Spectral radiance reconstruction from trichromatic camera responses based on orthogonal test and regularized algorithm

Reconstruction of spectral information based on multi‐channel image system is a significant problem in color reproduction, detection, and recognition. A spectral radiance reconstruction from trichromatic digital camera responses is researched in this article. The mapping relationship between the trichromatic imaging system response and the incident spectral radiance is analyzed. Then, in order to remove the ill‐posedness of the problem, a regularized constraint solution model of spectral radiance reconstruction matrix is established. And the spectral radiance can be reconstructed by spectral radiance reconstruction matrices and trichromatic imaging system response. Finally, the spectral radiance reconstruction matrix is estimated by the system radiometric calibration experiment. The input radiance is offered by a LCD display. A 3‐factor and 9‐level orthogonal test is designed for the calibration experiment, and a test set of 24 colors is used for precision analysis. The results show that the average relative mean error of our method is 8.69%, it is lower than that of Wiener filtering method by 2.84%. The method can reconstruct spectral radiance information effectively.     

Dictionary‐based estimation of spectra for wide‐gamut color imaging

With the widespread use of commercialized wide‐gamut displays, the demand for wide‐gamut image content is increasing. To acquire wide‐gamut image content using camera systems, color information should be accurately reconstructed from recorded image signals for a wide range of colors. However, it is difficult to obtain color information accurately, especially for saturated colors, if conventional color cameras are used. Spectrum‐based color image reproduction can solve this problem; however, bulky spectral imaging systems are required for this purpose. To acquire spectral images more conveniently, a new spectral imaging scheme has been proposed that uses two types of data: high spatial‐resolution red, green, and blue (RGB) images and low spatial‐resolution spectral data measured from the same scene. Although this method estimates spectral images with high overall accuracy, the error becomes relatively large when multiple different colors, especially those with high saturation, are arranged in a small region. The main reason for this error is that the spectral data are utilized as low‐order spectral statistics of local spectra in this method. To solve this problem, in this study, a nonlinear estimation method based on sparse and redundant dictionaries was used for spectral image estimation—where the dictionary contains a number of spectra—without loss of information from the low spatial‐resolution spectral data. The estimated spectra are represented by a mixture of a few spectra included in the dictionary. Therefore, the respective feature of every spectrum is expected to be preserved in the estimation, and the color saturation is also preserved for any region. Experiments performed using the simulated data showed that the dictionary‐based estimation can be used to obtain saturated colors accurately, even when multiple colors are arranged in a small region. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2013     

An integrated spectral imaging system for producing color images of static and moving objects

An integrated spectral imaging system constructed by synchronizing a programmable light source, a high‐speed monochrome camera, and a display device is proposed to produce tristimulus images of static and moving objects effectively in real time onto the display. This system is called the CIE‐XYZ display. Active spectral illuminants, containing both the device characteristics of camera and display, are projected onto object surfaces as time sequence. The images are captured synchronously by the camera and quickly transmitted to the display device in the RGB signal form so that the accurate tristimulus images are displayed. First, we describe the principle of the CIE‐XYZ tristimulus display. The theoretically optimal illuminants contain negative parts in the spectral curves. Second, we design practical illuminants with all positive spectral curves. The color images in our system are composed of the time sequence of RGB component images. Then, the synthesized color images on the display contain color artifacts when objects move fast. An image processing algorithm for correcting the motion color artifact is proposed based on optical flow estimation using a graphics processing unit. The comprehensive performance of the proposed system and algorithms is examined using both static and moving objects. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 329–340, 2015     

Precise color capture using custom color targets

We have developed a procedure to achieve a high accuracy of color capture for digital still cameras for cultural heritage digitization. The procedure uses a standard color target and additional spectral measurements directly on the artwork. A set of complementary colors is determined thanks to an initial analysis of the digital image and a comparison with the standard color target. The developed procedure results in a digital copy that better represents the colors of the original than using only standard color targets.     

Recovering spectral data from natural scenes with an RGB digital camera and colored filters

Many spectral‐recovery methods using RGB digital cameras assume the underlying smoothness of illuminant and reflectance spectra, and apply low‐dimensional linear models. The aim of the present work was to test whether a direct‐mapping method could be used instead of a linear‐models approach to recover spectral radiances and reflectances from natural scenes with an RGB digital camera and colored filters. In computer simulations, a conventional RGB digital camera with up to three colored filters was used to image scenes drawn from a hyperspectral image database. Three measures were used to evaluate recovery with the direct‐mapping method: goodness‐of‐fit, root‐mean‐square error, and a color‐difference metric. It was found that with two and three filters both spectral radiances and reflectances could be recovered sufficiently accurately for many practical applications. With little increase in computational complexity, an RGB camera and a few colored filters can provide significantly better recovery of natural scenes than an RGB camera alone. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 352–360, 2007     

