Guihua Cui

Measurement of the relationship between perceived and computed color differences

Using simulated data sets, we have analyzed some mathematical properties of different statistical measurements that have been employed in previous literature to test the performance of different color-difference formulas. Specifically, the properties of the combined index PF/3 (performance factor obtained as average of three terms), widely employed in current literature, have been considered. A new index named standardized residual sum of squares (STRESS), employed in multidimensional scaling techniques, is recommended. The main difference between PF/3 and STRESS is that the latter is simpler and allows inferences on the statistical significance of two color-difference formulas with respect to a given set of visual data.

Notes on the application of the standardized residual sum of squares index for the assessment of intra- and inter-observer variability in color-difference experiments

The standardized residual sum of squares index was proposed to examine the significant merit of a given color-difference formula over another with respect to a given set of visual color-difference data [J. Opt. Soc. Am. A 24, 1823-1829, 2007]. This index can also be employed to determine intra- and inter-observer variability, although the full complexity of this variability cannot be described by just one number. Appropriate utilization of the standardized residual sum of squares index for the assessment of observer variability is described with a view to encourage its use in future color-difference research. The main goal of this paper is to demonstrate that setting the F parameters of the standardized residual sum of squares index to 1 results in a loss of essential properties of the index (for example, symmetry), and is therefore strongly discouraged.

Assessing total differences for effective samples having variations in color, coarseness, and glint

Effect coatings have the unique property of large change of appearance under different viewing conditions. This results in quality control problems of related products. In this letter, samples of metallic panels with effect coatings are visually assessed and measured. Based on experimental results, we propose formulae to predict precisely the total differences of effective samples in terms of variations in color, coarseness, and glint. Under diffused illumination, the total difference formula includes color difference and coarseness difference. Under directional illumination, the total difference formula includes color difference and glint difference.

Evaluation of threshold color differences using printed samples

The performances of uniform color spaces and color-difference formulae for predicting threshold color differences were investigated based on visual assessments of 893 pairs of printed color patches under a D65 source. The average ΔE(ab,10)* of the pairs was 1.1 units. A threshold psychophysical experiment was repeated three times by a panel of 16 observers with normal color vision. The experimental data were used to evaluate nine color-difference formulae and uniform color spaces using the standardized residual sum of squares (STRESS) measure. The results indicated that all formulae and spaces performed very similarly to each other, and outperformed CIELAB for threshold color differences. The chromaticity-discrimination ellipses were used to compare with previous results from small color differences [Color Res. Appl. (2011), doi:10.1002/col.20689], and they agreed with each other, except for the purple color center.

Color-difference evaluation for digital images using a categorical judgment method

The CIELAB lightness and chroma values of pixels in five of the eight ISO SCID natural images were modified to produce sample images. Pairs of images were displayed on a calibrated monitor and assessed by a panel of 12 observers with normal color vision using a categorical judgment method. The experimental results showed that assuming the lightness parametric factor k(L)=1 to predict color differences in images, CIELAB performed better than CIEDE2000, CIE94, or CMC, which is a different result to the one found in color-difference literature for homogeneous color pairs. However, observers perceived CIELAB lightness and chroma differences in images in different ways. To fit current experimental data, a specific methodology is proposed to optimize k(L) in the color-difference formulas CIELAB, CIEDE2000, CIE94, and CMC. From the standardized residual sum of squares (STRESS) index, it was found that the optimized formulas, CIEDE2000(2.3:1), CIE94(3.0:1), and CMC(3.4:1), performed significantly better than their corresponding original forms with lightness parametric factor k(L)=1. Specifically, CIEDE2000(2.3:1) performed the best, with a satisfactory average STRESS value of 25.8, which is very similar to the 27.5 value that was found from the CIEDE2000(1:1) formula for the combined weighted dataset of homogeneous color samples employed at the development of this formula [J. Opt. Soc. Am. A25, 1828 (2008), Table 2]. However, fitting our experimental data, none of the four optimized formulas CIELAB(1.5:1), CIEDE2000(2.3:1), CIE94(3.0:1), and CMC(3.4:1) is significantly better than the others. Current results roughly agree with the recent CIE recommendation that color difference in images can be predicted by simply adopting a lightness parametric factor k(L)=2 in CIELAB or CIEDE2000 [CIE Publication 199:2011]. It was also found that the different contents of the five images have considerable influence on the performance of the tested color-difference formulas.

