Concerning the calculation of the color gamut in a digital camera

Several methods to determine the color gamut of any digital camera are shown. Since an input device is additive, its color triangle was obtained from their spectral sensitivities, and it was compared with the theoretical sensors of Ives‐Abney‐Yule and MacAdam. On the other hand, the RGB digital data of the optimal or MacAdam colors were simulated to transform them into XYZ data according to the colorimetric profile of the digital camera. From this, the MacAdam limits associated to the digital camera are compared with the corresponding ones of the CIE‐1931 XYZ standard observer, resulting that our color device has much smaller MacAdam loci than those of the colorimetric standard observer. Taking this into account, we have estimated the reduction of discernible colors by the digital camera applying a chromatic discrimination model and a packing algorithm to obtain color discrimination ellipses. Calculating the relative decrement of distinguishable colors by the digital camera in comparison with the colorimetric standard observer at different luminance factors of the optimal colors, we have found that the camera distinguishes considerably fewer very dark than very light ones, but relatively much more colors with middle lightness (Y between 40 and 70, or L* between 69.5 and 87.0). This behavior is due to the short dynamic range of the digital camera response. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 399–410, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20245     

Mathematical determination of the numerical data corresponding to the color‐matching functions of three real observers using the RGB CIE‐1931 primary system and a new system of unreal primaries X′Y′Z′

In this work, we determine the numerical data of the experimental color‐matching functions (cmf's) of three real observers (JAM, MM, and CF) for two small fields (2°). In previous works, these cmf's have been shown generically and expressed only in a new system of unreal X′Y′Z′ primaries. Here, we show results found with these cmf's for the visible spectrum in intervals of 10 nm, from 400 to 700 nm. The data refer to both the RGB CIE‐1931 system and a new system of unreal primaries X′Y′Z′, established by a procedure similar to that of the XYZ CIE‐1931 system. This transformation was needed, because negative values appeared in various cmf's when they were referred to the XYZ CIE‐1931 system. Recently, we have called this new system G94 (Granada ‘94). Here, we also describe the method and calculation of the matrix that enables this transformation; in testing six real observers with new cmf’s, we found positive results. We have used these new and experimental cmf's in several preceding works, as have other authors as well, to whom J. A. Martínez privately communicated the corresponding numerical data. The use of these cmf's by all the authors has led to noteworthy results. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 89–95, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10127     

Extending the color gamut and dynamic range of an sRGB image using a residual image

Image sources, such as digital camera captures and photographic negatives, typically have more information than can be reproduced on a photographic print or a video display. The information that is lost during the tone/color rendering process relates to both the extended dynamic range and color gamut of the original scene. In conventional photographic systems, most of this additional information is archived on the photographic negative and can be accessed by adjusting the way the negative is printed. However, most digital imaging systems have traditionally archived only a rendered video RGB image. As a result, it is not possible to make the same sorts of image manipulations that historically have been possible with conventional photographic systems. This suggests that there would be an advantage to storing images using an extended dynamic range/color gamut color encoding. However, because of file compatibility issues, digital imaging systems that store images using color encoding other than a standard video RGB representation (e.g., sRGB) would be significantly disadvantaged in the marketplace. In this article, we describe a solution that has been developed to maintain compatibility with existing file formats and software applications, while simultaneously retaining the extended dynamic range and color gamut information associated with the original scenes. With this approach, the input raw digital camera image or film scan is first transformed to the scene‐referred ERIMM RGB color encoding. Next, a rendered sRGB image is formed in the usual way and stored in a conventional image file (e.g., a standard JPEG file). A residual image representing the difference between the original extended dynamic range image and the final rendered image is formed and stored in the image file using proprietary metadata tags. This provides a mechanism for archiving the extended dynamic range/color gamut information, which is normally discarded during the rendering process, without sacrificing interoperability. Appropriately enabled applications can decode the residual image metadata and use it to reconstruct the ERIMM RGB image, whereas applications that are not aware of the metadata will ignore it and only have access to the sRGB image. The residual image is formed such that it will have negligible pixel values for those portions of the image that lie within the sRGB gamut, and will therefore be highly compressible. Tests on a population of 950 real customer images have demonstrated that the extended dynamic range scene information can be stored with an average file size overhead of about 8% compared to the sRGB images alone. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 251–266, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10160     

