Visualization of mathematical inconsistencies in CIECAM02

It has been reported that CIECAM02, the appearance model standardized by the CIE to be used for imaging applications, contains a number of mathematical inconsistencies. These shortcomings cannot be solved easily without changing the behavior of the model and hence a fundamental redesign seems to be needed. At the moment, the main problems with CIECAM02 are known, but there is no clear strategy yet to fix the model. To have an idea about the impact of the inconsistencies of the currently standardized CIECAM02 model and several proposed corrections, the shortcomings are visualized for a number of color/illuminant combinations. From this visualization, a practical and natural approach is obtained to adjust the model without changing the mathematics drastically. © 2011 Wiley Periodicals, Inc. Col Res Appl, 38, 188–195, 2013.     

Color appearance of afterimages compared to the chromatic adaptation to illumination

The color appearance of negative afterimages was measured by the elementary color naming method, and the results were compared with those obtained by the two‐room technique. Twenty adapting stimuli were presented on a display sequentially. Subjects first assessed the color appearance of the stimuli. After looking at the adapting stimulus for 10 seconds, the subjects assessed color of the afterimage. Apparent hue of the afterimage was in general not opponent color to the adapting color. The relation between the adapting stimuli and the afterimages was analyzed by the angle difference Δθ, when apparent hues are expressed by the angles of the points on the polar diagram of the opponent color theory. The relation relationship of Δθ to the angle of the adapting color θ_ing was quite similar to the results obtained by the two‐room technique, implying that the chromatic adaptation shown by the afterimage also occurs in the brain rather than in the retina.     

Irregularity in CIECAM02 and its avoidance

Were it not for an algorithm patch, the color‐appearance model CIECAM02 would sometimes be forced to evaluate fractional powers of negative numbers. The artifact arises because the red and green primaries of the initial CAT02 chromatic adaptation lie outside the positive gamut of the Hunt–Pointer–Estévez (HPE) primaries that subsequently convey the color signal in the model. Relocating the chromaticities of the HPE red and green primaries so as to lie on the CAT02 red–green line alleviates the problem, but adds a bit of X and Y to the revised HPE blue. An (x,y) diagram aids in visualizing the CIECAM02 gamut overlaps, with an extension that accommodates the HPE RGB triangle's enclosure of the point at infinity. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 142–145, 2006     

Comparing two‐step and one‐step chromatic adaptation transforms using the CAT16 model

Color‐appearance models, CIECAM02 and CAM16, usually include two one‐step chromatic adaptation transforms: a forward (one‐step) transform to convert data from a first illuminant to CIE illuminant E, plus a reverse (one‐step) transform to convert the results from CIE illuminant E to a second illuminant. In practice, however, one‐step chromatic adaptation models, that avoid the use of the intermediate CIE illuminant E, are also employed. Tests using the one‐step CAT16 model indicate failures of both the symmetry and transitivity properties, except in the case where the degree of adaptation D is equal to unity. The magnitude of these failures depends on the specific illuminants selected, and increases as the degree of adaptation decreases. From four possible two‐step CAT16 models, we have identified two that obey the symmetry and transitivity properties, one with slightly better predictions of the experimental corresponding‐color datasets available in the literature, and more consistent with the one‐step CAT16 model. The findings of this article confirm that, for incomplete adaptation, the use of the one‐step CAT is incorrect, and we propose that the use of a two‐step CAT16 model be mandatory for future applications.     

Repairing gamut problems in CIECAM02: A progress report

The color‐appearance model CIECAM02 has several problems, which can result in mathematical instabilities, due to the position of the chromatic‐adaptation primaries relative to the spectrum locus and to the presumed physiological cone primaries. To keep a corresponding (adapted) color within the positive gamut given by the chromatic adaptation primaries, the gamut must lie within the cone primary octant. To contain adapted colors within the positive cone‐primary octant, it suffices to truncate the action of adaptation at the boundary of that octant. Such modifications may be needed to avoid the mathematical problems in CIECAM02. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 424–426, 2008     

Further improvements to CIECAM97s

The modifications to the CIECAM97s color appearance model suggested by Fairchild⁵ are reviewed in light of some recent experimental results, and some suggestions are made for refining and extending these modifications. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 164–170, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10047     