Power functions improving the performance of color-difference formulas

Color-difference formulas modified by power functions provide results in better agreement with visually perceived color differences. Each of the modified color-difference formulas proposed here adds only one relevant parameter to the corresponding original color-difference formula. Results from 16 visual data sets and 11 color-difference formulas indicate that the modified formulas achieve an average decrease of 5.7 STRESS (Standardized Residual Sum of Squares) units with respect to the original formulas, signifying an improvement of 17.3%. In particular, for these 16 visual data sets, the average decrease for the current CIE/ISO recommended color-difference formula CIEDE2000 modified by an exponent 0.70 was 5.4 STRESS units (17.5%). The improvements of all modified color-difference formulas with respect to the original ones held for each of the 16 visual data sets and were statistically significant in most cases, particularly for all data sets with color differences close to the threshold. Results for 2 additional data sets with color pairs in the blue and black regions of the color space confirmed the usefulness of the proposed power functions. The main reason of the improvements found for the modified color-difference formulas with respect to the original color-difference formulas seems to be the compression provided by power functions.

Colour Difference Evaluation

For a pair of homogeneous colour samples or two complex images viewed under specific conditions, colour-difference formulas try to predict the visually perceived (subjective) colour difference starting from instrumental (objective) colour measurements. The history related to the five up-to-date CIE-recommended colour-difference formulas is reviewed, with special emphasis on the structure and performance of the last one, CIEDE2000. Advanced colour-difference formulas with an associated colour space (e.g., DIN99d, CAM02, Euclidean OSA-UCS, etc.) are also discussed. Different indices proposed to measure the performance of a given colour-difference formula (e.g., PF/3, STRESS, etc.) are reviewed. Among current trends on colour-difference evaluation, it can be mentioned the research activities carried out by different CIE Technical Committees (e.g., CIE TC’s 1-55, 1-57, 1-63, 1-81 and 8-02), the need of new reliable experimental datasets, the development of colour-difference formulas based on IPT and colour-appearance models, and the concept of “total differences,” which considers the interactions between colour properties and other object attributes like texture, translucency, and gloss.

Diffraction theory of high numerical aperture subwavelength circular binary phase Fresnel zone plate.

An analytical model of vector formalism is proposed to investigate the diffraction of high numerical aperture subwavelength circular binary phase Fresnel zone plate (FZP). In the proposed model, the scattering on the FZPs surface, reflection and refraction within groove zones are considered and diffraction fields are calculated using the vector Rayleigh-Sommerfeld integral. The numerical results obtained by the proposed phase thick FZP (TFZP) model show a good agreement with those obtained by the finite-difference time-domain (FDTD) method within the effective extent of etch depth. The optimal etch depths predicted by both methods are approximately equal. The analytical TFZP model is very useful for designing a phase and hybrid amplitude-phase FZP with high-NA and short focal length.

Color appearance and visual measurements for color samples with gloss effect

We assess the color appearance of the samples with different inks on glossy substrates, five kinds of paper with different gloss levels. The color samples are measured using spectrophotometers under different illuminating/viewing geometries and visually estimated using the psychophysical method of magnitude estimation. The results of the two approaches are compared through the color appearance model of CIECAM02. The experimental data analysis indicates that the 0/45 and 15/0 geometries can be used to describe the two major aspects of gloss effect, the enlargement of color gamut, and the reduction of lightness. The agreement for hue attribute between instrumental measurement and visual assessment is better than those for colorfulness and lightness.

Compact self-cascaded KTA-OPO for 2.6 μm laser generation

We reported a compact self-cascaded KTA-OPO source for 2.6 μm coherent light generation. The OPO is driven in a diode end-pumped and Q-switched Nd:YVO4 laser cavity. Two OPO processes occurred in the same KTA crystal with non-critical phase matching. At an incident diode pump power of 8.7 W and a pulse repetition frequency of 60 kHz, the OPO can generate a maximum average output power of 445 mW at 2.59 μm. The slope efficiency was about 12.7%, and the power fluctuation was less than 8%. Therefore, the self-cascade OPO based on KTA offers a promise scheme for the rugged and compact mid-infrared 2.6 μm laser generation.