Source-linked AI summary
History of art paintings through the lens of entropy and complexity
Higor Y. D. Sigaki, Matjaz Perc, Haroldo V. Ribeiro
TL;DR
The paper quantitatively analyzes artworks through local complexity-entropy measures connected to art-historical concepts. These measures trace historical transitions, distinguish and organize styles, while remaining limited by their local scale.
Problem
Quantitative measures are needed to connect artworks’ visual organization with art-historical concepts and cultural evolution.
Method
The study converts 137,364 WikiArt images into RGB matrices and estimates permutation entropy and statistical complexity from local spatial patterns.
Results
The complexity-entropy trajectory agrees with major art-historical periods, and styles can be distinguished, hierarchically grouped, and related to linear/haptic versus painterly/optic modes.
Takeaways & Limitations
Complexity-entropy measures provide a quantitative ruler for comparing artistic styles and tracing their historical evolution.
Takeaways & Limitations
Because both measures use only local artwork scales, they cannot capture all the uniqueness and complexity of art.
Abstract
from arXiv · showhide
Art is the ultimate expression of human creativity that is deeply influenced by the philosophy and culture of the corresponding historical epoch. The quantitative analysis of art is therefore essential for better understanding human cultural evolution. Here we present a large-scale quantitative analysis of almost 140 thousand paintings, spanning nearly a millennium of art history. Based on the local spatial patterns in the images of these paintings, we estimate the permutation entropy and the statistical complexity of each painting. These measures map the degree of visual order of artworks into a scale of order-disorder and simplicity-complexity that locally reflects qualitative categories proposed by art historians. The dynamical behavior of these measures reveals a clear temporal evolution of art, marked by transitions that agree with the main historical periods of art. Our research shows that different artistic styles have a distinct average degree of entropy and complexity, thus allowing a hierarchical organization and clustering of styles according to these metrics. We have further verified that the identified groups correspond well with the textual content used to qualitatively describe the styles, and that the employed complexity-entropy measures can be used for an effective classification of artworks.
Evolution of Art.
The study connects local pixel-order measures to art-historical concepts, using a large dataset to quantify artworks across styles and periods.
- Evolution of Art.: The complexity-entropy plane partially reflects Wölfflin’s linear–painterly and Riegl’s haptic–optic distinctions.These concepts describe differences in contour clarity, object separation, spatial depth, light, color, and shadow.
- Evolution of Art.: 137,364 visual artworks spanning more than a millennium were converted into RGB pixel matrices for quantitative analysis.The dataset comes from WikiArt.org and includes works by over two thousand artists and more than one hundred styles.
Results.
The measures reveal a robust temporal trajectory whose transitions correspond to major art-historical periods and relate to changing modes of representation.
- Results.: Artworks from the 9th–17th centuries are more regular than those from the 19th–mid-20th centuries, while post-1950 works are more regular still.Changes in the complexity-entropy plane also accelerate after the 19th century.
- Results.: The first transition agrees with a shift from linear/haptic to painterly/optic representation described by Wölfflin and Riegl.The authors note that these historical conceptions differ over whether the transition is continuous or cyclical.
- Results.: The measures expose a global evolution consistent with Wölfflin’s cyclical conception, although local temporal persistence and Gaiger’s critique challenge that interpretation.The paper presents the complexity-entropy trajectory as consistent with a spiral-like rather than exact return in art history.
- Results.: The study relates the intensified post-19th-century changes to styles such as Neoclassicism and Impressionism and to increased color-contrast diversity.This comparison connects the observed trajectory with prior findings on artistic styles and color contrast.
- Results.: The complexity-entropy trajectory identifies three regions corresponding to pre-Modern art, Modern Art, and the transition to Contemporary/Postmodern Art.The periods align with historical divisions including Impressionism, avant-garde styles, and the emergence of Pop Art.
Distinguishing among artistic styles.
Artistic styles occupy distinct regions of the complexity-entropy plane, enabling comparisons and grouping based on local pixel ordering.
- Distinguishing among artistic styles.: The 92 styles with more than 100 images occupy different average H–C locations, with 41 styles exceeding 500 images labeled for visualization.Error bars represent standard errors of the mean.
