用拓扑方法量化画风差异，区分真迹与AI仿作。
The persistence of painting styles
- 用持久同调分析画作笔触分布的拓扑结构
- 能统计显著区分不同流派及同一流派的艺术家
- 适合艺术鉴定、数字美学研究者参考
艺术是高度个人化且富有表现力的媒介，每位艺术家都将其独特的风格、技巧和文化背景融入作品中。传统上，识别艺术风格依赖艺术史学家或评论家的视觉直觉与经验。随着数学工具的进步，我们得以通过更系统的视角探索艺术。本文展示持久同调（PH）——一种拓扑数据分析方法——如何为艺术风格提供客观且可解释的洞察。我们证明，借助统计置信度，PH能够区分不同艺术流派的艺术家，也能区分同一流派中的不同创作者，并有效辨别艺术家真迹与以该风格生成的AI图像。
原文摘要 · Abstract (English)
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.
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