Color Matching Functions Research Articles

54.1: Color Prediction in an LCD using RGB‐LED Backlights

AbstractThe CIE standard color matching function is used in the description of color characteristics for stimuli reproduced on displays given that these represent visual sensitivity accurately. If this is not the case, the consequent estimation using the functions would be deviated from what we perceive. This study demonstrates the significant errors caused by applying the current standard color matching function for predicting visual results of color stimuli displayed on an LCD monitor equipped with RGB‐LED backlights. The modified version of the standard color matching function is also introduced with its verification results in the reduction of prediction errors.

Automated Design, Fabrication, and Characterization of Color Matching Plasmonic Filters

Plasmonic filters, with spectral responses matching the 1931 International Commission on Illumination (CIE) color matching functions, have been fabricated for use in digital imaging. The color matching filters are useful for effectively communicating color between color detection and output devices. A fully automated genetic algorithm that incorporated on-demand 3-D finite-difference time-domain simulations determined the dimensions for the red (600 nm), green (555 nm), and blue (445 nm) filters. The filters demonstrated resonances in the desired spectra with transmission of 25%-35%. These filters were simultaneously fabricated in a single electron beam lithography cycle using materials common to standard complementary metal-oxide-semiconductor production.

Helical structure of complementary colors' relative spectral distribution function

I report a curious double helix in psychophysical data. As recently reported, color complementarism structures at least 40 functional roles in vision including all Red-, Green-, Blue-peaked functions (e.g., color matching functions, Helmholtz–Kohlrausch effect, saturation discrimination, lightness discrimination, and wavelength discrimination). These can be modeled from the relative spectral power distribution (SPD) function of complementary colors (at requisite power ratios to neutralize complements). So, the SPDs three-dimensional (3D) structure is of interest. Extended to the hue cycle, the SPD is plotted in a rectilinear graph of wavelength versus wavelength with radiance vertical to the plane. In this rectilinear color mixture space, the white locus representing the illuminant chromaticity is not a single point (representing the junction of complementary pairs of wavelengths) but a sinusoidal curve whose 3D structure is a double helix, representing an SPD and its complementary SPD. The structure's purpose is possibly to store and access global complementary colors data across illuminants. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 292–296, 2013

Tristimulus colorimeter calibration matrix uncertainties

Measurement uncertainties are propagated through the matrix calibration of a tristimulus colorimeter. It is shown that reference spectral uncertainties and the colorimeter signal uncertainties during calibration are simply scaled and combined in an applied measurement. Modeling shows that transforming x, y chromaticity and Y luminance can lead to lower chromaticity uncertainties than transforming X, Y, Z tristimulus signals themselves. Accuracy depends on the set of colours used for calibration, especially for measurements of displays. Uncertainties can be large and dominate errors due to accuracy of spectral matching to the CIE colour-matching functions. This is particularly true if commision international de L'Eclariage (CIE) Lab values are to be derived. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 251–258, 2013

Individual differences in human colour vision as derived from stiles & Burch 10° colour matching functions

Individual differences between the 49 Stiles & Burch observers have been analyzed using the object-colour space put forth recently (J of Vision 2009;9:1–23). A set of rectangular reflectance spectra has been used as a common frame of reference for representing object colours for all the observers. Being metameric to one of these rectangular reflectance spectra, every reflectance spectrum can be geometrically represented as a point in the three-dimentional space. The interindividual differences reveal themselves in that, for various observers, the same reflectance spectrum maps to different points in this space. It has been found that on average such differences do not exceed the differences in object-colour appearance induced by an illumination shift from daylight to the fluorescent daylight simulator F1. Such small individual variations have been accounted for by the fact that the cone spectral tuning curves have a special form that mitigates the individual differences in cone spectral positioning. © 2012 Wiley Periodicals, Inc. Col Res Appl, 2013

Vectorial color

AbstractA set of orthonormal color matching functions is developed, in which the first is an all‐positive achromatic function, the second is red–green, and the third can be loosely described as blue–yellow. The achromatic function, proportional to the familiar $ \bar y $, is a sum of red and green cones. The red–green function uses the same cone sensitivities, but subtracted, with coefficients so that it is orthogonal to the achromatic one. The third function involves all three cones, but is primarily a blue sensitivity. Using this basis to compute the tristimulus vectors of narrow‐band lights at unit power gives Jozef Cohen's locus of unit monochromats, (LUM) an invariant shape now graphed in a space where the axes have intuitive meaning. The extreme points of the LUM reveal the wavelengths that act most strongly in mixtures, a close approximation to William Thornton's Prime Colors. In effect, decades of research converge in three functions and a vectorial schema, demystifying such issues as color rendering and the selection of additive primaries. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011.

