If one reads Brian Wandell's book without much previous knowledge of visual science, the overall view one would get of the visual system is of a modular, pre-programmed computing machine. One might be led to believe that the problem of seeing can be solved entirely by computation, without prior knowledge about objects in the world. The only hint that the computational machine is perhaps not preprogrammed at birth is one sentence in the final chapter, which discusses the problems experienced by those who had become blind in early infancy and had their sight restored in adulthood.

This is not to argue that the visual system does not contain an enormous amount of computational machinery; but most visual scientists would place more stress than does Wandell on the importance of top-down constraints on visual processing, and on the importance of visual experience in the development of the neural machinery underlying vision.

Despite the title, then, Wandell's book is no primer on visual science. But the book has a fair amount to offer those who are already familiar with the basic concepts and who are interested in computational vision, because it treats the subject from a different viewpoint to many existing texts. He breaks the subject up into three sections that he considers are basic problems in vision - encoding, representation and interpretation - and treats each section by considering how the visual system makes the best use of the information available to it, giving computational algorithms and engineering methods that the visual system might use to achieve this goal.

As one would expect in a book written from this viewpoint, Wandell makes no excuses for his liberal use of mathematics. At least in the first section, the maths is supported well by explanations that provide the reader with the basic idea. Later on, however, in his treatments of motion and image compression, the maths could prove overwhelming to readers with a biological or medical background. But readers who are most likely to be interested in reading about these subjects from a computational viewpoint will probably have enough background in maths to find his treatment useful.

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The other strength of the book is that Wandell attempts not only to explain current knowledge of how the visual system works, but also to make the reader understand the logic of the experiments through which that knowledge was obtained. This is clearest in the first half of the book, in the chapters on image formation, photoreceptor sampling, and the properties of the retinal and cortical cells of the visual system. However even early on in the book the sort of carelessness that makes it at times so irritating is apparent - the description of the Ishihara test for colour vision deficiencies is inaccurate and misleading.

The second half of the book is somewhat disappointing. The best chapters here are probably on image compression and motion, although the former offers most to engineers and computer scientists, being concerned mostly with engineering methods that may or may not be implemented in the visual system. Some aspects of visual performance (such as binocular vision) are barely touched upon. In many places the terminology becomes slack and the arguments difficult to follow.

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In the later chapters the descriptions of some of the experiments lack enough detail for the reader to understand what the experimenters did, and hence why they drew their conclusions. Many of the diagrams lack adequate explanations or labels, so that only readers familiar with the experiments can work out which line on a graph is which.

One diagram, showing a transformation of the results of an asymmetric colour-matching experiment, has acquired an extra data point between Wassef's publication in 1959 and Wandell's interpretation. It is also not clear on this diagram which pairs of data points are for pairs of colours that matched - which makes it hard to see the point of including it.

Despite these problems, I think that this book will appeal to mathematically minded scientists and engineers who wish to know how to study vision, especially those who want to create computer models of vision and visual processing, and those who want to do experiments (there is a good introduction to visual display calibration in an appendix). But because of the maths, and the careless, avoidable errors, parts of this book will leave many baffled and frustrated.

Benedict Regan is a final-year research student, department of experimental psychology, University of Cambridge.

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