Painting by numbers

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From Baroque painters to the aesthetics of environment, Felix Grant turns his attention to statistical analysis in the arts

One of the staple exercises in statistics education is to make a light-hearted foray into that old academic wrangle: were the Shakespeare plays and sonnets really written by William Shakespeare or by [insert your favourite candidate here]? Various metrics are analysed by whatever techniques are being taught, with a view to assessing similarity and difference.

Real literary academics, of course, have visited the same methods with serious intent, and similar debates exist within the visual plastic arts. Was this unsigned painting produced by old master X, or by unknown Y?

A very well-known example of such a dispute concerns the early 17th century Baroque painter, Artemisia Gentileschi. In the last 50 years she has been rehabilitated in art history circles and is now widely recognised, but for centuries much of her work was wrongly attributed to others. The most frequent misattributions were to her father Orazio (which most experts now regard as blatantly ridiculous but which can be blamed on signatures) or to Michelangelo Merisi da Caravaggio, who painted in a superficially similar style a generation earlier. Reattribution was in most cases visual by expert witnesses, but in a few cases appeal was made to more objective means.

Disputes still occur, however, and as recently as January of this year a bitter disagreement between two national art institutions, with significant financial implications, was finally settled. The process is plastered with nondisclosure clauses, but people love to talk about their interesting cases, whether in art or science or finance. In this case, the resolution of the quarrel was based on evidence from a number of computerised data analytic methods in a university statistical science back room. The painting in question (not, I hasten to emphasise, illustrated here) was an obscure minor piece and experts disagreed over whether it had been created by Gentileschi, by Caravaggio, or by some unknown artist imitating one of those.

The investigation involved isolating discriminant variables from hundreds of metrics sampled across numerous works by the two artists, then comparing the specifics of the disputed item with their general distributions. Some of those metrics were purely physical: thickness of paint film, for example, or exactly how that thickness is sub composed from glaze or scumble layers, microstructure of the underlying gesso primer layer, or the depth and structure of surface texturing. Others concerned qualities such as reflectivity or range and adjacency of hue. Others again were perceptual or representational; Caravaggio, for instance, particularly in representations of women, consistently rendered the human body with higher aspect ratios in all of its component parts than Gentileschi.

The final judgement was that this particular painting differed, over more than 20 discriminant variables and at the five per cent significance level or better in each case, from other works by either artist and could not, therefore, be realistically attributed to either.

So far, so concrete, and its principles would not have been alien to statisticians a century ago. The same can be said for similar data analytic approaches to forgery detection. At the opposite end of the scale are studies of how art is perceived by, and affects, the human viewer. These range from neurological investigations of perception itself to impacts on health and once again statistical views of the evidence are essential to separate overlapping and conceptually fuzzy bodies of experimental or observational data.

The idea that successful art depends upon inherent triggers within us is not, in itself, new. It is at least as old as the classical Greek philosophers, who tried to incorporate it within their unifications of human and cosmic systems. William Hogarth’s The analysis of Beauty[1] tried to introduce quantitative definitions 250 years ago, and Jay Appleton’s The experience of landscape[2] was a comprehensive attempt to tie aesthetics into Darwinian neurobiology four decades ago. Even detailed exploration of which stimulus to which part of the brain triggers which appreciative artistic response is older than I am, but real progress on this front only starts fairly recently with experiments made possible by the falling cost of computer mediated imaging techniques.

Data analyses from magnetoencephalographic experiments published three years ago, Cela-Conde and others[3] showed that there are identifiable patterns of brain activity in response to perceived beauty, with both differences (at the 99.9 per cent significance level) and similarities by gender. Female brains tend to show rapid responses in the left hemisphere followed by further areas of activity in the right, then reappearance after a brief lull by further, but smaller, left brain response in the initial area. Male brains, on the other hand, tend to be slower in responding and then show activity exclusively in the right hemisphere until, after a lull at the same time as its female counterpart, they too switch side to show a smaller response area on the left side. Both female and male also, however, have areas which show similar correlate response to perceptions of beauty.