Recovering spectral reflectance based on natural neighbor interpolation with model‐based metameric spectra of extreme points

In this article, we proposed a new method based on natural neighbor interpolation to recover the spectral reflectance of objects from an image captured by a traditional Red‐Green‐Blue (RGB) digital camera. The concept of model‐based metameric spectra of eight extreme points in the standard RGB (sRGB) color gamut was further introduced to ensure that almost all test samples in the entire gamut can be simply and properly recovered without needing the extrapolation or any other auxiliary techniques. The quasi‐Newton method was used to estimate iteratively the optimal parameters of these metameric spectra, satisfying the constraints of the gamut extreme points. Several experiments were performed. The effectiveness of the method with and without the metameric spectra was evaluated, including some performance comparisons with the principal component analysis (PCA) method of transformational type (classic PCA and weighted PCA) and that of interpolation type. The results showed that the proposed method greatly enlarged the accurately applicable domain of the interpolation strategy and offered spectra with feasibility and naturalness much superior to the PCA‐based methods. The proposed method was obviously better than the conventional interpolation ones, and had a similar performance with the weighted PCA method in terms of color difference.     

Particle surface temperature measurements with multicolor band pyrometry

A noncontact, color‐band pyrometer, based on widely available, inexpensive digital imaging devices, such as commercial color cameras, and capable of pixel‐by‐pixel resolution of particle‐surface temperature and emissivity is demonstrated and described. This diagnostic instrument is ideally suited to many combustion environments. The devices used in this method include color charge‐coupled device (CCD), or complementary metal oxide semiconductor (CMOS) digital camera, or any other color‐rendering camera. The color camera provides spectrally resolved light intensity data of the image, most commonly for three color bands (Red, Green, and Blue,), but in some cases for four or more bands or for a different set of colors. The CCD or CMOS sensor‐mask combination has a specific spectral response curve for each of these color bands that spans the visible and often near infrared spectral range. A theory is developed, based on radiative heat transfer and camera responsivity that allows quantitative surface temperature distribution calculation, based on a photograph of an object in emitted light. Particle surface temperature calculation is corrected by heat transfer analysis with reflection between the particle and reactor wall for particles located in furnace environments, but such corrections lead to useful results only when the particle temperature is near or below the wall temperatures. Wood particle‐surface temperatures were measured with this color‐band pyrometry during pyrolysis and combustion processes, which agree well with thermocouple measured data. Particle‐surface temperature data simultaneously measured from three orthogonal directions were also mapped onto the surface of a computer generated 3‐D (three‐dimensional) particle model. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Estimating black‐level emissions of computer‐controlled displays

It is quite common for computer‐controlled displays to emit light in image areas set to digital values of zero, referred to as their black level. This is expected for liquid–crystal displays and also can occur for cathode‐ray tube displays when the “brightness” (gun‐amplifier offset) is set excessively high. For either display, the light emission at the black level results in color channels whose chromaticities vary with luminance level. Consequently, typical methods of colorimetric characterization result in large error. When this black‐level emission is measured and accounted for suitably, characterization accuracy is dramatically improved. Unfortunately, many instruments used to measure displays have too low a sensitivity to measure black‐level emission with sufficient precision and accuracy. A method of estimating black‐level emissions was derived and tested. Because the optimal black‐level results in channel chromaticities that are invariant to the greatest extent with luminance level, an objective function was defined as the sum of chromaticity variances of each channel over a range of measurements. Minimizing this objective function resulted is an estimate of a display's black level. The estimated black level resulted in equivalent or superior performance to direct measurements. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 379–383, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10181     

Colour‐imager characterization by parametric fitting of sensor responses

This study describes a novel method for characterizing the colorimetric and photometric properties of three‐channel color imaging devices. The method is designed to overcome some undocumented aspects of the imager‐characterization problem: The effective spectral sensitivity profiles of the imager's color channels depend on the level of radiant input energy, and these profiles must be known in order to determine the true intensity‐response characteristics of the three channels. By fitting the response distributions of the three color channels explicitly with low‐dimensional models, the method takes these dependencies into account, and may, therefore, offer several advantages over other imager‐characterization methodologies, particularly where illuminant‐independent characterization is required. An application of the technique is detailed, in which a CCD camera is characterized using only the Macbeth ColorChecker and a number of artificial illuminants. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 442–449, 2001     

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     

Assessing the performance of a spectral reflectance estimation method based on a diffraction grating and a spectroradiometer