Estimating spectral reflectance from camera responses based on CIE XYZ tristimulus values under multi‐illuminants

A new spectral reflectance estimation method based on CIE XYZ values under multi‐illuminants was proposed to obtain multi‐spectral images accurately by using digital still cameras. CIE XYZ values under multi‐illuminants were initially predicted from raw RGB responses by using a polynomial model with local training samples. Then, spectral reflectance was constructed from the predicted CIE XYZ values via the pseudo‐inverse method. Experimental results indicated that the new spectral reflectance estimation method significantly outperformed the traditional colorimetric characterization method without requiring extra training samples or greatly increasing computational complexities. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 68–77, 2017     

Color errors of digital cameras

The mean color errors of a high‐quality digital camera are defined in CIELAB and CIEDE2000 ΔE units by using 16 ceramic color samples, whose accurate CIELAB values have been measured by a calibrated spectrophotometer. The bandwidths of CCD's color filters are evaluated by taking photographs of CRT‐display primaries. The lowest mean color errors were 13.1 CIELAB ΔE units and 8.1 CIEDE2000 ΔE units before corrections. Large color errors are decreased successfully by using three different methods: simple photoeditor, gamma correction, and multiple regression. © 2004 Wiley Periodicals, Inc. Col Res Appl, 29, 217–221, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20007     

Improve neural network‐based color matching of inkjet textile printing by classification with competitive neural network

Nowadays, with increasing use of digital printing in the textile industry, characterization and color matching are very much considered. There is a very complicated relationship between pixel values of input digital image and colorimetric parameters of printed textile samples. One of the most important used methods for inverse characterization of printer and prediction of CMYK digital values is neural network. In this study, the prediction accuracy of CMYK digital values were improved by dividing the training samples into 2, 4, 6, 8, and 10 subgroups using creating a competitive neural network. For classification of samples, L*a*b* or XYZ were introduced to a competitive neural network as input parameters. Then, the classification of test samples was performed by trained competitive neural network. To predict the of CMYK digital values of input digital image, a cascade‐forward back propagation neural network is trained by L*a*b* of each subgroup. The results obtained show that the prediction accuracy of CMYK digital values were improved by suggested method. The best result was obtained by classification of samples with L*a*b* into eight subgroups and using a cascade‐forward back propagation neural network with 4, 4, and 4 neurons in hidden layers.     

Judd's 1951 color-mixture diagram

Vos demonstrated that the Judd 1951 color-mixture diagram is a projective transformation of the CIE 1931 mixture diagram. He has provided transformation formulas for computing values of x′ and y′ from x and y, but he does not explain how the one set of data is derived from the other. Neither does Judd. Judd wanted the CIE to replace the 1931 V(Λ) curve with a new V(Λ) curve and to replace the 1931 XYZ diagram with a new X′Y′Z′ diagram. I have assumed that Judd started with the CIE 1931 RGB diagram. His X′Y′Z′ diagram can be derived from the RGB diagram if we use a different set of luminosity coefficients than those specified by the CIE. This change in luminosity coefficients was no doubt intended to compensate for the use of a new V(Λ) curve, but Judd has ignored the effect that this change in the luminosity coefficients should have on the alychne of the RGB diagram and the locus of spectral colors. This makes Judd's X′Y′Z′ diagram inappropriate for use in colorimetry and for use in building color-vision models. I have proposed a new solution to this problem.     