Complementary colors: The structure of wavelength discrimination,uniform hue,spectral sensitivity,saturation, chromatic adaptation,and chromatic induction

Complementary colors have long been thought important to color vision due to their ability (as admixed pairs) to extinguish all chromaticity, and to adapt automatically (i.e., wavelength pairs and radiant power ratios) to illuminant. Their role in color mixture and chromatic induction is well documented but other roles have not been demonstrated. This article studies the structure of complementary colors in the wavelength and radiance dimensions over the hue cycle (the nonspectrals are represented by a nominal‐wavelength metric). In the wavelength dimension, the basic structure of complementary colors is the complementary intervals ratio (ratio of a wavelength interval to its complementary interval of 1 nm). The ratio has RGB peaks, complementary CMY troughs, and provides models of chromatic induction, wavelength discrimination, and uniform hue difference in good agreement with data. Novel analyses of six color order/UCS hue circles indicate essential characteristics of a uniform hue scale. In the radiance dimension, basic structure is the complementary powers ratio (power of a stimulus required to neutralize its complementary of 1 Watt). The inverse structure has RGB peaks, complementary CMY troughs, and provides models of saturation, spectral sensitivity, and chromatic adaptation to illuminant. The RGB peaks demonstrate spectral sharpening, implying a postreceptoral location in the physiology. The models indicate that complementary colors have a significant role in color appearance besides their well known role in color mixture. © 2009 Wiley Periodicals, Inc. Col Res Appl, 34, 233–252, 2009     

Prediction of simultaneous contrast between map colors with Hunt's model of color appearance

The objective of this research was development of a quantitative model of simultaneous contrast (induction) to aid selection of sets of easily identified map colors. The model is an extension of R. W. G. Hunt's model of color appearance. Contrasts between central and proximal colors were used to adjust Hunt's lightness, relative redness-greenness, and relative yellowness-blueness measures. Human subject responses to CRT displays in an experiment were analyzed to produce a set of rules for selecting map colors. Rather than predict average perceptions for central/proximal color combinations, acknowledgment was made of the inherent variability in map readers' perceptions of color by developing generalized perception buffers that accounted for at least 90% of test subject responses. The task of selecting colors that will not be confused once they appear with numerous proximal colors on a map thus becomes a task of selecting colors that do not have buffers that overlap in color space. © 1996 John Wiley & Sons, Inc.     

Color constancy from invariant wavelength ratios: An algorithm to simplify the chromatic adaptation model

In a recent article on color constancy, the chromatic adaptation model was of a novel type comprising three components separately calculated—hue, chromaticness, and lightness. The constant hue component was a simple calculation of predicted wavelength but the other two components were less direct. This article provides an algorithm to simplify the model's calculation. Calculation is far simpler and more intuitive than conventional models using complex 3 × 3 matrix transforms with their various and contentious adaptation primaries and potential disadvantages (e.g., in brightness and color gamut). The model is shown to be at least as accurate as six other (conventional) models and does not require high math skill. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 468–476, 2016     

Optimum solution of the CIECAM02 yellow–blue and purple problems

Brill [Color Res Appl 2006;31:142‐145] and Brill and Süsstrunk [Color Res Appl 2008;33:424‐426] found that CIECAM02 has the yellow–blue and purple problems and gave partial solutions to them. In this article we model the optimum solution to the yellow–blue and purple problems simultaneously as a constrained non‐linear optimization problem. An optimum solution resulting in a new CAT02 matrix is numerically obtained. This new matrix satisfies the nesting rule and performs better than the Hunt‐Pointer‐Estévez (HPE) matrix in predicting both corresponding colours and colour appearance data sets. Specifically, it was found that the new and HPE matrices performed significantly different on nine (out of 21) corresponding colour data sets and on all corresponding colours data sets as a whole. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 491–503, 2015     

Proposed modification to the CIECAM02 colour appearance model to include the simultaneous contrast effects

A modified CIECAM02 colour appearance model, named CIECAM02‐m2, is proposed to enable CIECAM02 to predict the simultaneous contrast effect. The structure of the CIECAM02‐m2 is a development from CIECAM02, and contains two different procedures for modifying the reference white; one is for lightness and the other is for hue. The model was tested using a data set accumulated in this study and the LUTCHI data. The CV values for three colour attributes between predictions and experimental data were used to evaluate the accuracy of the model. The low CV values obtained show the performance of the CIECAM02‐m2 model to predict the simultaneous contrast effect satisfactorily. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 121 – 129, 2007     

