Page last updated at 20:11 GMT, Monday, 4 January 2010

Computer method 'spots art fakes'

'The Witch of Malleghem' by Pieter Bruegel the Elder (SPL)
The method spots imitations of works by Pieter Bruegel the Elder

A simple method to distinguish artistic fakes and imitations has been demonstrated by researchers.

The approach, known as "sparse coding", builds a virtual library of an artist's works and breaks them down into the simplest possible visual elements.

Verifiable works by that artist can be rebuilt using varying proportions of those simple elements, while imitators' works cannot.

The work is reported in Proceedings of the National Academy of Sciences.

The mathematical analysis of artworks is a relatively new discipline, which gained worldwide attention when it emerged in 1999 that Jackson Pollock's "drip paintings" could be cast in the mathematics of fractals - patterns that repeat at ever-smaller scales.

However, the claim that a fractal analysis could be used to identify Pollock-like paintings of unknown provenance remains a subject of some controversy.

Sparse richness

Since that time, a number of approaches to identify the origins of artworks have been attempted, yielding varying degrees of certainty in the results.

Now, Daniel Rockmore of Dartmouth College in the US and his colleagues have shown a straightforward method known as sparse coding that, so far, appears to be significantly more accurate than previous attempts.

Visual elements in "sparse coding" technique
Each of an artist's works is cut into 144 pieces (12 rows and 12 columns)
A set of 144 random elements the size of each piece is generated
Each element is altered by a computer until some combination of them can recreate each piece from the original artwork
The elements (shown above) are refined until the fewest are required to recreate each piece
Those refined pieces will be unable to reproduce the work of an imitator or a fake

The method works by dividing digital versions of all of an artist's confirmed works into 144 squares - 12 columns of 12 rows each.

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

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

The basis functions are refined further 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.

The team tried the approach on the works of Pieter Bruegel the Elder, a 16th century Flemish painter whose original works are well-known and who had a number of imitators.

Upon using the sparse coding approach on the artist's known works, the Dartmouth team showed that the optimised basis functions were unable to reproduce the imitations.

However, Professor Rockmore said that although authentication of works was an application that would appeal to many people, sparse coding could lend its analysis to a number of problems in the study of art.

"Our hope is that it becomes more of what people call technical art history," he told BBC News.

"Instead of asking 'was this painting done 40 years after these drawings?', one might instead ask 'how are these statistics evolving over time and what does that say about the working style?'.

"For many people those are more central questions, and probably more substantial questions."

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