Constant improvements in digital cameras have made it possible to use these devices for colour acquisition and reproduction at an advanced level. It is known that a colour match for all observers when changing illumination can only be achieved by matching spectral data. Obtaining spectral data from digital camera RGB values could provide a new way of using the digital camera as a spectrophotometric tool or as a high‐quality colour‐capturing system that is required in more demanding applications. In the present study, two spectral reflectance estimation methods were examined – the Imai–Berns method (ImaiBerns) and the spectral‐sensitivity‐based method (SpecSens). The purpose of the research was to simplify the procedure of the SpecSens method by using a diffraction grating and a spectroradiometer instead of a monochromator, and to compare the results with those of the ImaiBerns approach. Obtained spectral reflectance estimates were evaluated using the root‐mean‐square error and ?E₀₀ metrics. Results of the research show that the ImaiBerns method was superior to SpecSens, most likely because the former method does not require knowledge of the camera spectral sensitivities, which often introduces errors into reflectance estimation calculations. Both methods were successful in predicting black, brownish, and dark patches, as indicated by a low root‐mean‐square error, as well as unsaturated pastel, pink, or skin colours, which produced low ?E₀₀ values. On the other hand, many of the patches with a low root‐mean‐square error also exhibited high ?E₀₀ values, while bright, nearly‐white patches were characterised by a high root‐mean‐square error.     

Image‐based spectral reflectance reconstruction using the matrix R method

The ultimate goal of spectral imaging is to achieve high spectral accuracy, so that the spectral information can be used to calculate colorimetrically accurate images for any combination of illuminant and observer. A new spectral reconstruction method, called the matrix R method, was developed to reconstruct spectral reflectance factor accurately while simultaneously achieving high colorimetric performance for a defined illuminant and observer. The method combines the benefits of both colorimetric and spectral transformations. Tristimulus values were predicted by a colorimetric transformation from multi‐channel camera signals, while spectral reflectance factor was estimated by a spectral transformation from the same signals. The method reconstructed reflectance factor by combining the fundamental stimulus from the predicted tristimulus values with the metameric black from the estimated spectral reflectance, based on the Wyszecki hypothesis. The experimental results verified the new method as a promising technique for building a spectral image database. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 343–351, 2007     

Spectral‐reflectance‐factor deconvolution and colorimetric calculations by local‐power expansion

The experimental data of the spectral‐reflectance factor are considered as dependent on the instrument‐spectral‐bandwidth function in order to perform their deconvolution and to compute the tristimulus values. The deconvolution is performed by local‐power expansion. In the case that the spectral‐bandpass dependence regards only the spectral transmittance of the monochromator, the goodness of this technique is evaluated by simulation (1325 reflectance factors of the Munsell samples are considered as trial functions) and compared with other usual techniques: Stearns and Stearns method for bandpass error, ASTM‐weighting function interpolation, and Venable‐ASTM weighting function. The zero order of the deconvoluted spectral‐reflectance factor can be related to the Stearns and Stearns method for bandpass error. With respect to any other technique, the second‐order deconvolution, for the CIE standard illuminants, gives color differences lower by a factor 0.1 or more for a bandpass Δλ = 10 nm, color differences lower by a factor 0.3 or more for a bandpass Δλ = 20 nm and, for the CIE fluorescent illuminants, color differences generally lower. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 176–185, 2000     

Physics‐based spectral sharpening through filter‐chart calibration

The spectral overlap of color‐sampling filters increases errors when using a diagonal matrix transform, for color correction and reduces color distinction. Spectral sharpening is a transformation of colors that was introduced to reduce color‐constancy errors when the colors are collected through spectrally overlapping filters. The earlier color‐constancy methods improved color precision when the illuminant color is changed, but they overlooked the color distinction. In this article, we introduce a new spectral sharpening technique that has a good compromise of color precision and distinction, based on real physical constraints. The spectral overlap is measured through observing a gray reference chart with a set of real and spectrally disjoint filters selected by the user. The new sharpening method enables to sharpen colors obtained by a sensor without knowing the camera response functions. Experiments with real images showed that the colors sharpened by the new method have good levels of color precision and distinction as well. The color‐constancy performance is compared with the data‐based sharpening method in terms of both precision and distinction. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 564–576, 2015     

The optimal number of sensors for a digital imaging system from the perspective of metamer mismatching

Metamer mismatching occurs in both the human visual system and digital imaging systems. Increasing the number of sensors in digital imaging systems is an efficient method to reduce the degree of metamer mismatching. This study investigates the number of sensors that are needed for the digital imaging systems to have a similar ability to the human sensor system in distinguishing colors from the perspective of metamer mismatching. Optimal spectral reflectance was generated, and a dataset with more than 47 million previously collected practical spectral reflectance functions was used to derive the metameric color pairs. Different sets of Gaussian-shaped functions were designed to model the spectral sensitivity functions of the digital imaging systems. Both the metamer mismatching volumes and color differences were used to characterize the degree of metamer mismatching for pairs of samples, which were metameric to the imaging systems but appeared different to the human sensor system. The results show that the practical metamer mismatching volumes are substantially smaller than the theoretical ones. The results also show that both the metamer mismatching volumes and color differences are significantly reduced by increasing the number of sensors from three to five for the digital imaging system but are only slightly reduced by further increasing the number of sensors from five to seven. This indicates that five sensors is an efficient and optimal solution for an imaging system with Gaussian-shaped sensors to have a similar ability in distinguishing colors compared to the human sensor system.     