Applications of vectorial color

AbstractA companion article introduced a set of orthonormal opponent color matching functions (CMFs). That “orthonormal basis” is an expedient for plotting lights in Cohen's logical color space. Indeed, graphing the new CMFs together (as a parametric plot) gives Cohen's invariant locus of unit monochromats (LUM). In this article, the functions and related vector methods are applied to fundamental problems. In signal transmission and propagation‐of‐errors work, it is desirable to describe stimuli by decorrelated components. The orthonormal CMFs inherently do this, and an example is worked out using a large set of color chips. Starting with the orthonormal functions, related functions, such as cone sensitivities, are graphed as directions in color space, showing their intrinsic relationships. Building on work of Tominaga et al., vectorial plots are related to the problem of guessing the illuminant, a step toward a constancy method. The issue of color rendering is clarified when the vectorial compositions of test and reference lights are graphed. A single graph shows the constraint that the total vectors are the same, but also shows the differences in colorimetric terms. Since the LUM summarizes a trichromatic system by a three‐dimensional graph, dichromatic observers can be represented by 2‐D graphs, revealing details in a consistent way. The “fit first method” compares camera with human, applying the Maxwell‐Ives criterion in graphical detail. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011.

A Constrained Band Selection Method Based on Information Measures for Spectral Image Color Visualization

We present a new method for the visualization of spectral images, based on a selection of three relevant spectral channels to build a red–green–blue composite. Band selection is achieved by means of information measures at the first, second, and third orders. Irrelevant channels are preliminarily removed by means of a center-surround entropy comparison. A visualization-oriented spectrum segmentation based on the use of color matching functions allows for computational ease and adjustment of the natural rendering. Results from the proposed method are presented and objectively compared to four other dimensionality reduction techniques in terms of naturalness and informative content.

Color of TiN and ZrN from first-principles calculations

The optical properties, especially the colors, of transition metal nitrides (TiN and ZrN) are studied using first-principles method. Full ab-initio procedure of color-prediction including plasma frequency is presented. The dielectric functions and reflectivity of the compounds are calculated including both intraband and interband transitions. The color of the compounds is then produced by calculating the red-green-blue color codes through the convolution of color matching functions and the calculated reflectivity. Calculated colors and screened plasma frequency for the materials are in good agreement with measurement. The color variation due to chemical doping is also studied within the rigid band approximation.

From CIE 2006 physiological model to improved age-dependent and average colorimetric observers

In the context of color perception on modern wide-gamut displays with narrowband spectral primaries, we performed a theoretical analysis on various aspects of physiological observers proposed by CIE TC 1-36 (CIEPO06). We allowed certain physiological factors to vary, which was not considered in the CIEPO06 framework. For example, we analyzed that the long-wave-sensitive (LWS) or medium-wave-sensitive (MWS) peak wavelength shift in the photopigment absorption spectra, a factor not modeled in CIEPO06, contributed more toward observer variability than some of the factors considered in the model. Further, we compared the color-matching functions derived from the CIEPO06 model and the CIE 10° standard colorimetric observer to the average observer data from three distinct subgroups of Stiles-Burch observers, formed on the basis of observer ages (22-23 years, 27-29 years, and 49-50 years). The errors in predicting the x(λ) and y(λ) color-matching functions of the intragroup average observers in the long-wave range and in the medium-wave range, respectively, were generally more in the case of the CIEPO06 model compared to the 10° standard colorimetric observer and manifested in both spectral and chromaticity space. In contrast, the short-wave-sensitive z₁₀(λ) function of the 10° standard colorimetric observer performed poorly compared to the CIEPO06 model for all three subgroups. Finally, a constrained nonlinear optimization on the CIEPO06 model outputs showed that a peak wavelength shift of photopigment density alone could not improve the model prediction errors at higher wavelengths. As an alternative, two optimized weighting functions for each of the LWS and MWS cone photopigment densities led to significant improvement in the prediction of intra-age-group average data for both the 22-23 year and 49-50 year age groups. We hypothesize that the assumption in the CIEPO06 model that the peak optical density of visual pigments does not vary with age is false and is the source of these prediction errors at higher wavelengths. Correcting these errors in the model can lead to an improved age-dependent observer and can also help update the current CIE 10° standard colorimetric observer. Accordingly, it would reduce the discrepancies between color matches with broadband spectral primaries and color matches with narrowband spectral primaries.

