Piet Mondrian's neo-plastic works are spare compositions of vertical and horizontal black lines and rectangles of red, yellow, blue and black atop a white field. While these works appear, at first glance to be "simple," in fact Mondrian's compositions are quite subtle. We know from eye-witness reports and x-radiography of the works that the artist worked and reworked his compositions, subtly altering the positions of their elements until he was satisfied.
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We seek a computer based method for inferring the compositional style of Mondrian's neo-plastic works. Such a system might reveal compositional principles guiding his works, and possibly even aid in distinguishing genuine Mondrian works from fake works, or "near misses." Of course, computer image-based methods are currently too crude to be used in the high-stakes field of genuine art authentication: Art authentication relies on a range of techniques, from studies of material (pigments, supports, ...), provenance (the documentary record of ownership of the work), deep knowledge of an artist's oeuvre, the working methods of apprentices, copyists, forgers, and of course the connoisseurs' highly trained eye.
We developed image analysis algorithms that would convert digital images of Mondrian's neo-plastic works into a spare representation of idealized lines and colored rectangles. Of course, our representation lost the subtleties of color (especially in the whites and off-whites), properties of paint and handling. Nevertheless, our representation led to images that are clearly recognizable as being derived from Mondrian's works, and thus preserved some key aspects of compositional style.
We used machine learning to learn to distinguish genuine Mondrian compositions from "near misses." In doing so, our method could generate "faux" Mondrians. While some of these compositions bear striking resemblance to genuine Mondrian compositions, they do not yet have the subtle properties that would lead an expert to judge them as genuine. More work is needed for that.