The persistence of painting styles

2025-11-17

AI Summary

This study addresses the challenge of objectively quantifying and distinguishing individual artistic styles, inter- and intra-school stylistic variations, and human-created versus AI-generated artworks. We propose a topological style representation method grounded in persistent homology—the first systematic application of this algebraic topological tool to painting style analysis—by extracting multi-scale topological features from images to construct metricizable style vectors. Experiments demonstrate high discriminative accuracy (>92% average) across three tasks: cross-school classification, intra-school artist identification, and human–AI artwork differentiation. The method exhibits strong robustness to common image perturbations, including preprocessing variations and resolution changes. Our core contribution is the establishment of the first algebraic-topological framework for mathematically characterizing artistic style, offering a novel, interpretable, unsupervised, and geometry-driven paradigm for style analysis.

Technology Category

• Humans and AI: Other Foundations of Human Computation & AI
• Computer Vision: Visual Reasoning & Symbolic Representations
• Machine Learning: Representation Learning

Application Category

• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Art is a deeply personal and expressive medium, where each artist brings their own style, technique, and cultural background into their work. Traditionally, identifying artistic styles has been the job of art historians or critics, relying on visual intuition and experience. However, with the advancement of mathematical tools, we can explore art through more structured lens. In this work, we show how persistent homology (PH), a method from topological data analysis, provides objective and interpretable insights on artistic styles. We show how PH can, with statistical certainty, differentiate between artists, both from different artistic currents and from the same one, and distinguish images of an artist from an AI-generated image in the artist's style.

Problem

• Using persistent homology to objectively differentiate artistic styles
• Distinguishing between artists from different and same artistic movements
• Identifying human-created versus AI-generated artworks in specific styles

Innovation

• Persistent homology analyzes artistic styles objectively
• Topological data differentiates artists across art movements
• Method distinguishes human artworks from AI-generated imitations