Perceptual Color Difference Modeling Using Machine Learning and Human Similarity Judgments

• Traditional color-difference metrics approximate perceptual uniformity but may miss subtle human judgments, while perception varies with context and observer.Source: §I · p. 1
• The dataset is also used to learn perceptual similarity thresholds with logistic regression and quantify inter-observer agreement with Fleiss’ Kappa.Source: §I · p. 1
• The work frames perceptual color difference as supervised similarity learning, using human-labeled data and computational intelligence to pursue adaptive metrics.Source: §I · p. 1
• The authors construct a dataset of 2,000 systematically generated RGB color pairs with human similarity ratings from two controlled experiments.Source: §I · p. 1
• The study compares human similarity judgments with analytical metrics and proposes regression coefficients for computing perceptual differences from RGB values while quantifying feature contributions.Source: §I · p. 1
• The study reports that spatial presentation conditions significantly affect perceptual similarity thresholds.Source: §I · p. 1

• Earlier studies found CIEDE2000 agreed better with human judgments than alternative models, while an ANFIS was proposed as an alternative to fixed formula-based evaluation,.Source: §II · p. 2
• Limitations of earlier formulas in modeling viewing conditions and perceptual adaptation motivated color appearance models, while proLab aimed to improve perceptual uniformity and retain linear color relationships –.Source: §II · p. 2
• Work on color-space geometry found substantial differences in perceptual distance regions, especially for saturated colors, and argued that no single space suits every perception-based task,.Source: §II · p. 2
• Color-difference metrics have been applied to image quality, saliency, sharpness, and object detection, with several studies reporting benefits from perceptually motivated representations –.Source: §II · p. 2
• Applications also include context-sensitive color encoding in visualization, perceptually consistent palette construction, and printing approaches that preserve perceptual quality while reducing ink use –.Source: §II · p. 2
• The review identifies relatively limited attention to emotional meaning in color differences and calls for fuzzy, multimodal representations that account for uncertainty and subjectivity.Source: §II · p. 3

• The experiment examines how spatial separation influences judgments of color differences.Source: §III · p. 3
• Subjective similarity assessments are used to build a machine-learning training dataset and compare human judgments with existing color-difference measures.Source: §III · p. 3
• The study evaluates different feature representations and learning algorithms to determine which combination best reflects human perception.Source: §III · p. 3

A. Data collection

• 2,000 distinct RGB color pairs were generated to span a broad range of perceptual color differences, with channel values sampled from 0 to 255.The full RGB space contains 16,777,216 colors and more than 1.4 × 10^14 unordered pairs, making exhaustive evaluation impractical.Source: A. Data collection · pp. 3–4
• A random reference color was paired with a second color whose RGB Euclidean distance matched a predefined shift magnitude within a specified tolerance.The shift levels were varied to sample color differences uniformly across the designated range.Source: A. Data collection · p. 4
• Shift levels from 0 to 220 produced distances of roughly 1.00 to 221.79; pairs above 220 were excluded as trivially unlike.The range reflects the applied tolerance and discrete RGB space.Source: A. Data collection · p. 4
• Generated pairs were saved with RGB values, hexadecimal codes, and precise computed distances for reproducibility and additional analysis.The sampled differences covered both very small and very large color differences.Source: A. Data collection · p. 4

B. Experiment Design

• A web-based interface standardized stimulus presentation and automated data collection; participants completed a practice trial before the main task.Practice-trial responses were excluded from analysis.Source: B. Experiment Design · p. 4
• Participants rated similarity on a four-point ordinal scale from “Not similar” to “Very similar.”The scale also included “Somewhat similar” and “Similar.”Source: B. Experiment Design · p. 4
• Experiment 1 displayed color patches separately, while Experiment 2 displayed them adjacent with no spatial separation.The second experiment used the same stimulus pool and rating scale as the first; other settings were identical.Source: B. Experiment Design · pp. 4–5
• The second experiment repeated a randomly selected subset of 400 pairs, enabling assessment of intra-participant consistency.Repeated pairs were shuffled among the full set so their reappearance was unpredictable.Source: B. Experiment Design · p. 5

C. Spatial Separation Conditions

• With visible gaps, samples are spatially separated, and prior evaluations reportedly align more consistently with conventional color-difference models than no-separation evaluations,.The gap reduces spatial interaction between adjacent colors.Source: C. Spatial Separation Conditions · p. 5
• Without separation, adjacent samples can shift the perceived balance of lightness and chromatic differences; some conditions increase lightness sensitivity and diverge from traditional formula predictions,,.The text describes this arrangement as representative of printed images and digital displays.Source: C. Spatial Separation Conditions · p. 5
• Presentation conditions can systematically influence color-difference judgments across materials and viewing conditions,,.The three configurations described are hairline separation, visible-gap separation, and no separation.Source: C. Spatial Separation Conditions · p. 5
• To the authors’ knowledge, no prior study examined separation effects across a wide ΔE range (0–220) on a display medium.This is the gap that the present work identifies.Source: C. Spatial Separation Conditions · p. 5

D. Color Models

• RGB represents color through Red, Green, and Blue numerical channels and is standard for digital images.The study includes RGB as one of its three complementary color models.Source: D. Color Models · pp. 5–6
• HSI separates color into hue, saturation, and intensity components.These components are described as perceptually meaningful.Source: D. Color Models · p. 6
• COLIBRI represents hue, saturation, and intensity with perceptually motivated fuzzy linguistic categories and gradual rather than strict membership boundaries.The study considers COLIBRI alongside RGB and HSI.Source: D. Color Models · pp. 5–6