- Distinguishing among artistic styles.: Styles with low complexity and high entropy, including Impressionism, Pointillism, and Fauvism, use diffuse brushstrokes and blended colors.These visual features avoid sharp edges and correspond to their positions in the complexity-entropy plane.
- Distinguishing among artistic styles.: Euclidean distances between styles in the complexity-entropy plane serve as dissimilarities based on local pixel ordering.Closer styles are treated as more similar, while larger distances indicate greater dissimilarity.
- Distinguishing among artistic styles.: Style groups partially reflect temporal proximity and organize representation along the linear/haptic–painterly/optic scale.Several groups consist mainly of Postmodern styles, while other clusters include styles such as Kinetic Art, Hard Edge Painting, and Concretism.
Hierarchical structure of artistic styles.
The study hierarchically organizes artistic styles using distances in the complexity-entropy plane, producing groups that partially reflect historical timing, visual representation, and textual descriptions.
- Historical and visual structure: The resulting groups partially reflect temporal localization, with several styles emerging together or near each other assigned to the same group.The first five groups contain mainly Postmodern styles, while other groups combine styles with related local pixel arrangements.
- Historical and visual structure: The hierarchy also organizes styles along the linear/haptic versus painterly/optic representation scale, including diffuse-brushwork styles at one extreme.Impressionism, Pointillism, and Divisionism are among the styles associated with small brush strokes and softened edges.
- Textual validation: A text-based Wikipedia clustering yields 24 groups, while its agreement with the complexity-entropy clustering is above the null model with h = 0.49, c = 0.40, and v = 0.44.The comparison uses TF-IDF keywords and homogeneity, completeness, and v-measure.
Predicting artistic styles.
The study tests whether permutation entropy and statistical complexity can predict artistic styles from only two image-derived values. Across four classifiers, accuracy is about 18% and significantly exceeds chance, though the authors describe it as modest for practical applications.
- Model behavior: For nearest neighbors, training and cross-validation scores show no significant improvement beyond roughly 50% of the training data or above approximately 250 neighbors.The figure reports 95% confidence intervals from 10-fold cross-validation.
- Classification results: ≈18% accuracy is achieved by nearest neighbors, random forest, support vector machine, and neural network classifiers across 20 styles, exceeding chance but remaining modest for practical applications.The classification uses only the two features H and C, representing roughly one million-pixel images by two values.
- Classification results: The values of H and C encode information about artistic style, supporting their use for style classification after a severe dimensionality reduction.The authors note that the measures are fast, easy to parallelize, and scalable because they are local.
- Feature basis: The broader analysis characterizes almost 140 thousand artworks with permutation entropy H and statistical complexity C, mapping local pixel order onto order-disorder and simplicity-complexity scales.These measures also distinguish styles by their average entropy and complexity and support hierarchical organization.
Discussion and Conclusions.
The study traces art’s historical evolution using local complexity measures, while showing that these metrics connect with art-historical concepts but cannot capture every aspect of artistic uniqueness.
- Discussion and Conclusions.: Transitions in the complexity-entropy trajectory align with major art-historical periods, including shifts from linear/haptic to painterly/optic and back again.Each period exhibits a distinct degree of entropy and complexity.
- Discussion and Conclusions.: Local complexity measures connect artworks’ spatial organization with art-historical distinctions such as Wölfflin’s linear–painterly and Riegl’s haptic–optic categories.The correspondence is partial and local rather than a complete account of these categories.
- Discussion and Conclusions.: The study’s local-scale measures cannot capture all the uniqueness and complexity of art, limiting the complexity-entropy plane to one possible projection of artistic evolution.The authors frame this projection through Wölfflin’s metaphor of art as a spiral movement.
- Discussion and Conclusions.: The analysis uses local ordinal patterns from image matrices, converting artwork pixels into permutation distributions from which normalized entropy and statistical complexity are calculated.The method uses 2 × 2 sliding partitions, yielding 24 possible ordinal patterns.
- Discussion and Conclusions.: The statistical complexity complements entropy by measuring structural organization beyond randomness, with complexity vanishing at both complete order and complete disorder.The complexity-entropy plane represents complexity as a function of entropy.