Music and Painting: A Study in Comparative Ideas from Turner to Schoenberg by Edward Lockspeiser (review)

370 Books The concluding essay by Thomas I. Emerson is about communication and the freedom of expression. One would expect that ‘freedom of expression’ would be defined as a system of communication but, unexpectedly, it is linked with the First Amendment of the U.S.A. Constitution and, therefore, the essay is primarily of interest to those concerned with such constitutional affairs. Short ‘Lives’ of the authors, selected short bibliographies and a useful index conclude the book. The essays aim at the educated general reader. Although one might dislike the layout of the book, one must concede that it is a recommendable introduction to communication studies. Artists should begin with Gombrich’s essay, which might give them a wider view of the implications of their work and might even help them to come to a deeper understanding of themselves. Pattern Classification and Scene Analysis. Richard 0. Duda and Peter E. Hart. Wiley-Interscience, London, 1973. 482 pp., illus. f11.25. Reviewed by Michael Thompson* The book presents theoretical principles for techniques used in both pattern classification and scene analysis. The word ‘techniques’ is necessary here, for as yet we do not have a unified theory of patterns and scenes. Indeed, much of the mathematics that can be applied to patterns and scenes is absent from this book, for instance, symmetry groups, series, some discussion of adjacency in a plane surface etc. In fact, it is hardly concerned at all with patterns, as such, and only in the last chapter with scenes as images that can be perceived meaningfully. Part I deals with the statistical decision theory needed for current application of pattern classification. ‘Patterns’ are nowhere discussed in visual terms and, indeed, there are almost no illustrations of visual material. The text covers Bayesian decision theory, supervised and unsupervised learning, nonparametric techniques, discriminant analysis and clustering. Much of this is quite general and may be applied in many areas other than the visual. The level of a first-year university course in statistics is needed for this part. Part I1 deals with ‘scene analysis’, implying somz form of description of an image having two or three dimensions. Not everything in the scene is to be described, only that which is relevant for the particular purpose. Many of the techniques deal with simplification of images-for suppressing irrelevant detail, characterizing shapes and sizes of objects in pictures, integrating parts of a picture into meaningful entities and, in general, reducing the complexity of the data. What is relevant from the point of view of the artist or art teacher is that many of these techniques deal directly with the constituents of visual material, such as lines, boundaries, regions, textures and shape. Understanding the mathematical description and characterization of these constituents can lead to a broader appreciation of visual matters. I should point out that many of the techniques, which are very close to actual visual content, require very little mathematics indeed and have a strong intuitive appeal, such as the ‘prairie fire’ method of turning a form into a ‘skeleton’. Two chapters are devoted to perspective. Given an image, what do we know of the object? Given two images, could they be of the same object from two viewpoints? Clearly, a problem of practical importance in robot perception is to be able to deal with three-dimensional data and compare a model to a stereoscopic image. Readers of Leonardo may find this an unusual and interesting approach to perspective, however, linear algebra (vector notation) is needed to follow much of the geometry. The last chapter is possibly the most interesting from the point of view of the artist or art teacher. Entitled ‘Descriptive Methods in Scene Analysis’, it deals with techniques that can provide understanding of a scene. *I Remez Road, Kadimah, Israel. Included are syntatic descriptions, relational graphs and the analysis of polyhedra. It is a pity that the amount of space in the book devoted to a particular technique seems to be inversely proportional to its proximity to the visual content of patterns and scenes. However, for those with a mathematical bent, it will be obvious that the writers have gone out of their way to help the reader gain...