L. Rueschendorf (University of Freiburg, Germany), Zentralblatt fuer Mathematik, 1997

In this book a statistical theory is developed for robotics and computer vision. Three main problems are considered in detail, the 3-D motion analysis, 3-D interpretation of optical flows and 3-D computation by stereo vision. For stereo vision one computationally involved method is based on matching of stereo images. In this book a second simpler approach based on reconstruction of images by triangulations is described. Since image data contain noise, the reconstructed 3-D image is not necessarily accurate. A geometric correction method is used to evaluate the reliability of the reconstructed images.

Similar also for motion analysis and optical flow the reconstruction problem and the estimation of reliability of the estimates given noisy data is considered. The noise level is determined by a priori knowledge of the noise structure and by model comparison methods (like AIC).

The theory developed in this book has a lot of mathematical prerequisites which are systematically developed in separate chapters. These range from linear algebra, optimization and geometry to a detailed statistical theory of geometric patterns, fitting estimates and model selection.

This book can be considered as an important contribution to the analytical approach to computer vision and robotics. The relative practical merits of the approach compared to more empirical approaches like in artificial intelligence, fuzzy inference or neuro computing still have to be established.