In the world of art, the authenticity of a work can make millions of dollars worth of difference. Although it's possible to detect recent frauds based on objective measures like chemicals in the paints, it often requires subjective judgements to determine the difference between the work of a true master having an off week and the product of one of that master's students. A paper that will appear in PNAS suggests that a technique borrowed from vision research may help take some of the subjectivity out of this sort of analysis.

The study of artwork through math and statistics is known as "stylometry," and is a relatively recent development—similar methods have been used to analyze literature for much longer. The new paper uses a technique called sparse coding, in which analysts break down works of art into tiny patches and represent them as a series mathematical functions. By comparing the functions produced with authentic artwork to those from possible imitators, they can produce an objective measure of whether the piece in question is real or fake.

Sparse coding was originally developed for studying how neurons in the brain responded to visuals. It works by breaking down an image—for simplicity's sake, usually one in grayscale—into mathematical functions, pixel by pixel. The images that are broken down are just small patches of whole works, not much more than a dozen pixels square.

In their experiments, the researchers used the works of Flemish artist Pieter Bruegel the Elder as guinea pigs. Bruegel's art often depicts pastoral scenes, an image type that sparse coding is very good at processing, and his work spawned many imitators in his time, making him an ideal subject. First, the researchers took several known authentic Bruegel works, rendered them in grayscale, and processed them with sparse coding in tiny patches of 8x8, 12x12, and 16x16 pixels in different trials, making them into maps of math functions.

Once this was done, they processed patches from other drawings onto the authentic work, and looked at the probability of whether the new image's functions mapped onto the original. If the average probability peak for each pixel comparison was very sharp, the second image was more likely to be authentic; if the peak was more spread out or less prominent, the second image was probably a fake.

For their trials, they broke eight authentic Bruegel works down into mathematical functions, and did pairwise comparisons of their patches with those of a second authentic work and those of a fake. In seven of the eight cases, the method produced correct results; that is, a second authentic work had a higher probability of mapping correctly to the first authentic work, while the fake did not map as well.

While the application of sparse coding is decidedly effective in this case, its usefulness is still somewhat limited. It does not process all artistic styles equally well and, generally speaking, the process needs a good-sized body of consistent work from a single artist before it can compare possible imitations. Sparse coding also doesn't work as well when given paintings of different subject matter, and still is best at landscapes. The authors acknowledge that sparse coding is far from a replacement for tools already in use, but conclude that, in certain situations, it has a pretty good eye, and can be a useful supplement.

PNAS, 2010. DOI: 10.1073/pnas.0910530107