Media‐dependent color appearance modeling based on artificial neural networks

In this study, we tried to consider various color appearance factors and device characterization together by visual experiment to simplify the across‐media color appearance reproduction. Two media, CRT display (soft‐copy) and NCS color atlas (hard‐copy), were used in our study. A total of 506 sample pairs of RGB and HVC, which are the attributes of NCS color chips, were obtained according to psychophysical experiments by matching soft copy and hard copy by a panel of nine observers. In addition, a set of error back‐propagation neural networks was used to realize experimental data generalization. In order to get a more perfect generalizing effect, the whole samples were divided into four parts according to different hues and the conversion between HVC and R_HVCG_HVCB_HVC color space was implemented. The current results show that the displays on the CRT and the color chips can match well. In this way, a CRT‐dependent reproduction modeling based on neural networks was formed, which has strong practicability and can be applied in many aspects. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 218–228, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20209     

Impact of the adapted white point and the cultural background on memory color assessments

With their inherent ability of serving as an internal reference, memory colors provide a very powerful concept in the evaluation of color rendering properties of white light sources with respect to visual appreciation. Recent results for example suggest fairly good correlations between memory-based color quality metrics and the observers' general color preferences. However, due to technical limitations in the design of the underlying psychophysical experiments, they generally lack the explicit inclusion of realistic viewing and adaptation conditions, which is supposed to have a nonnegligible impact on the model prediction performance. In addition, intercultural effects might play a crucial role in the context of memory colors. For these reasons, the current article investigates the impact of both the adapted white point and the observers' cultural background on memory color assessments in order to contribute to a better understanding of these dependencies and their interactions. For this purpose, the color appearance rating results of Chinese and German observers were collected for a selection of 12 different familiar test objects assessed under two different adaptation conditions at 3200 K and 5600 K, respectively. From the statistical analysis of the experimental data, it is shown, in accordance to previous studies, that the impact of the observed intercultural deviations is likely to be of no practical importance even though significance is found. Despite considerably larger effect sizes, the same must be concluded for the two tested adaptation conditions.     

Applying chromatic adaptation transforms to mixed adaptation conditions

A set of psychophysical experiments was conducted to investigate the state of adaptation between hardcopy and softcopy images when viewed under mixed illumination conditions. The performance of three chromatic adaptation transforms, CMCCAT97, CMCCAT2000 and CIECAT94, was compared to that of the S‐LMS, a mixed adaptation model. The adaptation ratios of each model were varied to investigate the state of adaptation of the human visual system. Printed complex images were used as originals. A series of softcopy reproduction pairs was displayed on a CRT with a D93 white point and compared to the original in an illuminated room. Three ambient lights were studied: a D50 simulator, an Illuminant A simulator and a Cool‐white fluorescence lamp. The experiments were divided into nine phases according to the changes of illuminants and the luminance levels. A simultaneous binocular matching technique was employed. Observers compared the hardcopy with a given pair of softcopies and identified which reproduction was the closer colour match. The results showed that the state of adaptation of the human visual system was between 40–60% adapted to the white point of the monitor regardless of the changes in illumination conditions. The overall results showed that CMCCAT2000 with proper adaptation ratio outperformed the other models and could be applied to mixed adaptation conditions. © 2003 Wiley Periodicals, Inc. Col Res Appl, 28, 436–444, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10196     

On attributes of achromatic and chromatic object‐color perceptions

Adapting luminance dependencies of various color attributes of object colors (lightness, brightness, whiteness‐blackness, whiteness‐blackness strength, chroma, and colorfulness) were clarified under white illumination with various adapting illuminances. The correlation between the perceptions of lightness and brightness and those of whiteness‐blackness and whiteness‐blackness strength is also clarified for achromatic object colors. The difference between the increase of brightness and that of whiteness‐blackness contrast (the effect studied by Stevens and Jameson—Hurvich) by raising their adapting illuminance is resolved without any contradiction. It is also shown that the nonlinear color‐appearance model developed by the author and his colleagues is able to explain the complex characteristics of all the above color attributes of object colors by making minor modifications to it. In addition, two kinds of classifications of various color attributes are given; one is based on the similarity of perception level, and the other on the degree of adapting illuminance dependency. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 318–332, 2000     

