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Researcher uses math to probe art fakes

Six faces in Perugino's “Madonna With Child” were analyzed for high-resolution consistencies. The faces labeled 1, 2 and 3 showed a consistent style, while the others exhibited wide variations. The color image was converted to grayscale for the analysis.
Six faces in Perugino's “Madonna With Child” were analyzed for high-resolution consistencies. The faces labeled 1, 2 and 3 showed a consistent style, while the others exhibited wide variations. The color image was converted to grayscale for the analysis.PNAS
/ Source: The Associated Press

True art would never be mistaken for a crude, paint-by-the-numbers copy. But a researcher has developed a statistical tool for determining whether a purported masterpiece is only a skilled imitation, suggesting that art may be a numbers game after all.

Using high-resolution digital images and complex mathematical formulas, associate professor Hany Farid of Dartmouth College analyzed works by Renaissance artists to determine their authenticity.

His computer program was able to accurately separate eight drawings by 16th century Flemish artist Pieter Bruegel the Elder from five drawings by imitators. It also found that portions of a painting by Italian artist Pietro di Cristoforo Vannucci, known as Perugino, were probably done by Perugino's apprentices.

Farid described his work, presented Monday in the Proceedings of the National Academy of Sciences, as "simply another tool that is contributing to the dialogue of art authenticating" and said more work is needed before digital analysis of art could be done on a wider scale.

Art experts reacted warily to the prospect that a masterpiece could be reduced to the sum of its digital parts.

"I'm highly skeptical of using the computer for this kind of approach," said Laurence Kanter, curator in charge of the Robert Lehman collection at the Metropolitan Museum of Art in New York City. "It's very possible that a program like that could be exploited to great advantage, but I still need to be persuaded."

Farid, a professor of applied mathematics and computer science, said his computer program was similar to digital analysis of other visual media like photographs, in which digital compression converts the photograph or image to an accessible, lower-resolution format like JPEG.

Masterpiece broken into 'wavelets'
In this case, high-resolution photographs of the painting and drawings were digitally compressed so the art image could be broken down into simpler, varying elements -- called "wavelets."

With the Perugino painting, "Madonna with Child" -- which depicts the madonna, baby Jesus and two saints on either side of the pair -- characteristics like the distance between faces and the orientation of horizontal, vertical and diagonal elements were subjected to statistical analysis based in part from what was known about the style of the Italian master.

Before the analysis could be done, however, the painting was first converted to a grayscale that eliminated the painting's color. That, combined with the fact that the analysis was conducted on a photographic image of the painting and not the painting itself, were obvious limitations of the tool, Farid acknowledged.

"We did delete some valuable information," he said in a telephone interview.

Science has previously attempted to quantify art, with varying degrees of success. Researchers have used complex mathematical relationships derived from chaos theory to study Jackson Pollack's drip paintings. Other empirical methods have looked at the crack lines that appear over time in older paintings. And art historians and scientists often use forensic methods like X-ray analysis and surface analysis of painting materials to help authenticate old paintings.

"What we've tried to do is capture certain mathematical properties of an artist in terms of their underlying style, properties almost certainly not visible to human eyes," he said.

In the Perugino case, Farid's analysis found that Perugino painted only a portion of the work and his apprentices other parts -- a common practice among Renaissance masters whose work was in such high demand that they kept workshops of painters to carry out their many commissions.

Farid worked with Dartmouth's Hood Museum of Art, which had purchased the painting in 1999 not knowing whether it was actually done by Perugino. Kathy Hart, the museum's interim director, said Farid's analysis was "falling into line" with the opinions of other art experts.

One those experts was the Metropolitan's Kanter.

"You can compute it in your mind. You don't need a machine," Kanter said. "Everything lies in the interpretation of evidence."

A clear beneficiary of the Farid and Kanter analyses was the Hood Museum, since both agree Perugino painted part of the painting. Kanter estimated the authenticated painting's worth at about $10 million. The museum paid "substantially less," said a Hood spokeswoman who wouldn't divulge the exact cost.