Color matching of fiber blends: Stearns‐Noechel model of digital rotor spun yarn

Stearns‐Noechel model was utilized as a primary reference to study color matching principles of digital rotor spun yarn. Three primary colored (red, yellow and blue) cotton fibers were used to spin blended yarns. Spectral reflectance of the two‐component and three‐component samples was measured with data color spectrophotometer. For these samples, the Stearns‐Noechel model parameter M was determined. Four methods were employed to calculate the M value to improve accuracy of the model, 1.Classical method, named as M1; 2.Optimizing the M1 value obtained by the classical method considering the wavelength factor, named as M2; 3.Simplified M2 according to the linear correlation with the wavelength, named as M3; 4. Simplified M2 according to the segmentation correlation with the wavelength, named as M4. The study shows that average color difference of the two‐component decreases from 2.7 to 1.48, and for three‐component samples from 3.32 to 1.66, by using M2 instead of M1. While calculated using M3, the color difference of the two types of samples will be 1.73 and 2.19, correspondingly. This cannot meet color matching needs. As for M4, the average color difference of the two categories will be 1.54 and 1.91, better than the result obtained using M1 and M3, worse than M2.     

Calibrated color mapping between LCD and CRT displays: A case study

The primary goal of a color characterization model is to establish a mapping from digital input values d_i (i = R,G,B) to tristimulus values such as XYZ. A good characterization model should be fast, use a small amount of data, and allow for backward mapping from tristimulus to d_i. The characterization models considered here are for the case of an end user who has no direct knowledge of the internal properties of the display device or its device driver. Three characterization models tested on seven different display devices are presented. The characterization models implemented in this study are a 3D look up table (LUT) (Raja Balasubramanian, Reducing the Cost of Lookup Table Based Color Transformations, Proc IS&T/SID 7th Color Imaging Conference 1 ), a linear model (Fairchild MD, Wyble DR. Colorimetric Characterization of the Apple Studio Display (Flat Panel LCD). Munsell Color Science Laboratory Technical Report, 1998), and the masking model (Tamura N, Tsumura N, Miyake. Masking Model for accurate colorimetric characterization of LCD. Proc IS&T/SID 10th Color Imaging Conference 3 ). The devices include two CRT monitors, three LCD monitors, and two LCD projectors. The results of this study indicate that a simple linear model is the most effective and efficient for all devices used in the study. A simple extension to the linear model is presented, and it is demonstrated that this extension improves white prediction without causing significant errors for other colors. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 438–447, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.     

A novel Color Rendition Chart for digital tongue image calibration

Digital tongue images are usually acquired by a camera under specific illumination environments. In order to guarantee better color representation of the tongue body, we propose a novel tongue Color Rendition Chart acting as a color reference to be used in color calibration algorithms to standardize the captured tongue images. First, based on a large tongue image database captured with our digital tongue image acquisition system, we establish a statistical tongue color gamut. Then, from the first step, different quantities of colors in the Color Rendition Chart are determined via experimentation. Afterwards, results using X‐Rite's ColorChecker® Color Rendition Chart (a standard in the color calibration field) are compared with the proposed tongue Color Rendition Chart by applying the color difference calculation formula of CIELAB and CIEDE2000 as a reference for the mean color calibration error. The results show that the proposed tongue Color Rendition Chart, which has 24 colors, produces a much smaller error (CIELAB —8.0755/CIEDE 2000—6.3482) compared with X‐Rite's ColorChecker® Color Rendition Chart (CIELAB 1976—14.7836/CIEDE 2000—11.7686). This demonstrates the effectiveness of the novel tongue Color Rendition Chart.     

Michromatic scope for enhancement of color difference

A michromatic (microscope plus chromatic) scope is a device that enhances the color discrimination between two spectral color datasets. Three spectral filters are required, instead of the conventional red, green, and blue filters, for the implementation of a michromatic camera. In this study, we describe two approaches to the design of these filters: in the first case, the design is based on the direct optimization of the filter characteristics (transmittance), whereas in the second case, the design is based on the nonnegative tensor factorization (NTF) of the spectral datasets. A michromatic camera can be implemented using these filters along with compatible postprocessing in‐camera firmware. Here, we performed experiments with two color datasets: one comprising skin and vein colors, and one comprising skin and cosmetics colors. These were further divided into a training set and a test set. The filters were defined using the training set, and the operation of the filters was tested and magnified using the test set. Our experiments demonstrated that the proposed approaches are suitable for color discrimination. For the first color dataset, the enhancement produced using the optimized filters was up to 252% of the original value, and the average color difference ΔE was increased from 2.82 to 9.93. NTF and preprocessing further enhanced the ΔE up to 21.84. For the second color dataset, NTF and postprocessing enhanced the ΔE from 4.33 to 29.19. The proposed discrimination enhancement could be physically implemented in a designated digital charge‐coupled device camera with proper filter installation and compatible postprocessing. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Camera characterization for improving color archaeological documentation

