Eric Kirchner

Performance measures of color-difference equations: correlation coefficient versus standardized residual sum of squares

For evaluating the performance of color-difference equations, several goodness-of-fit measures were proposed in the past, such as Pearson’s correlation coefficient (r), the performance factor PF/3, and the recently proposed standardized residual sum of squares (STRESS) measure. The STRESS shares its main advantage, which is the possibility to statistically test performance differences, with the correlation coefficient. We show, by mathematical analysis supported by instructive numerical examples, that the STRESS has no meaningful interpretation in this regression analysis context. In addition, we present objections to the use of the STRESS for evaluating color-difference equations. Therefore, we recommend using the correlation coefficient in combination with a graphical and diagnostics analysis to ensure proper application as with any statistical technique.

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.

Isochromatic lines as extension of Helmholtz reciprocity principle for effect paints.

Flake-based parameters were recently introduced as a physical concept to predict a series of measurement geometries producing similar reflection data for effect paints. We derive expressions to calculate these so-called isochromatic lines, connecting the two Helmholtz-reciprocal in-plane geometries with a series of out-of-plane geometries. Thus isochromatic lines can be regarded as an extension of the Helmholtz reciprocity principle, which is valid for effect paints. We experimentally studied seven effect paint samples with large angular color variation along the length of four isochromatic lines. A change in illumination angles by up to 75° while following isochromatic lines led to a standard deviation in color parameters of less than two units. When isochromatic lines were not followed, these colorimetric parameters varied by more than 10 units already by change in detection angle of 10°. Therefore the concept of isochromatic lines works well for effect paints.

Towards a better understanding of the color shift of effect coatings by densely sampled spectral BRDF measurement

To completely characterize the color of effect coatings, the spectral BRDF should be measured for a large number of illumination/detection geometries. This is possible with the GEFE, the gonio-spectrophotometer developed at Instituto de Óptica in CSIC (IO-CSIC). Twenty-four effect coating samples were prepared by AkzoNobel, containing metallic and/or interference flake pigments. The spectral BRDF of all samples was measured by GEFE using a normalized procedure under 448 different geometries. The results are presented in two-dimensional a*-b* diagrams and in three-dimensional CIELAB diagrams to show the color travel. Four different descriptors were used to quantify the color travel of these samples. We show that for many samples and geometries, the resulting colors fall outside the color gamut of a typical display. It was found that the reflection data do not vary considerably at reciprocal geometries, allowing a reduction of geometries to be done. Finally, we show that for 3D rendering applications, the reflection data from BRDF can be strongly reduced. For example, we show that using the concept of flake-based parameters it is possible to only use inplane geometries. The resulting rendered images were shown to be accurate enough for rendering on displays.

How psychophysical methods influence optimizations of color difference formulas

For developing color difference formulas, there are several choices to be made on the psychophysical method used for gathering visual (observer) data. We tested three different psychophysical methods: gray scales, constant stimuli, and two-alternative forced choice (2AFC). Our results show that when using gray scales or constant stimuli, assessments of color differences are biased toward lightness differences. This bias is particularly strong in LCD monitor experiments, and also present when using physical paint samples. No such bias is found when using 2AFC. In that case, however, observer responses are affected by other factors that are not accounted for by current color difference formulas. For accurate prediction of relative color differences, our results show, in agreement with other works, that modern color difference formulas do not perform well. We also investigated if the use of digital images as presented on LCD displays is a good alternative to using physical samples. Our results indicate that there are systematic differences between these two media.

Improving color reproduction accuracy of a mobile liquid crystal display

The default method for color representation on displays involves sRGB as device-independent encoding color space. For improving color reproduction accuracy, we develop a device-specific display characterization model for the Apple iPad Air 2. In separate articles, we will evaluate the same method for other devices and for other display technologies. This model is combined with an easy-to-implement new method to account for the influence of illuminance from ambient light. The combination is called the mobile display characterization and illumination model (MDCIM) for the iPad Air 2, representing modern liquid crystal displays. Seven observers performed psychophysical tests at ambient illuminance levels from 600 to 3000 lx. They visually compared colors of calculated images with those of physical samples. The MDCIM model achieves similar color reproduction accuracy as when using the default method involving sRGB encoding at 1000 lx, while considerably improving color accuracy at other illuminance levels. At 600 lx, 98% of the observers prefer images directly generated with the MDCIM model over those created using the default method. The average color reproduction accuracy improves by two categories on a five-point scale. At 3000 lx, the percentage of colors that is represented at least reasonably well, according to the subjective assessment of visual observers, increased from 0% to 60%.

