Esther Perales

Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source

We present a systematic algorithm capable of searching for optimal colors for any lightness L* (between 0 and 100), any illuminant (D65, F2, F7, F11, etc.), and any light source reported by CIE. Color solids are graphed in some color spaces (CIELAB, SVF, DIN99d, and CIECAM02) by horizontal (constant lightness) and transversal (constant hue angle) sections. Color solids plotted in DIN99d and CIECAM02 color spaces look more spherical or homogeneous than the ones plotted in CIELAB and SVF color spaces. Depending on the spectrum of the light source or illuminant, the shape of its color solid and its content (variety of distinguishable colors, with or without color correspondence) change drastically, particularly with sources whose spectrum is discontinuous and/or very peaked, with correlated color temperature lower than 5500 K. This could be used to propose an absolute colorimetric quality index for light sources comparing the volumes of their gamuts, in a uniform color space.

The achromatic locus: Effect of navigation direction in color space

An achromatic stimulus is defined as a patch of light that is devoid of any hue. This is usually achieved by asking observers to adjust the stimulus such that it looks neither red nor green and at the same time neither yellow nor blue. Despite the theoretical and practical importance of the achromatic locus, little is known about the variability in these settings. The main purpose of the current study was to evaluate whether achromatic settings were dependent on the task of the observers, namely the navigation direction in color space. Observers could either adjust the test patch along the two chromatic axes in the CIE u*v* diagram or, alternatively, navigate along the unique-hue lines. Our main result is that the navigation method affects the reliability of these achromatic settings. Observers are able to make more reliable achromatic settings when adjusting the test patch along the directions defined by the four unique hues as opposed to navigating along the main axes in the commonly used CIE u*v* chromaticity plane. This result holds across different ambient viewing conditions (Dark, Daylight, Cool White Fluorescent) and different test luminance levels (5, 20, and 50 cd/m(2)). The reduced variability in the achromatic settings is consistent with the idea that internal color representations are more aligned with the unique-hue lines than the u* and v* axes.

Spectral BRDF-based determination of proper measurement geometries to characterize color shift of special effect coatings

A reduced set of measurement geometries allows the spectral reflectance of special effect coatings to be predicted for any other geometry. A physical model based on flake-related parameters has been used to determine nonredundant measurement geometries for the complete description of the spectral bidirectional reflectance distribution function (BRDF). The analysis of experimental spectral BRDF was carried out by means of principal component analysis. From this analysis, a set of nine measurement geometries was proposed to characterize special effect coatings. It was shown that, for two different special effect coatings, these geometries provide a good prediction of their complete color shift.

Colorimetric and spectral evaluation of the optical anisotropy of metallic and pearlescent samples

The visual and optical anisotropies of metallic and pearlescent samples have been evaluated using a multi-gonio-spectrophotometer and by adapting a gonio-template over the instrument aperture for measuring the relative spectral reflectance factor when the sample is rotated around an axis normal to its surface. The results show that spectral data greatly vary as the azimuth angle changes, especially in pearlescent samples. Spectral and colorimetric data of the same sample for the interference and aspecular lines seen in complementary angle pairs have been compared, resulting in hue angle being kept constant, but lightness L* and chroma variations are high. In particular, the colour differences ΔEab calculated for pearlescent and metallic samples show that these visual differences can be clearly appreciable, even in metallic samples, but especially in pearlescent ones. Therefore, these types of optical materials do not verify the Helmholtz reciprocity, which is usually applied for digital modelling of material appearance.

Measuring color differences in automotive samples with lightness flop: A test of the AUDI2000 color-difference formula

From a set of gonioapparent automotive samples from different manufacturers we selected 28 low-chroma color pairs with relatively small color differences predominantly in lightness. These color pairs were visually assessed with a gray scale at six different viewing angles by a panel of 10 observers. Using the Standardized Residual Sum of Squares (STRESS) index, the results of our visual experiment were tested against predictions made by 12 modern color-difference formulas. From a weighted STRESS index accounting for the uncertainty in visual assessments, the best prediction of our whole experiment was achieved using AUDI2000, CAM02-SCD, CAM02-UCS and OSA-GP-Euclidean color-difference formulas, which were no statistically significant different among them. A two-step optimization of the original AUDI2000 color-difference formula resulted in a modified AUDI2000 formula which performed both, significantly better than the original formula and below the experimental inter-observer variability. Nevertheless the proposal of a new revised AUDI2000 color-difference formula requires additional experimental data.

Color representation and interpretation of special effect coatings

A representation of the color gamut of special effect coatings is proposed and shown for six different samples, whose colors were calculated from spectral bidirectional reflectance distribution function (BRDF) measurements at different geometries. The most important characteristic of the proposed representation is that it allows a straightforward understanding of the color shift to be done both in terms of conventional irradiation and viewing angles and in terms of flake-based parameters. A different line was proposed to assess the color shift of special effect coatings on a*,b*-diagrams: the absorption line. Similar to interference and aspecular lines (constant aspecular and irradiation angles, respectively), an absorption line is the locus of calculated color coordinates from measurement geometries with a fixed bistatic angle. The advantages of using the absorption lines to characterize the contributions to the spectral BRDF of the scattering at the absorption pigments and the reflection at interference pigments for different geometries are shown.