Determining the correct color is essential for proper cultural heritage documentation and cataloging. However, the methodology used in most cases limits the results since it is based either on perceptual procedures or on the application of color profiles in digital processing software. The objective of this study is to establish a rigorous procedure, from the colorimetric point of view, for the characterization of cameras, following different polynomial models. Once the camera is characterized, users obtain output images in the sRGB space that is independent of the sensor of the camera. In this article we report on pyColorimetry software that was developed and tested taking into account the recommendations of the Commission Internationale de l'Éclairage (CIE). This software allows users to control the entire digital image processing and the colorimetric data workflow, including the rigorous processing of raw data. We applied the methodology on a picture targeting Levantine rock art motifs in Remigia Cave (Spain) that is considered part of a UNESCO World Heritage Site. Three polynomial models were tested for the transformation between color spaces. The outcomes obtained were satisfactory and promising, especially with RAW files. The best results were obtained with a second‐order polynomial model, achieving residuals below three CIELAB units. We highlight several factors that must be taken into account, such as the geometry of the shot and the light conditions, which are determining factors for the correct characterization of a digital camera.     

Integer programming for optimal reduction of calibration targets

Calibration targets are widely used to characterize imaging devices. The question addressed in this article is that of how many surfaces in a calibration target are needed to account for the performance of the whole target. Different to previous research where the problem of reducing calibration charts is addressed independently of the calibration problem; in this article we tackle the reduction question based on the calibration performance. We argue that the outcome of both spectral and colorimetric calibration is dependent on the properties of the cross‐product matrix encompassing the color‐signals. Further, we show that by careful mathematical manipulation it is possible to write the cross‐product matrix as a linear sum of the submatrices corresponding to each individual color signal. This formulation allows us to cast the reduction problem as a quadratic minimization where we ask: given the spectral properties of the available color signals, what is the minimum number of surfaces needed to emulate the global cross‐product matrix. To reduce the number of surfaces we impose an integer constraint on the minimization, where the weight of each surface can only assume a value of 1 or 0. Our results show that around 13 surfaces are sufficient to account of the 24 surfaces of the Macbeth color checker. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 212–220, 2008     

Application of improved back propagation algorithm in color difference detection of fabric

Color is an indispensable indicator of product quality evaluation. To detect the color difference of fabrics, the Levenberg–Marquardt optimized back propagation (BP) algorithm is adopted to extract the color feature values of fabric images. First, RGB values are three inputs of BP neural network, and L*a*b* values measured by spectrophotometer are three outputs of the network. The trained network can obtain the corresponding L*a*b* values conveniently. Then the color difference can be calculated through color difference formula and the characteristic values obtained above. Finally, compared with the color difference calculated by the spectrophotometer, the most appropriate formula can be selected from the four formulas listed in the article (CIEDE2000, CMC, CIE94, and CIELAB) to acquire satisfying results. The experimental results reveal that the color difference of fabrics can be detected with a high accuracy and efficiency with this method. Plenty of duplication workloads and some complex conversion formulas can be avoided, making the acquirement of color difference more efficiently. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 311–317, 2015     

Effects of cold plasma on the color parameters of Hyssop (Hyssopus officinalis L.) using color imaging instrumentation and spectrophotometer