E. Machine Learning algorithms

• Five algorithms span a linear baseline and nonlinear tree-based and ensemble models, enabling comparison of simple and more complex representations of perceptual color differences.The models are Linear Regression, Decision Tree, Random Forest, LightGBM, and XGBoost.Source: E. Machine Learning algorithms · p. 6
• Linear Regression predicts color differences from input features using an intercept and learned, interpretable coefficients.Each feature coefficient represents its contribution to the prediction.Source: 1) Linear Regression · p. 6
• Decision Tree selects feature-threshold splits that minimize weighted impurity, using within-node mean squared error for regression.Each split creates left and right subsets.Source: 2) Decision Tree · p. 6
• Random Forest averages predictions from decision trees trained on bootstrap samples with randomized feature selection.The ensemble prediction averages the outputs of its trees.Source: 3) Random Forest · p. 6
• LightGBM iteratively adds trees and grows them leaf-wise, splitting the leaf with the largest reduction in the objective function.Its design targets computational efficiency and scalability.Source: 4) LightGBM · p. 6
• XGBoost sequentially adds decision trees to correct previous errors, using explicit regularization and second-order gradient information.It also handles sparse and missing data.Source: 5) XGBoost · p. 6

Color difference metrics

• CIE94 weights lightness, chroma, and hue; CIEDE2000 adds nonlinear and chroma–hue corrections, while CMC tunes lightness/chroma tolerances.The CIELAB uniformity assumption is described as inaccurate in high-chroma, low-lightness regions.Source: 2) CIE94 · p. 6, 1) CIE76 (CIELAB Euclidean Distance) · p. 6, 3) CIEDE2000 · p. 7

Dataset

• The dataset contains 2,000 unique color pairs rated by seven experts, with each pair represented by its RGB values and four-point similarity score.The ratings total 28,600 individual judgments.Source: 1) Dataset · p. 7

Model Training

• The four ordinal ratings were normalized to [0, 1] under an equal-spacing assumption, and models were evaluated with grouped five-fold cross-validation.Each unique pair was kept entirely in either the training or test subset; performance was assessed with MSE, RMSE, and R2.Source: 1) Dataset · p. 7, 3) Model Training · pp. 8–9

Feature Generation

• Seven feature sets use RGB channel differences, HSI differences, and COLIBRI category differences alone or in combination.COLIBRI represents each color with 9 hue categories, 4 saturation levels, and 5 intensity levels.Source: 2) Feature Generation · p. 7

Comparative evaluation of models

• R2 was 0.5954 ± 0.023 for COLIBRI, versus 0.4790 ± 0.016 for RGB and 0.4932 ± 0.017 for HSI under Linear Regression.Adding RGB to COLIBRI raised average R2 to 0.6253 ± 0.025; the full feature set reached 0.6273 ± 0.023.Source: 4) Comparative evaluation of models · p. 9, Table III · p. 10

Experimental results analysis

• Figure 4 shows similar ΔE values for “Not similar” in both experiments; ratings correlated 0.817, with ICC(2,1)=0.826 and Fleiss’ Kappa of 0.679 and 0.417.The Fleiss’ Kappa values correspond to Experiments 1 and 2, respectively.Source: Figure 4 · p. 9, 4) Comparative evaluation of models · pp. 9–10

Comparative evaluation of models

• R2 = 0.7031 ± 0.013 for LightGBM with RGB+HSI+COLIBRI, the numerically highest average coefficient of determination reported.The same configuration achieved RMSE=0.2002±0.002 and MSE=0.0401±0.001, with low variability across folds.Source: 4) Comparative evaluation of models · p. 9, Table III · p. 10

Experimental results analysis

• Linear regression coefficients quantify each feature’s contribution direction and magnitude, while logistic regression fits ΔE thresholds for ratings ≥4, ≥3, and ≥2.The thresholds are used to obtain numerical boundaries between perceptual similarity categories.Source: 4) Comparative evaluation of models · pp. 9–10, Table IV · p. 10, Table V · p. 10

Performance evaluation

• The proposed model’s normalized color-difference score ranges from 0 to 1, with larger values indicating greater perceived difference.The section compares its predictions with CIE76, CIE94, CIEDE2000, and CMC (2:1).Source: B. Performance Evaluation · p. 11
• Similarity predictions are assigned to the nearest anchor: 0, 1/3, 2/3, or 1 for the four linguistic categories.The category boundaries are 0.167, 0.500, and 0.833.Source: B. Performance Evaluation · p. 11
• CIEDE2000 interpretations use conventional ranges from Hardly perceptible to Strongly different, and Table VI compares its interpretations with the proposed model.The comparison uses selected color pairs.Source: B. Performance Evaluation · p. 11

• Two experiments collected 28,600 evaluations from seven observers on 2,000 color pairs presented under separated and adjacent conditions.Source: §V · p. 11
• LightGBM with RGB+HSI+COLIBRI features achieved R2 = 0.7031 and RMSE = 0.2002, the best reported performance.Source: §V · p. 11
• The “Very Similar” boundary shifted from ∆E ≤4.221 under separation to ∆E ≤2.069 under no separation.Source: §V · p. 11
• The study is limited by a relatively small observer group, web-based displays, and treating ordinal similarity categories as equally spaced during normalization.The authors describe equal spacing as a practical modeling approximation, not evidence that adjacent categories are perceptually equidistant.Source: §V · p. 11
• Future work will use larger-scale perceptual experiments, controlled display conditions, and adaptive neuro-fuzzy approaches.Source: §V · p. 11