A New Algorithm to Attack Art Fraud

Sparse-coding technique spots fakes

Photos: Metropolitan Museum of Art

Spot the Fake: These drawings were long attributed to Pieter Bruegel the Elder, but only the top one is authentic.

Every few years, we're wowed by news of some jaw-dropping sum paid for a previously unknown painting or drawing by a famous artist. But how can a buyer truly be sure that a piece is a legitimate creation of, say, Leonardo or Gauguin? Mathematicians at Dartmouth College, in Hanover, N.H., may have the answer. They recently presented a computer-based statistical analysis technique which they say will help art historians and conservators discover even the most skilled forgery.

Their method, called sparse coding, learns what characterizes the artist's style at a level of detail that is practically imperceptible to the eye of even the most experienced appraiser. It works by examining small patches of a picture and breaking them down to a set of essential elements.

"The aim is to establish for each artist a vocabulary of brush strokes or pencil marks that defines his or her style," says James M. Hughes, a doctoral candidate at Dartmouth who coauthored the research reported in Proceedings of the National Academy of Sciences. The style of a great painter like van Gogh is so distinctive that if his craft had been writing memos, it would seem as though he'd had a typewriter with its own custom-made font and type size. No matter the document, it would comprise a set of characters with the same font and proportions. And although cutting up a memo and rearranging the letters would change the message, it would still be clear that it came from the same author. Conversely, a document created by someone else might deliver the exact same message yet not pass a careful examination for authenticity, because the underlying characters would be slightly—or even vastly—different.

The researchers focused on the notion of sparseness, which refers to the ability to represent an image with as little information as possible. The concept is analogous to digital compression.

To test sparse coding, the researchers used it to compare the drawings of 16th-century Flemish artist Pieter Bruegel the Elder with known Bruegel knockoffs. The model was trained on swatches from eight real Bruegel drawings. The sparse-coding algorithm stripped each of them down to a set of basic elements needed to re-create the full drawing. When sections taken from any of the five imitations were stripped down, the model revealed that more often than not, there were readily apparent differences in the sparsity of information, meaning that the imitations were significantly different from the authentic Bruegel drawings.

Asked if sparse coding could be used by a technically savvy art forger to, in effect, reverse engineer an artist's technique, Hughes replies, "The short answer is no." First of all, he says, size matters. The code makes a determination of what the important features are at three different scales—something that would be nearly impossible for a forger to keep track of as he moves a brush across a canvas. Second, he says, sparse coding reports its findings as a set of statistical distributions, making it very difficult to turn that information into something that a forger would find useful.

Hughes says that sparse coding should be viewed as a new addition to the suite of tools used by a conservator or art historian for authentication [see "Art Fraud Forensics," IEEE Spectrum, July 2009]. James Coddington, chief conservator at the Museum of Modern Art, in New York City, agrees. "Computers can be helpful," Coddington admits, "but art is far too complex to expect that you could just put a painting in one side of a machine and a green light or a red light will tell you whether the piece is authentic."

Coddington says he sees how sparse coding could help identify a drawing, because "there's going to be an internal consistency among the artist's works." But the software won't replace human connoisseurship, historical knowledge, chemistry, and other tools.

This article originally appeared in print as "A New Attack on Art Fraud".

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