This research was conducted to evaluate the effects of cold atmospheric plasma treatment on the color of Hyssop (Hyssopus officinalis L.) and also to compare the usage of the spectrophotometer vs the color imaging instrumentation for the evaluation of the treatment on the color parameters. The experiments were investigated at different treatment times of 1, 5, and 10 minutes and the voltage values of 17, 20, and 23 kV. Possible changes of color were evaluated by using CIE L*a*b* values obtained with HunterLab colorimeter and CIE L*a*b* values obtained with a digital still camera (DSC) using digital image processing (MATLAB software). The values of L*, a*, and b* of the samples were obtained using both the methods. The results revealed that the L*, a*, and b* values of the treated Hyssop samples changed with increasing the treatment time and the voltage applied. Evaluating the interaction effects revealed that there was a significant difference in the (−a^*/b^* ) ratio. In addition, the results showed that the effects of all variables on the color parameters were significantly different in the case of the DSC using digital image processing. However, these effects were not significantly different using HunterLab colorimeter except for time variable and interaction effects of a* and (−a^*/b^* ) ratio. The lightest green color and the maximum chlorophyll content loss were observed for 23 kV applied over 10 minutes. Based on the results, the digital image processing can be used as a practical tool to study the variations at the color of dried Hyssop leaves after cold plasma treatment.     

Color prediction models for digital Jacquard woven fabrics

The current industry practice for producing jacquard fabrics uses computer‐aided design (CAD) systems that provide visual simulations of the final color appearance of actual fabrics prior to production. This digital process is fundamentally based on the prediction of combined weave‐color effects, which can be successfully achieved by accurate color mixing models and the structural details of the fabrics. With the accurate models used in CAD systems, designers would see simulations more closely resembling fabrics to be produced. By checking the previews, the designers can easily modify, that is, recolor, the designs on the display monitor without doing repetitive physical sampling with the adjustment of the weaves and the yarn colors. However, there is no ready applicable accurate color mixing model for woven structures and there has not been sufficient investigation of the color prediction despite its usefulness for the current digital CAD process. Our study investigated the, color prediction of jacquard woven fabrics designed based on the principle of optically subtractive color mixing with the use of CMY colors. The color prediction was firstly done through the application of the six color mixing models previously developed for various other applications including fiber blending and printing. The performance of each model was evaluated by calculating the difference between the predicted and the measured colorimetric data, using ΔE_CMC(2:1). The average color difference from the models was 11.93 ΔE_CMC(2:1), which is hardly acceptable in textile industry. In order to increase the accuracy in color prediction, the six models were then optimized. As a result, substantial improvements for all models were obtained with a decrease in color difference to 4.83 ΔE_CMC(2:1) on average after the optimizations. Among the six optimized color mixing models, the optimized Warburton‐Oliver model, that is, W‐O model, was found to have the lowest average ΔE_CMC(2:1) value of approximately equaling to 2, which is considered potentially useful to be applied to the current digital fabric color prediction. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 64–71, 2016     

New deviate observer (JF‐DO) obtained from experimental color‐matching functions for small fields of real observers

The CIE established the Standard Deviate Observer (SDO) CIE 1989 for fields of 10°, enabling the evaluation of discrepancies caused by the variability among these observers. This observer could also be applied to smaller fields, depending on the physiological causes of this variability in color‐matching functions (cmf's) among observers. Here, we have obtained a new Deviate Observer (which we call JF‐DO) established from the cmf's for small fields (2°) corresponding to two groups of real observers: JAM, MM and CF; AY, JR, MR, JL, JA and FA. Both groups of cmf's were measured experimentally in our laboratories using one for each of the different experimental methods and devices. All the new cmf's of the 9 real observers were referred to a new, unique system of unreal primaries, which we call X′Y′Z′ (derived in a way similar to that of the CIE 1931 XYZ system of unreal primaries). To establish a new JF‐DO for small fields, we followed a procedure similar to the one used by the CIE to establish the CIE 1989 SDO. A comparative study was also made between the cmf's of the CIE 1989 SDO (established for fields of 10°), the SDO from Stiles‐Burch (which we call Poza‐SDO, developed for small fields), and our JF‐DO. For this comparison, the cmf's of all these deviate observers were referred to the new system of unreal primaries X′Y′Z′. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 209–215, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10146     

