When the brain processes visual input, information is mapped into patterns of neural activation, with some form of code defining which neural-activity pattern corresponds to a certain piece of information in the input image. Although many aspects of this coding process are yet to be understood, there exists a body of theoretical, computational and experimental evidence suggesting that the 'neural code' is sparse. This means that if a set of basis functions is found that can be used to reconstruct all images, then any given image is represented in terms of a linear superposition of only a small number of these functions.

Credit: © ALBERTINA, VIENNA

James Hughes and colleagues have now taken the idea of sparse coding into a very different context — showing its usefulness for quantifying artistic style (Proc. Natl Acad. Sci. USA doi: 10.1073/pnas.0910530107; 2010). In particular, they have looked at drawings by the Netherlandish Renaissance artist Pieter Bruegel the Elder (believed to be seen as 'the painter' in his drawing, The Painter and The Connoisseur), and have set up a sparse-coding model which, after suitable training, can discriminate successfully between authentic Bruegel drawings and imitations.

Several ways of using mathematical and statistical methods for analysing visual art have been investigated over the past decade or so, not least with a view to helping art historians authenticate works. Such 'stylometric' approaches include fractal analysis (famously applied to Jackson Pollock's drip paintings), wavelet-based techniques and so-called multiresolution hidden Markov methods. But Hughes et al. expect that the sparse-coding approach should, given its success in analysing natural images, offer a straightforward and germane route to modelling drawings and other two-dimensional media, and one that provides, unlike other approaches, a simple quantitative metric.

In their study of Bruegel drawings, Hughes et al. used a set of works securely attributable to Bruegel to train their sparse-coding model, and then showed that the resulting basis functions can be combined to sparsely rebuild established Bruegel drawings; this sparseness, however, is lost when reconstructing known Bruegel imitations. Their approach compares favourably with an earlier wavelet-based analysis of the same Bruegel drawings, but a number of caveats still remain: specifically, sparsecoding requires a sufficient number of known examples to build the basis set; also, the style of an artist must not vary significantly across the works considered. Nonetheless, the results are encouraging and indicate that statistics could usefully complement the traditional tools of art analysis.