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Image - Separating the authentic from the forgeries

Image - Separating the real from the fake

"Return of the Hunters," an image known to be made by Pieter Bruegel the Elder, a Dutch master active during the region's 'golden era' in the 1500s. Oxford University art historian Martin Kemp described the painting in Nature as "testimony to the scientific observation of light and geographical features." Original image in Kunsthistorisches Museum, Vienna, Austria

Pieter Breugel the Elder was a very popular painter, with a huge body of work that was closely imitated - so, there are a lot of outright forgeries.

Now, however, researchers at Dartmouth College, New Hampshire, have found a new way to separate the real from the fake, by mathematically analyzing images that are known to be genuine, such as "Return of the Hunters," and comparing to images whose authenticity is questionable.

Writing in the Proceedings of the National Academy of Sciences (PNAS), Daniel Rockmore describes how he and his team used an approach known as 'sparse coding' to build a virtual library of an artist's works, and break them down into the simplest possible visual elements.

With sparse coding analysis, the digital elements of an artist's known works (shown above) are refined until the fewest are required to recreate a piece.

The result is used as a sort of template which can only reproduce the exact, fractal-like style of an original, thereby theoretically weeding out imitations.

According to the summary explanation he gave in a BBC News article, the method works by dividing digital versions of all of the artist's confirmed works into 144 squares, or a dozen columns of 12 rows each.

Then a set of "basis functions" was constructed, which was initially a set of random shapes and forms in black-and-white.

A computer then modified them until, for any given cut-down piece of the artist's work, some subset of the basis functions could be combined in some proportion to recreate the piece.

The basis functions are then further refined to ensure that the smallest possible number of them is required to generate any given piece - they are the "sparsest" set of functions that reproduces the artist's work.

It's an approach that has the potential to work well in distributed computing, with, say, one computer assigned to each square.

When used in conjuction with laser spectroscopic analysis and other tools, the method can help to pin down whether an image is real or an imitation.

-Dan Drollette, iSGTW. For details of this computer-aided mathematical technique, see "Article #09-10530: Quantification of artistic style through sparse coding analysis in the drawings of Pieter Bruegel the Elder," in the upcoming issue of PNAS.

What do you think of sparse coding and its potential in distributed computing? See our iSGTW forum on Nature Networks.

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