Analysis of the colorimetric properties of goniochromatic colors using the MacAdam limits under different light sources

Technological innovation in all areas has led to the appearance in recent years of new metallic and pearlescent materials, yet no exhaustive studies have been conducted to assess their colorimetric capabilities. The chromatic variability of these special-effect pigments may largely be due to the three-dimensional effect of their curved shapes and orientations when they are directionally or diffusely illuminated. Our study examines goniochromatic colors using the optimal colors (MacAdam limits) associated with normal colors (photometric scale of relative spectral reflectance from 0 to 1) under certain conventional illuminants and other light sources. From a database of 91 metallic and interference samples and using a multi-gonio-spectrophotometer, we analyzed samples with lightness values of more than 100 and others with lightness values of less than 100, but with higher chromaticities than optimal colors, which places them beyond the MacAdam limits. Our study thus demonstrates the existence of chromatic perceptions beyond the normal solid color associated with these materials and independent of the light source. The challenge for future research, therefore, is to replicate and render these color appearances in current and future color reproduction technologies for computer graphics.

Number of discernible colors for color-deficient observers estimated from the MacAdam limits

We estimated the number of colors perceived by color normal and color-deficient observers when looking at the theoretic limits of object-color stimuli. These limits, the optimal color stimuli, were computed for a color normal observer and CIE standard illuminant D65, and the resultant colors were expressed in the CIELAB and DIN99d color spaces. The corresponding color volumes for abnormal color vision were computed using models simulating for normal trichromatic observers the appearance for dichromats and anomalous trichomats. The number of colors perceived in each case was then computed from the color volumes enclosed by the optimal colors also known as MacAdam limits. It was estimated that dichromats perceive less than 1% of the colors perceived by normal trichromats and that anomalous trichromats perceive 50%-60% for anomalies in the medium-wavelength-sensitive and 60%-70% for anomalies in the long-wavelength-sensitive cones. Complementary estimates obtained similarly for the spectral locus of monochromatic stimuli suggest less impairment for color-deficient observers, a fact that is explained by the two-dimensional nature of the locus.

Application of the S-CIELAB color model to processed and calibrated images with a colorimetric dithering method

This work uses the S-CIELAB color model to compare images that have been calibrated and processed using a colorimetric dithering method which simulates increments in viewing distance. Firstly, we obtain XYZ calibrated images by applying the appropriate color transformations to the original images. These transformations depend on whether the image is viewed on a display device or encoded by a capture device, for example. Secondly, we use a colorimetric dithering method consisting of a partitive additive mixing of XYZ tristimulus values. The number of dithered pixels depends on simulated viewing distance. The dithered tristimulus values are transformed to digital data to observe the dithering effects in the image. Finally, we predict color differences using the S-CIELAB model as color appearance model for images. Moreover, this paper proposes some applications of this method to artistic and industrial problems where one must compare two images that appear different at close viewing distance, but match when they are seen from afar.

Global color estimation of special-effect coatings from measurements by commercially available portable multiangle spectrophotometers

Optical fiber with high numerical aperture (NA) can efficiently relieve the degeneracy of higher-order linearly polarized modes. The degeneracy relief is investigated in two types of high-NA fibers, i.e., low-index-cladding fiber and high-index-core fiber. A naked-core fiber, as with low-index cladding, can be used theoretically to generate the orbital-angular-momentum mode (OAMM) HE21 and the cylindrically symmetric modes (CSMs) TM01 and TE01. A high-index-core fiber incorporated with high-contrast-index structure can be used similarly to obtain OAMM HE31. The generation of both CSMs and OAMMs required tilted optical gratings to couple the fundamental core mode HE11 into these modes. The tilt angle and modulation period of the grating fringes can be calculated simply and visually with the method proposed in this article.Colors of special-effect coatings have strong dependence on illumination/viewing geometry and an appealing appearance. An open question is to ask about the minimum number of measurement geometries required to completely characterize their observed color shift. A recently published principal components analysis (PCA)-based procedure to estimate the color of special-effect coatings at any geometry from measurements at a reduced set of geometries was tested in this work by using the measurement geometries of commercial portable multiangle spectrophotometers X-Rite MA98, Datacolor FX10, and BYK-mac as reduced sets. The performance of the proposed PCA procedure for the color-shift estimation for these commercial geometries has been examined for 15 special-effect coatings. Our results suggest that for rendering the color appearance of 3D objects covered with special-effect coatings, the color accuracy obtained with this procedure may be sufficient. This is the case especially if geometries of X-Rite MA98 or Datacolor FX10 are used.