Computational Investigation of Abstraction in Claude Monet's Water Lilies Through Brushstroke Analysis

Claude Monet's late paintings of Water Lilies exhibit stylistic transformations that are often characterized by art historians as increasingly abstract and gesturally expressive. However, it remains challenging to define and systematically identify this stylistic shift. Here, we introduce a machine learning framework for analyzing Monet's evolving brushwork using streamline curves: computational representations that capture the dynamic movement patterns inherent in brushstrokes. From 554 image patches sampled from 47 paintings spanning early (pre-1913) and later (post-1913) periods of Monet's output, we extract streamlines and compute geometric features for each, including smoothness of curvature and directional variability. Each image is represented as a set of streamline feature vectors, a data type referred to as distributional. A new deep neural network architecture named Composition to Attribute (C2A) is designed for classifying distributional data. We hypothesize that Monet's so-called 'abstract' style does not uniformly characterize all late-period Water Lilies, and that non-abstract flowers, regardless of period, share similar brushwork qualities. Under these assumptions, building on C2A, we propose a novel learning paradigm named Discover Embedded Group with Asymmetry (DEGA) which enforces a shared distribution of DNN-extracted features for non-abstract flower patches across both periods while distinguishing the abstract ones. DEGA reveals a meaningful two-dimensional feature space, where one dimension differentiates abstract from mimetic Water Lilies, while the other separates abstract flowers from close-up flowers of the early period. Our findings suggest that the so-called 'abstract' qualities of Monet's late style retain certain visual affinities with his earlier approach to depicting close-up floral motifs. When this brushwork is used in more expansive scenes, the depiction of flowers shifts away from realistic renderings of individual petals toward a looser, more allusive expression, conveying a sense of floral presence rather than botanical detail. This study highlights the value of computational analysis for a more accurate understanding of an artist's stylistic development.