J. Eur. Opt. Society-Rapid Publ. 21, 36( 2025) 53
most satisfying images possible with the available means, emphasizing the need for metrics to evaluate them.
To obtain information about image quality, human judgments are required to perform a subjective IQA which is then averaged over all the results since observers have different standards. In the literature, objective evaluation methods are categorized as full-reference, reduced-reference or no-reference methods [ 29 ]. The full-reference method consists in comparing a degraded image with its original( reference), these difference methods can be performed:
Pixel-by-pixel, using metrics like CIEDE2000 color difference formula or the DUCS if performed in the OSA-UCS space [ 30 ];
Based on the structure of the image, with metrics such as the Structure Similarity( SSIM) Index or Visual Information Fidelity [ 31 ];
Based on perception, using metrics like the Visual Difference Predictor( VDP).
Reduced-reference methods rely on only a portion of the reference image, while utilizing the full information of the degraded image to compute the quality metrics. No-reference methods are based on metrics without any reference image at all, such as the Blind / Reference less Image spatial Quality Evaluator( BRISQUE) or the Naturalness Image Quality Evaluator( NIQE) [ 32 ]. In the present study, the distortion of the laser-induced gamuts, relative to the sRGB gamut, necessitated the addition of a reference image to prevent the observers’ aesthetic and color preferences from dominating in the quality assessment.
As mentioned in the introduction, objective IQA can be conducted using a large variety of metrics. Accordingly, the one-way ANOVA method was used to identify the most relevant objective IQA metrics compared to subjective IQA. One-way ANOVA is a statistical technique used to compare the means of three or more independent groups to determine if there is a statistically significant difference between them. It assumes that the groups are normally distributed with equal variances. The method calculates the F-statistic, which is the ratio of the variance between the group means to the variance within the groups. A significant F-statistic suggests that at least one group means differs significantly from the others, which may require further post hoc analysis to pinpoint the differences.
In evaluating the relevance of metrics within a linear model, one-way ANOVA is a useful tool for determining whether different metrics, treated as categorical variables, lead to significant differences in the model’ s performance. It is important to understand the effect of individual parameters to explain observations. For example, Jost- Boissard et al. [ 33 ] used the one-way ANOVA to investigate whether there was a link between observer characteristics( skin type, age, gender and expertise) and their appreciation of different light sources. By applying one-way ANOVA, significant effects of changes in these metrics on the model’ s output can be assessed, thereby identifying which metrics are most influential. This approach ensures that the final model remains both efficient and interpretable by focusing on metrics that significantly contribute to explain the model.
Coupling this method with Akaike Information Criterion( AIC) can yield the most promising models that ensure strong predictive performance while avoiding overfitting. AIC is a method for comparison and selection models in statistical modeling, it is based on the trade-off between the goodness of fit of the model and its complexity. It is defined as:
AIC ¼ 2k � 2lnðLÞ ð1Þ
where k is the number of parameters in the model, and L is the maximum likelihood of the model. Lower AIC values indicate a model that better balances fit and complexity, making it preferred over models with higher AIC values. The AIC penalizes models with more parameters, thus helpingtoavoidoverfitting.
When evaluating the relevance of metrics within a linear model, AIC can be used to compare different models that include different sets of metrics. By calculating the AIC for each model, the combination of metrics that results in the most parsimonious model – one that provides a good fit with minimal complexity – can be identified. This method is particularly useful in model selection, where the goal is to retain only the most relevant metrics that contribute to the model’ s predictive power while avoiding unnecessary complexity. The purpose of this study is to evaluate the quality of the plasmonic colors presented on a sample by establishing the IQA. While the laser-induced colors on semi-transparent random plasmonic metasurfaces are promising for many applications, such as image multiplexing, the colors produced tend to be less saturated and not centered within the color gamut when compared to those of a CMYK inkjet printer. As a result, a tailored IQA approach is required to accurately evaluate their reproduction quality. To better understand the characteristics of the tested samples, Figure 1 shows the back side of a sample with a semi-transparent plasmonic metasurface deposited on the front side. The colored areas were produced by laser processing [ 1 ]. The sample is illuminated by an LED panel( 4000 K, 350 lm) and observed in specular reflection. The transmitted light is reflected by a black mirror positioned beneath the sample. The black mirror was used to balance the amount of transmitted and reflected light from the sample, making it possible to observe color areas in both reflection and transmission modes on a single photograph. The image illustrates the potential of laser-induced gamut generation on a specific random plasmonic metasurface, showing the achievable colors in two distinct observation modes. Such samples and setup allow to record color datasets pertaining to a single observation mode and sample, with each color area associated with a distinct laser parameter set. Each data set corresponds to a distinct color gamut.
Six gamuts were utilized to generate a series of images for ranking by human observers. The first three ones, displayed in Figures 2a – 2c were directly built from the colors of laser-processed random plasmonic metasurfaces measured in the back side reflection mode on three different samples:
1 _ BR corresponds to a low chromaticity gamut( C * below 20) but presents colors of all different hues( h *), its lightness values( L *) are between 20 and 60.