Hop forward to last year, and another study[4] using neuroimaging illustrates aspects of financial influence on assessment of aesthetic value. Two groups of subjects, one with and the other without formal art training, were asked to subjectively rate projected copies of paintings by preference. Each respondent was paid to participate in the study, the money being provided by company sponsorship, and the paintings as viewed on screen were preceded by a reminder of this fact accompanied by the company logo. Each painting was then displayed with an accompanying logo – sometimes that of the sponsor, sometimes not. Parametric regression analysis of the results showed that there was a significant tendency for the group without formal art training to value those images associated with the sponsoring company’s logo more highly than those with an unrelated one. The formally-trained subjects, on the other hand, showed no such tendency.

That formal training insulates judgement from influence was a pre-existing hypothesis which the researchers were further testing. They were also, however, looking for linkages of the two separate judgement aspects (preference and influence) with neural activity. Here, the data showed that blood oxygen level dependent signals from the ventromedial prefrontal cortex (VMPFC) reflected preference levels in both groups while activity in the dorsolateral prefrontal cortex (DLPFC) was differentially expressed. Analysis of the results suggests that the DLPFC is acting as a moderator which interdicts external bias in the VMPFC’s operation.

Stepping back a little from the neurological level and returning to the phenomenological, another study[5] picks up the thread of Appleton’s biological approach to the aesthetics of environment but adds a statistical layer of rigor. Order of preference of college students for different auditory and visual features in a single streetscape were recorded at different times of year, and the resulting data set analysed. Naturally occurring components consistently tended to rank highest in both visual and auditory preference lists throughout spring, summer and autumn, but fell back to be dominated by artificial (in the visual lists) and social (auditory) in the winter.

Investigations of that kind are valuable in themselves to environmental designers such as architects and town planners. They can also inform studies of the influence that designed environments in general and installed art in particular can have on somatic and psychological resilience. There is widespread conviction, with strong anecdotal support, that art on the walls of hospitals improves the rate and quality of successful clinical outcomes. Hard statistical evidence for this, however, is only gradually accumulating and tends to come from very small projects since there is an understandable reluctance to divert overstretched health funding from treatment into research which may seem to the public diffuse and tangential.

Artist Luke Palmer, for instance, works in a children’s hospital with cystic fibrosis patients who, by the nature of their treatment, are isolated learners. He conducts outcomes research whose results he feeds to medical and management staff, pharmaceutical companies and others, but his co-synchronous samples are usually three or four in size so statistically significant results take time to assemble. Compounding this is the fact that interest in researching the issue is likely to be prior to investment and disappear once money has been committed. Larger scale studies of the types and styles of work which generally induce feelings of contentment or wellbeing in viewers tend to show wide variations, which isn’t helpful. Environmental preference analyses from other sources, such as the Korean streetscape example, therefore provide valuable triangulation.

Direct evidence of value in mental and psychological health is easier to come by. Examination of stress levels amongst office workers in differing environments yields data whose analysis recalls gender differences in neural response to beauty: male subjects tended towards significantly reduced states of anger and stress in offices decorated with art posters (of whatever kind), while female subjects do not. Similar results, though with reduced magnitude, are found in studies of patients in psychiatric care.

From another perspective, the arts industries relate to the health sector through their close and frequent habitual exposure to hazardous materials and conditions. It seems intuitively reasonable to anticipate that they would be at increased risk of respiratory and other upper body conditions. Hard data is again thin on the ground but at least one recent Croatian paper[6] suggests that the obvious may be fallacious. No statistically significant difference emerged between arts or cultural heritage restorers and control subjects in any respect except (at the 95 per cent level) nasal hyper-responsiveness.

Statistical data analysis is often described as being as much an art as a science. It can also be described as the essential interface between the arts and the sciences, bridging the perceived gulf between them.