Science: Transformation scenes: Hugh Aldersey-Williams explains how computer technology is being used to reshape the theories of an almost forgotten Edwardian scientist
Morphing takes an image of one thing - either a video still that has been digitised or an already digital synthetic computer graphic - and transforms it gradually into something quite different. The technique is being used to great effect in television advertising to transmute a galloping horse into a Volvo car or, for Andersen Consulting, a frog into a snail. The post-production houses where this work is done use software called TMorph that runs on expensive Silicon Graphics image workstations, resources well beyond the range of most laboratories.
As a theoretical exercise, however, the idea of transforming one species into another is not new to science. Champion of the technique was one D'Arcy Wentworth Thompson. The zoologist and author Stephen Jay Gould has called Thompson (1860-1948) 'perhaps the greatest polymath of our century'. Professor of zoology at the University of St Andrews, Thompson left his legacy in a massive essay, On Growth and Form, which Dr Gould - himself no slouch with a pen - describes as 'one of the great lights of science and of English prose, the greatest work of prose in 20th-century science'. This 1917 classic has recently been reissued (Cambridge University Press, 1992, pounds 7.95).
Thompson's aim was to show that the shape of living things has a mathematical basis. His argument is completely general. It applies to plants and animals, to airborne, waterborne and land creatures of all sizes. He cites the Eiffel tower and John Smeaton's design for the Eddystone lighthouse for taking the form of the trunk of an oak tree. Both man and nature take the most economical course of action prescribed by physical laws.
Having conjectured that the size and shape of all things is determined by the action of physical forces, it was a small, but at the time revolutionary, step to explore the relation between different-looking creatures from this standpoint. This Thompson did in a remarkable series of graphical studies. By drawing, say, a fish on a rectangular grid on a sheet of rubber and then distorting that grid by stretching the rubber in different ways, Thompson could produce new warped and distorted shapes that surprisingly corresponded to the shapes of quite different species. He applied the same technique to everything from leaves to skulls, finding simple mathematical relations between species often only distantly related according to Darwin's theory.
Brilliant scholar though he was, Thompson could work only with the tools available to him in Edwardian Britain. This situation is now changing, however, as the biological sciences begin to employ computers to model and visualise growth and form. Philip Benson of Oxford University employs morphing for a variety of practical ends. One of his projects involves accentuating mugshots of people to make them more recognisable. This procedure, a formalised sort of caricature, could potentially be used to find wanted or missing persons, although there are ethical issues to be addressed. Dr Benson has also created 'average' human faces, which, perhaps unsurprisingly, look like fashion models. In order to study what elements make a face look male or female, Dr Benson has also morphed from one to the other. The midpoint of the transition is not a sexless androgyne but actually looks more male than female. What this means, in effect, is that female faces have more highly distinctive features that make them look feminine than male faces have that make them look masculine.
Brian Sleeman of the University of Dundee cites Thompson in his papers. 'We want to understand mathematically how tumour boundaries grow,' he says. Prof Sleeman has developed a mathematical function that describes this growth. The function varies in a complex fashion based on such factors as the elasticity of the tumour boundary. There are periods of instability during tumour growth that, it is thought, might be the trigger for malignancy. Computer graphics in itself would not solve this puzzle, but its visualisation power would be a useful interpretive tool, he says.
Gherardo Gheri and Sylvia Bryk of the University of Florence have used similar techniques to study the growth of organs in chick embryos. They found that different parts developed at different rates at various times during incubation. They, too, say that more powerful visualisation techniques would benefit their research by revealing these phenomena at a glance.
At the University of Medicine and Dentistry of New Jersey, Robert Nagele has also studied chick embryos in an attempt to identify the physical forces that drive the formation of the neural tube that carries nerve impulses along the back of a vertebrate species. Measurement of changes of shape over time gives information on the distribution of these forces. But, says Dr Nagele, it is with the addition of three-dimensional computerised reconstruction that the data can be best understood.
Embryology is not the only discipline that stands to benefit. Changes of shape over far longer periods of time are also of interest. One of Thompson's graphical comparisons drew a mathematical relation of the human skull to that of the chimpanzee. Using a Macintosh computer and comparatively primitive software, the zoologist Richard Dawkins of Oxford University has performed a similar study, interpolating between Homo sapiens and Australopithecus of 3 million BC to produce the skull shape of man's ancestor, Homo erectus. Dr Dawkins also extrapolated this series of skulls to generate a picture of what man might look like in the distant future.
Improvements in the technology now promise to open up a rich new seam of mathematical biology. Last summer, Silicon Graphics brought out a sophisticated desk-top system that allows users to capture real-life images and then manipulate them graphically. 'Most scientists haven't had access to this sort of hardware,' says Steve Clement-Hayes of 5D Solutions, which supplies TMorph software. 'It's only been used to the full in the post-production industry. But now there's no reason why people who work with Macs can't use this technology.'
The advance could complete the rehabilitation of Thompson. 'We have to simulate these processes in three dimensions, or four, including time,' says Brian Goodwin of the Open University. 'We are only now beginning to gain the computing capacity needed to explore Thompson's ideas. His time is yet to come.'
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