Visual color matching under various viewing conditions

In this article, we provide colorimetry data for which it was judged that the colors between different media matched under various viewing conditions. Painted color patches, a monitor, and printed color patches were used in the color matching experiments, in which we compared the appearances of the painted color patch and the monitor, or the monitor and the printed color patch, using the method of constant stimuli. The nine types of viewing conditions we used could be envisaged to occur when comparing different device outputs indoors. The experimental data obtained were compared with corresponding colors predicted with the use of five types of color appearance model, including color appearance formulae. We found that when the viewing conditions were the same for the different media, there was good agreement between the experimental data and the CIECAT94 model. And by adjusting the brightness induction and the chromatic induction factors, it was possible to improve conformity for the lightness and the chromaticity. Moreover, it was possible to improve the white point shift, which cannot be adjusted with the use of optimized parameters by introducing incomplete adaptation. By optimizing the parameters and introducing incomplete adaptation, it is possible to make the mean color difference ΔE between the corresponding color and the color matching point less than 10 CIELAB units for all of the viewing conditions.     

Some modifications to Hering's opponent‐colors theory

Some modifications are made to the achromatic color perceptions in Hering's opponent‐colors theory. They are the introduction of the reference color Gray and the use of the orthogonal coordinate system. The modified opponent‐colors theory has a symmetrical structure for the three opponent‐colors axes, whiteness‐grayness‐blackness, redness‐grayness‐greenness, and yellowness‐grayness‐blueness, and it unifies the Hunt and the Stevens and Jameson–Hurvich effects. It is also noted that two kinds of color‐appearance spaces exist. One is the color‐appearance space derived from color perceptions of object colors (called the CPS color‐appearance space). The other is that modeled from their colorimetric values for predicting color perceptions (called the UCS color‐appearance space). The CPS color‐appearance space is mainly described in this article. Scaling of the CPS color‐appearance space and the existence of the reference color perception Gray are discussed in detail. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 290–304, 2001     

Differences in attributes between color difference and color appearance (chroma and hue) for near‐neutral colors

Chroma‐step perception and its corresponding color difference in the same hue direction are the different attributes on color perception. The differences between them are different for different hues. Hue‐appearance step and its corresponding color difference along the same hue circle also have completely different concepts. The causes of the above two facts are clarified. The information based on various experiments and theoretical considerations are given for supporting the facts. In addition, it is clarified that the relationship on color‐appearance step and color difference has completely different characteristics between the quantitative (chroma) and the qualitative (hue) attributes of object colors. The importance of chromatic strength (CS) on hue is clarified in each of the three color attributes hue, value, and chroma. © 2004 Wiley Periodicals, Inc. Col Res Appl, 30, 42–52, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20073     

Comprehensive color solutions: CAM16, CAT16, and CAM16‐UCS

The CIECAM02 color‐appearance model enjoys popularity in scientific research and industrial applications since it was recommended by the CIE in 2002. However, it has been found that computational failures can occur in certain cases such as during the image processing of cross‐media color reproduction applications. Some proposals have been developed to repair the CIECAM02 model. However, all the proposals developed have the same structure as the original CIECAM02 model and solve the problems concerned at the expense of losing accuracy of predicted visual data compared with the original model. In this article, the structure of the CIECAM02 model is changed and the color and luminance adaptations to the illuminant are completed in the same space rather than in two different spaces, as in the original CIECAM02 model. It has been found that the new model (named CAM16) not only overcomes the previous problems, but also the performance in predicting the visual results is as good as if not better than that of the original CIECAM02 model. Furthermore the new CAM16 model is simpler than the original CIECAM02 model. In addition, if considering only chromatic adaptation, a new transformation, CAT16, is proposed to replace the previous CAT02 transformation. Finally, the new CAM16‐UCS uniform color space is proposed to replace the previous CAM02‐UCS space. A new complete solution for color‐appearance prediction and color‐difference evaluation can now be offered.