Enhanced Visualization of Hyperspectral Images

We present an enhanced visualization algorithm for hyperspectral images (HSIs). The visualization is based on the projection onto color matching functions of the human vision system. A contrast enhancement procedure is introduced by the fusion of the gradient information of the individual HSI bands. Both visualization and enhancement are combined into a multiresolution framework using wavelets. The HSI is transformed into a specific representation (HSI wavelet representation), in which the enhancement is performed at the level of the wavelet detail subbands, whereas the visualization is performed at the level of the low-resolution subbands. Specific objective quality measures are applied to demonstrate that the proposed procedure provides visualization results with a high contrast. Results are compared with state-of-the-art HSI visualization techniques and with the postprocessing enhancement.

Mathematical approach for predicting non-negative tristimulus values using the CAT02 chromatic adaptation transform

It has been reported that for certain colour samples, the chromatic adaptation transform CAT02 imbedded in the CIECAM02 colour appearance model predicts corresponding colours with negative tristimulus values (TSVs), which can cause problems in certain applications. To overcome this problem, a mathematical approach is proposed for modifying CAT02. This approach combines a non-negativity constraint for the TSVs of corresponding colours with the minimization of the colour differences between those values for the corresponding colours obtained by visual observations and the TSVs of the corresponding colours predicted by the model, which is a constrained non-linear optimization problem. By solving the non-linear optimization problem, a new matrix is found. The performance of the CAT02 transform with various matrices including the original CAT02 matrix, and the new matrix are tested using visual datasets and the optimum colours. Test results show that the CAT02 with the new matrix predicted corresponding colours without negative TSVs for all optimum colours and the colour matching functions of the two CIE standard observers under the test illuminants considered. However, the accuracy with the new matrix for predicting the visual data is approximately 1 CIELAB colour difference unit worse compared with the original CAT02. This indicates that accuracy has to be sacrificed to achieve the non-negativity constraint for the TSVs of the corresponding colours. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2011

Analyzing small suprathreshold differences of LCD-generated colors

Small suprathreshold color differences around five CIE color centers were investigated on a typical liquid crystal display (LCD) with fluorescent backlight using the method of constant stimuli. The results were evaluated using probit analysis and compared with surface-color differences of the RIT-DuPont dataset. We focused especially on the relationship between T50 distances obtained from LCD and surface-color stimuli and on the influence of the display's narrowband primaries and its relatively low luminance level on interobserver uncertainty. The low luminance level of the LCD decreases the perceived color differences. However, considering the visual uncertainty of the experimental data, we could not reject the hypothesis that T50 distances from the RIT-DuPont and our experiment agree up to a constant scaling factor. In addition, we found significantly higher interobserver variability in the estimation of small color differences if the colors are viewed on an LCD. There are some indications that color-difference perception might be influenced by individual color-matching functions and, thus, by the spectral power distribution of the stimuli. We provide the experimental data, including all spectral stimuli shown to the observers, on our website.

Transmission of colour and acuity signals by parvocellular cells in marmoset monkeys

The red-green axis of colour vision evolved recently in primate evolutionary history. Signals serving red-green colour vision travel together with signals serving spatial vision, in the parvocellular (PC) division of the subcortical visual pathway. However, the question of whether receptive fields of PC pathway cells are specialized to transmit red-green colour signals remains unresolved. We addressed this question in single-cell recordings from the lateral geniculate nucleus of anaesthetized marmosets. Marmosets show a high proportion of dichromatic (red-green colour-blind) individuals, allowing spatial and colour tuning properties of PC cells to be directly compared in dichromatic and trichromatic visual systems. We measured spatial frequency tuning for sine gratings that provided selective stimulation of individual photoreceptor types. We found that in trichromatic marmosets, the foveal visual field representation is dominated by red-green colour-selective PC cells. Colour selectivity of PC cells is reduced at greater eccentricities, but cone inputs to centre and surround are biased to create more selectivity than predicted by a purely 'random wiring' model. Thus, one-to-one connections in the fovea are sufficient, but not necessary, to create colour-selective responses. The distribution of spatial tuning properties for achromatic stimuli shows almost complete overlap between PC cells recorded in dichromatic and trichromatic marmosets. These data indicate that transmission of red-green colour signals has been enabled by centre-surround receptive fields of PC cells, and has not altered the capacity of PC cells to serve high-acuity vision at high stimulus contrast.