Influence of a holistic color interval on color harmony

This study investigates how a holistic color interval, i.e., the nondirectional color difference between a pair of colors in a CIELAB uniform color space, influences perceived color harmony. A set of 1035 test color pairs displayed on a CRT was evaluated for the degree of harmony. These test color pairs consist of pairs combined from among the selected 46 test colors evenly distributed in color space. The subjects were asked to select their three preferred colors from these 46 test colors and then to evaluate the degree of harmony of the test color combinations. The color intervals (ΔE) of each test color combination were calculated and treated as values of an independent variable. In addition, the evaluated degrees of color harmony were considered as values of a dependent variable, in which statistical analysis confirmed the relationship: the degree of harmony is a cubic function of the color interval. Moreover, the plot of this relationship allowed us to identify four color intervals: roughly corresponding to the regions of first ambiguity, similarity, second ambiguity, and contrast in Moon and Spencer's model. However, our results indicated that Moon and Spencer's principles for classifying harmonious/disharmonious regions in terms of the color interval for three color attributes—lightness, chroma and hue—may be inappropriate in predicting perceived color harmony. As for the color intervals between a pair of colors considered as a function of the three attributes, the interval for lightness may have a predominant effect on color harmony, expressed in terms of a cubic relationship. Results of the study further demonstrated that the subject's choice of colors significantly influences perceived color harmony. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 29–39, 2001     

Establishment of a color tolerance for yarn-dyed fabrics from different color-depth yarns

Yarn-dyed fabric is often woven from warp and weft yarns in the same color depth to ensure a uniform color appearance. The difference in color depth between warp and weft tends to result in the uneven color of the yarn-dyed fabric. This article aims to establish a color tolerance for yarn-dyed fabric that can be woven with a qualified color appearance but from the warp and weft yarns in different color depths. A total of 27 yarn-dyed fabric samples in three color series (red, yellow, and blue) were evaluated by using the yarn-dyed fabric from warp and weft yarns in the same color depth of 2% (on weight of fabric, owf) as the standard. Visual assessment and instrumental measurement of color were carried out to establish the color tolerance ellipse that was defined as CMC (Color Measurement Committee) color differences (2:1) of no more than 1.00. It was found that the color strengths (K/S) and color differences (ΔE_CMC(2:1)) of these fabric samples for each color series had linear relationships with the color depths of warp and weft yarns. The color tolerance ellipses indicated that, even though the warp and weft yarns had an apparent color difference, they could be woven in fabrics with relatively uniform color appearance and meet the requirements for yarn-dyed fabric. This work provided valuable insight into the production of qualified yarn-dyed fabrics from unqualified dyed yarns.     

Monitoring of degradation of porous silicon photonic crystals using digital photography

We report the monitoring of porous silicon (pSi) degradation in aqueous solutions using a consumer-grade digital camera. To facilitate optical monitoring, the pSi samples were prepared as one-dimensional photonic crystals (rugate filters) by electrochemical etching of highly doped p-type Si wafers using a periodic etch waveform. Two pSi formulations, representing chemistries relevant for self-reporting drug delivery applications, were tested: freshly etched pSi (fpSi) and fpSi coated with the biodegradable polymer chitosan (pSi-ch). Accelerated degradation of the samples in an ethanol-containing pH 10 aqueous basic buffer was monitored in situ by digital imaging with a consumer-grade digital camera with simultaneous optical reflectance spectrophotometric point measurements. As the nanostructured porous silicon matrix dissolved, a hypsochromic shift in the wavelength of the rugate reflectance peak resulted in visible color changes from red to green. While the H coordinate in the hue, saturation, and value (HSV) color space calculated using the as-acquired photographs was a good monitor of degradation at short times (t < 100 min), it was not a useful monitor of sample degradation at longer times since it was influenced by reflections of the broad spectral output of the lamp as well as from the narrow rugate reflectance band. A monotonic relationship was observed between the wavelength of the rugate reflectance peak and an H parameter value calculated from the average red-green-blue (RGB) values of each image by first independently normalizing each channel (R, G, and B) using their maximum and minimum value over the time course of the degradation process. Spectrophotometric measurements and digital image analysis using this H parameter gave consistent relative stabilities of the samples as fpSi > pSi-ch.