The persistence of painting styles
Reetikaa Reddy Munnangi, Barbara Giunti
TL;DR
This work introduces a persistent homology ($PH$) based framework to quantify artistic styles by converting paintings into multi-channel representations and computing $0$-PH and $1$-PH across a pixel-threshold filtration. Distances between signatures are measured with the bottleneck distance ($d_B$) and the $1$-Wasserstein distance ($d_W^1$), with statistical significance established via permutation tests. The method successfully differentiates artists across currents and within currents, and can separate AI-generated images in an artist's style, though some features are non-significant yet still informative about shared stylistic traits. While offering a principled, interpretable, and scalable approach, the method is computationally intensive, motivating future work on higher-resolution data and potential extensions to 3D objects or sculpture as well as collaboration with art experts for deeper interpretation.
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.