In recent years, art historians have deployed increasingly sophisticated scientific tools--from analysis of isotopes to infrared reflectography--to evaluate the authenticity of artworks. Most of these require physical testing. Now, three mathematicians have proposed a purely mathematical technique that requires only a digitized image and shown that they can use it to distinguish authentic drawings by Flemish artist Pieter Bruegel the Elder (ca. 1525-1569) from imitations by his contemporaries and followers.
Siwei Lyu, Daniel Rockmore, and Hany Farid of Dartmouth College in Hanover, New Hampshire, applied "wavelet decomposition" (the same trick used to compress JPEG images) to 13 drawings: eight authentic Bruegels and five imitations. As anyone with a slow Internet connection has noticed, JPEGs can be compressed so that a rough version appears right away, followed by progressive refinements.
The trio speculated that these refinements contain information that our eyes recognize as the style of the artist: how often the artist employs lines of a certain shape or degree of tilt. "The good analogy is to stylometry in literature," says Rockmore. "Words like 'but' don't carry context information, but the frequency with which you use them is a pretty good signature of your writing style." The team's computer program decided whether a drawing was a genuine Bruegel based on statistics of how frequently the artist made a stroke within 15 degrees of vertical or 15 degrees of horizontal, along with more subtle statistics on correlations between nearby strokes.
Bruegel made a good subject for several reasons. "He has a huge body of work, and he was very heavily imitated, so there's a lot of fakes," Farid says. The fakes have been spotted by forensic clues such as watermarks on the paper that were not used in Bruegel's lifetime. As Farid had hoped, the computer was able to tell the difference on the basis of style alone in every case--no watermarks required. They report the details online this week in the Proceedings of the National Academy of Sciences.
Statisticians and art curators say that wavelet analysis looks like a promising tool, but it has yet to pass one important test. "It would be more persuasive if they announced a painting accepted as legitimate was fraudulent," says David Donoho, a statistician at Stanford University. "If they made a call like that, and further work showed they were correct, it would be a much more powerful conclusion." Nadine Orenstein, the curator of the 2001 Bruegel exhibition at the Metropolitan Museum of Art from which the researchers got their digital images, suggests that they should try Rembrandt, several of whose paintings (or alleged paintings) remain controversial.