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Artsy Math

If you think science and mathematics have no place in art, then think again. If you're an artist, you're probably not going to spend your time calculating your every stroke. However, if you're a curator of an art museum, in time you may be relying on a computational technique called wavelet decomposition to detect forgeries and frauds from the real thing.

The technique works by breaking down a high-resolution digital scan of an image into more basic images called subbands. These subbands focus on particular elements of the original image, filtering out other elements. Subbands allow a computer to analyze an image for various statistics, such as for broad brush strokes and smaller, quicker, detail brush strokes, and for darkness and lightness.

In theory, an individual artist's subbands will have a certain consistency, and they will be distinguishable from another artist's subbands. For example, in the case of a forgery, the imitator may exhibit jerkier brush strokes than those of the master artist. Wavelet decomposition can expose differences in technique that the naked eye cannot see.

Researchers have used the technique to compare subbands from genuine paintings by the 16th-century artist Pieter Brueghel the Elder to five imitations believed up until a decade ago to have been genuine Brueghels as well. They found that the subbands of the genuine Brughels all shared similar statistics while the imitations varied greatly from the genuine Brughels, as well as from each other.

Significantly more studies like this one will need to be conducted before the art world goes so far as to adopt wavelet decomposition as a foolproof method of fraud detection, but the technique does look promising.

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