An image processing technique that is used to analyze galaxies might also have applications in the world of abstract art. Scientists in the US and Canada have shown that it might be possible to use "multi-fractal" analysis to distinguish between works by different artists (Phys. Rev. E72 046101).
The works of the abstract expressionist painter Jackson Pollock have already been analyzed with fractal techniques by Richard Taylor of the University of Oregon and others. This work concentrated on analysing actual patterns or “blobs” formed by a specific colour on a canvas. Now Jonas Mureika of Loyola Marymount University in California and colleagues at the University of Toronto have gone a step further and analysed the “edges” of these blobs as well.
They looked at over 40 abstract works of art by Pollock (figure 1) and members of a movement known as Les Automatistes. To analyse the blobs Mureika and co-workers used digital filtering techniques to isolate specific colours in the painting (figure 2). To analyze the edges they used a Sobel gradient filter: basically, areas of high colour contrast, such as red against green or black against white, appear bright under this filter, while areas of low colour contrast are dull (figure 3).
They then used a standard “box-counting” technique to determine the fractal dimension of these filtered patterns. This involves covering a pattern by a set of squares and counting the number of squares, N, that contain the pattern. Each box is then divided into four smaller boxes and the number of boxes that contain the pattern is counted again. This process is repeated to produce a log-log plot with N on the vertical axis and the size of the boxes on the horizontal axis. The fractal dimension is given by the gradient of this graph.
Mureika and co-workers found that the fractal dimension of the blobs could not distinguish between different artists. However, the edge technique showed that the fractal dimensions of paintings by Pollock were statistically significant higher than those by Les Automatistes.
“Since part of the human visual processing system is based on the detection of such contrast edges, this suggests that there is a perceptually unique quality about paintings by particular artists,” says Mureika. “It also suggests that edge identification is an important contribution to ‘aesthetic’, and might explain why we find one abstract image more artistically appealing than another, even though we have no reference point to judge either as ‘good’ or ‘bad’.”
The technique could also be used to authenticate works of art and identify forgeries.
