic pigments [azurite (blue), cinnabar (red), orpiment (yellow), ancient graphite (black), clam shell powder (white)], commonly used in Chinese traditional paintings. Through the experiment, we found that the illumination causes a color change to inorganic pigments, and the degree of which is related to the photochemical stability of pigments and the high energy shortwave radiation in the light source spectrum. We also obtain the color change laws of the five pigments and the quantitative relationships of color damage for different painting types. These results can provide data basis for related research on Chinese traditional painting illumination and choice basis for light sources in museum lighting designs.     

Color matching algorithms in ceramic tile production

In the present work, the possibility of transferring in the ceramic tiles production the know-how developed in the field of the paints by using the Kubelka–Munk theory, in the form used for opaque surface coatings, have been evaluated. Five different target colors have been chosen as target and tried to reproduce with an industrial glaze in a cycle for fine porcelain stoneware tiles. Four industrial pigments have been chosen as basic stains for the formulations. The results show a good efficiency of the color matching algorithm applied to pigments for glazes for fine porcelain stoneware tiles. All the formulations, in fact, have allowed to obtain a value of ΔE^* lower to the accepted limit.     

Determining dimensioned values of kubelka–munk scattering and absorption coefficients

If hiding computations are to be made in conjunction with computer color matching, the Kubelka–Munk absorption and scattering coefficients, K and S, must be dimensioned (absolute) coefficients. Two procedures for calculating the dimensioned coefficients were compared. In the first, the coefficients were calculated directly by two different methods from films applied at incomplete hiding over white and black substrates. In the second, previously calculated dimensioned coefficients for titanium dioxide formed the basis of determining the coefficients for the remaining pigments from films applied at complete hiding. Experimental results showed the second procedure superior to either method of the first procedure, except for determining dimensioned K and S for titanium dioxide.     

Mathematical and empirical evaluation of accuracy of the Kubelka–Munk model for color match prediction of opaque and translucent surface coatings

Attempts were made to evaluate mathematically and empirically the accuracy of the Kubelka–Munk model for color match prediction of opaque and translucent surface coatings in the color using industries. To this end, an innovative inversed mathematical evaluation procedure was concocted which comprised of plotting the absorption and scattering constants of the Kubelka–Munk model or any of its various modified form or replacements theories against the intrinsic optical coefficients of the respective exact radiation transfer theories, namely Chandrasekhar for opaque and van de Hulst for translucent media. The results prove mathematically that the Kubelka–Munk model for opaque media is a sound theory and its various suggested modifications or replacements do not improve the color match prediction of opaque surface coating media. This mathematical conclusion was further confirmed by color match prediction of actual opaque paint samples. On the other hand, the mathematical prediction for translucent media illustrated a completely different picture, depicting nonlinearity between the optical constants and the respective concentrations of colorants. This implies that much further work has to be carried out to derive invertible new equations to enforce linearity to such situations or make use of alternative artificial intelligent procedures which are designed especially for nonlinearity.