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Reviewer: Fabian Ernst

Reconstruction of geometry from multiple images is gaining more and more importance in several application fields, both for professional and for entertainment-oriented purposes. Furthermore, the area of computer vision is using ever more sophisticated tools to deal with the reconstruction problem. Hartley and Zisserman discuss mathematical techniques and algorithms that provide solutions to problems of increasing complexity. After providing a background on projective geometry and estimation algorithms, several topics are discussed. First camera models are described, along with ways to compute the camera matrix and do camera calibration. The second part is dedicated to two-view geometry. The main topics here are epipolar geometry, the fundamental matrix, and the reconstruction of structure. The part on three-view geometry focuses on the concept of the trifocal tensor. The last part is devoted to N-view geometry, considering amongst others auto- calibration of cameras. I am very positive about this book. The authors have succeeded very well in describing the main techniques in mainstream multiple view geometry, both classical and modern, in a clear and consistent way. The book’s parts each contain a “road map,” in which the main steps are outlined. It is self-contained in the sense that the most important mathematical techniques, such as projective geometry, are introduced in the first part. The figures are adequate in illustrating important concepts and results, and do not provide unnecessary detail. Algorithms and their suitability are analyzed from a theoretical point of view, and this is supported by simple examples. Subsequently, they are applied to real-life images. In view of the amount of material discussed, I admire the fact that the authors have managed to fit it all within 600 pages. Since the book contains theoretical considerations (starting with the mathematical basis, and then subsequently considering 1, 2, 3 and N images), it is suitable as a textbook in an advanced computer vision course. Someone wanting to get a good overview of the field and its mathematical background will also certainly benefit from this book. The notation is very clear and consistent throughout the book. The exercises help to get hands-on experience with the techniques, and introduce special cases and extensions. For people interested in a quick solution to an application-specific problem at hand, algorithms are provided (and can easily be found using the index), but for a full understanding of how they work, a more extensive study of the text is probably required. For readers requiring even more background, a list of references is given. The references, however, contain many PhD theses, technical reports and papers from smaller conferences that might be hard to obtain for the average reader. Although no solid mathematical background is required, it is certainly helpful. The authors go to great lengths to explain vector, matrix and tensor notation, and the basics of projective geometry, but terms such as “groups” and “manifolds” are not explained. From a practical point of view, it would also be helpful to discuss the merits and drawbacks of different algorithms in terms of different classes of images. Although the algorithms are discussed with respect to noise, this noise is usually supposed to be relatively small. The algorithms are based on a set of point correspondences. However, hardly any attention is paid to how these point correspondences can be found, and what the consequences are of an unsuitable set of correspondences for the algorithm. However, the main drawback of the book is one that can probably not be blamed on the authors: the pages are very full. The margins are about one centimeter, which makes it hard to scribble any notes there. This aside, I heartily recommend this book to anyone interested in the theoretical basis of conventional and modern techniques in multiple view geometry. Online Computing Reviews Service