Modeling Spectral Alteration and Color Vision Performance

Laser Eye Protection (LEP) devices selectively alter the spectral environment and affect the ability to identify and discriminate color. Pilots and mariners must wear LEP for their safety and still make decisions based on colored lights and objects. These abilities can be compromised with LEP. Determining the level of degradation caused by LEP remains challenging; LEP devices are not uniform in construction and results from laboratory tests may be poor indicators of actual user performance. In addition, performance deficits in the maritime and aviation environment can be exacerbated by cognitive distracters. However there is little known about the interaction of attentional effects with color performance deficits from the use of LEP. Several different mathematical models of color vision were utilized to model and predict color vision performance. Spectral reflectance or transmission was measured and placed into equations utilizing color matching functions of the standard observer. These values were then translated into different color spaces. These results were compared with actual performance. Results for modeling indicate that models that take into account color zone shifts, rather than color shifts are more accurate, and that models cannot yet account for all aspects of color vision performance such as when cognitively distracted.

Lossless and lossy coding for multispectral image based on sRGB standard and residual components

In this paper, we present a multispectral image (MSI) compression method using a lossless and lossy coding scheme, which focuses on the seamless coding of the RGB bit stream to enhance the usability of the MSI. The proposed method divides the MSI data into two components: RGB and residual. The RGB component is extracted from the MSI by using the XYZ color matching functions, a color conversion matrix, and a gamma curve. The original MSI is estimated by an RGB data encoder and the difference between the original and the estimated MSI, which is referred to as the residual component in this paper. Next, the RGB and residual components are encoded by using JPEG2000, and progressive decoding is achieved from the losslessly encoded code stream. Experimental results show that a high-quality RGB image can be obtained at a low bit rate with primary encoding of the RGB component. In addition, by using the proposed method, the quality of a spectrum can be improved by decoding the residual data, and the quality is comparable to that obtained by using JPEG2000. The lossless compression ratio obtained by using this method is also similar to that obtained by using JPEG2000 with the integer Karhunen-Loeve transform.

A Novel Method for Representation of Spectral Images Based on Color Matching Functions

Spectral images contain a large volume of data and the development of multispectral imaging systems places considerable demands on computer hardware and software compared with standard three-component or trichromatic image storage and processing. This study is concerned with lossy compression techniques for spectral images since many color images are intended for display for human perception and it is well established that images contain redundancies (in terms of their color, spatial and temporal properties) that can be removed without any loss in image quality. The lossy compression technique that is considered in this work is a low-dimensional linear model of spectral reflectance, with which the basis function are derived from color matching functions that are correlated with human visual system.

Confocal mosaicing microscopy of human skin ex vivo: spectral analysis for digital staining to simulate histology-like appearance

Confocal mosaicing microscopy enables rapid imaging of large areas of fresh tissue, without the processing that is necessary for conventional histology. Mosaicing may offer a means to perform rapid histology at the bedside. A possible barrier toward clinical acceptance is that the mosaics are based on a single mode of grayscale contrast and appear black and white, whereas histology is based on two stains (hematoxylin for nuclei, eosin for cellular cytoplasm and dermis) and appears purple and pink. Toward addressing this barrier, we report advances in digital staining: fluorescence mosaics that show only nuclei, are digitally stained purple and overlaid on reflectance mosaics, which show only cellular cytoplasm and dermis, and are digitally stained pink. With digital staining, the appearance of confocal mosaics mimics the appearance of histology. Using multispectral analysis and color matching functions, red, green, and blue (RGB) components of hematoxylin and eosin stains in tissue were determined. The resulting RGB components were then applied in a linear algorithm to transform fluorescence and reflectance contrast in confocal mosaics to the absorbance contrast seen in pathology. Optimization of staining with acridine orange showed improved quality of digitally stained mosaics, with good correlation to the corresponding histology.

(How) Do Observer Categories Based on Color Matching Functions Affect the Perception of Small Color Differences?

(How) Do Observer Categories Based on Color Matching Functions Affect the Perception of Small Color Differences?

Measurement of color matching functions with a compact and simple apparatus using LEDs

Measurement of color matching functions with a compact and simple apparatus using LEDs