Applying metamer sets to investigate data dependency of principal component analysis method in recovery of spectral data

Principal component analysis (PCA) has been widely studied for reconstruction of spectral reflectance of a color sample from its tristimulus values. One of the most important factors that influences the recovery performance is the characteristic of the data set used for obtaining principal vectors. In this article, we investigated the influence of color similarities or color differences between the recovered and principal component (PC) data sets on the reconstruction error. For this purpose, two metamer sets that have similar color differences with the recovered samples, are used. The results show that two metamer sets can make completely different performance in recovery of specific color samples. It was shown that the most important factor that influences the recovery of spectral reflectance by PCA method is the characteristics of the data set used for obtaining PC vectors independent of the recovered samples. Another factor that influences the performance of PCA for spectral recovery is the characteristic of the sample that would be recovered. Some spectral data cannot be recovered precisely even applying different PC data sets. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

Spectral color reproduction minimizing spectral and perceptual color differences

In this article, we are combining minimization criteria in the colorant separation process for spectral color reproduction. The colorant separation is performed by inverting a spectral printer model: the spectral Yule‐Nielsen modified Neugebauer model. The inversion of the spectral printer model is an optimization operation in which a criterion is minimized at each iteration. The approach we proposed minimizes a criterion defined by the weighted sum of a spectral difference and a perceptual color difference. The weights can be tuned with a parameter α ∞ [0, 1]. Our goal is to decrease the spectral difference between the original data and its reproduction and also to consider perceptual color difference under different illuminant conditions. In order to find the best α value, we initially compare a pure colorimetric criterion and a pure spectral criterion for the reproduction, then we combine them. We perform four colorant separations: the first separation will minimize the 1976 CIELAB color difference where four illuminants are tested, the second separation will minimize an equally weighted summation of 1976 CIELAB color difference with the four illuminants tested independently, the third colorant separation will minimize a spectral difference, and the fourth colorant separation will combine a weighted sum of a spectral difference and one of the two first colorimetric differences previously introduced. This last colorant separation can be tuned with a parameter in order to emphasize on spectral or colorimetric difference. We use a six colorants printer with artificial inks for our experiments. The prints are simulated by the spectral Yule‐Nielsen modified Neugebauer model. Two groups of data are used for our experiments. The first group describes the data printed by our printing system, which is represented by a regular grid in colorant space of the printer and the second group describes the data which is not originally produced by our printing system but mapped to the spectral printer gamut. The Esser test chart and the Macbeth Color Checker test chart have been selected for the second group. Spectral gamut mapping of this data is carried out before performing colorant separation. Our results show improvement for the colorant separations combining a sum of 1976 CIELAB color difference for a set of illuminants and for the colorant separation combining a sum of 1976 CIELAB color difference and spectral difference, especially in the case of spectral data originally produced by the printer. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 494–504, 2008     

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 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.     

Evaluating the 1931 CIE color‐matching functions

The use of colorimetry within industry has grown extensively in the last few decades. Central to many of today's instruments is the CIE system, established in 1931. Many have questioned the validity of the assumptions made by Wright¹ and Guild,² some suggesting that the 1931 color‐matching functions are not the best representation of the human visual system's cone responses. A computational analysis was performed using metameric data to evaluate the CIE 1931 color‐matching functions as compared to with other responsivity functions. The underlying assumption was that an optimal set of responsivity functions would yield minimal color‐difference error between pairs of visually matched metamers. The difference of average color differences found in the six chosen sets of responsivity functions was small. The CIE 1931 2° color‐matching functions on average yielded the largest color difference, 4.56 ΔE. The best performance came from the CIE 1964 10° color‐matching functions, which yielded an average color difference of 4.02 ΔE. An optimization was then performed to derive a new set of color‐matching functions that were visually matched using metameric pairs of spectral data. If all pairs were to be optimized to globally minimize the average color difference, it is expected that this would produce an optimal set of responsivity functions. The optimum solution was to use a weighted combination of each set of responsivity functions. The optimized set, called the Shaw and Fairchild responsivity functions, was able to reduce the average color difference to 3.92 ΔE. In the final part of this study a computer‐based simulation of the color differences between the sets of responsivity functions was built. This simulation allowed a user to load a spectral radiance or a spectral reflectance data file and display the tristimulus match predicted by each of the seven sets of responsivity functions. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 316–329, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10077