Visibility of sparkle in metallic paints

For suitable illumination and observation conditions, sparkles may be observed in metallic coatings. The visibility of these sparkles depends critically on their intensity, and on the paint medium surrounding the metallic flakes. Based on previous perception studies from other disciplines, we derive equations for the threshold for sparkles to be visible. The resulting equations show how the visibility of sparkles varies with the luminosity and distance of the light source, the diameter of the metallic flakes, and the reflection properties of the paint medium. The predictions are confirmed by common observations on metallic sparkle. For example, under appropriate conditions even metallic flakes as small as 1 μm diameter may be visible as sparkle, whereas under intense spot light the finer grades of metallic coatings do not show sparkle. We show that in direct sunlight, dark coarse metallic coatings show sparkles that are brighter than the brightest stars and planets in the night sky. Finally, we give equations to predict the number of visually distinguishable flake intensities, depending on local conditions. These equations are confirmed by previous results. Several practical examples for applying the equations derived in this article are provided.

Reconstructing Van Gogh’s palette to determine the optical characteristics of his paints

The colors of Field with Irises near Arles, painted by Van Gogh in Arles in 1888, have changed considerably. To get an idea of how this painting, as well as other works by Van Gogh, looked shortly after their production, the Revigo (Re-assessing Vincent van Gogh’s colors) research project was initiated. The aim of this project was to digitally visualize the original colors of paintings and drawings by Vincent van Gogh, using scientific methods backed by expert judgement where required. We adopted an experimental art technological approach and physically reconstructed Van Gogh’s full palette of oil paints, closely matching those he used to paint Field with Irises near Arles. Sixteen different paints were reconstructed, among which the most light-sensitive pigments and linseed oil, which is prone to yellowing, were produced according to 19th century practice. The resulting pigments and oils were chemically analyzed and compared to those used by Van Gogh. The ones that resembled his paints the most were used in the paint reconstructions. Other pigments were either obtained from the Cultural Heritage Agency’s collection of historical pigments, or purchased from Kremer Pigmente. The reconstructed paints were subsequently used to calculate the absorption K and scattering S parameters of the individual paints. Using Kubelka–Munk theory, these optical parameters could in turn be used to determine the color of paint mixtures. We applied this method successfully to digitally visualize the original colors of Field with Irises near Arles. Moreover, the set of optical parameters presented here can similarly be applied to calculate digital visualizations of other paintings by Van Gogh and his contemporaries.

Mathematical limitations when choosing psychophysical methods: geometric versus linear grey scales

The grey scale method is commonly used for investigating differences in material appearance. Specifically, for testing color difference equations, perceived color differences between sample pairs are obtained by visually comparing to differences in a series of achromatic sample pairs. Two types of grey scales are known: linear and geometric. Their instrumental color differences vary linearly or geometrically (i.e., exponentially), respectively. Geometric grey scales are used in ISO standards and standard procedures of the textile industries. We compared both types of grey scale in a psychophysical study. Color patches were shown on a color-calibrated display. Ten observers assessed color differences in sample pairs, with color differences between ΔEab = 0.13 and 2.50. Assessments were scored by comparison to either a linear or a geometric grey scale, both consisting of six achromatic pairs. For the linear scale we used color differences ΔEab = 0.0, 0.6, 1.2,..., 3.0. For the geometric scale this was ΔEab=0.0, 0.4, 0.8, 1.6, 3.2, 6.4. Our results show that for the geometric scale, data from visual scores clutter at the low end of the scale and do not match the ΔEab range of the grey scale pairs. We explain why this happens, and why this is mathematically inevitable when studying small color differences with geometric grey scales. Our analysis explains why previous studies showed larger observer variability for geometric than for linear scales.

Improving Color Accuracy of Colorimetric Sensors

Accurate measurements of reflectance and color require spectrophotometers with prices often exceeding