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Reviewer: Michael Goldberg

The field of computational neuroscience has made tremendous progress in modeling the visual cortex. The authors of this book use the statistical structure of natural images to construct a comprehensive model of the scene. This parallels the manner with which the brain analyzes the statistical patterns of streaming visual data. The computational approach is enhanced by the efficient construction of probabilistic inference. While the book concentrates on natural image statistics for early vision tasks, the framework provided could be applied to general engineering applications that require computer vision algorithms. The book introduces the basics of signal processing and neural science in the first chapter. In addition to fundamental mathematics, such as multivariate probability and statistics, it also presents advanced topics, such as linear filters and frequency analysis. These topics comprise Part 1. Part 2 elaborates on the statistics of linear features. This includes principal component computations, independent component analysis, and the effects of sparse coding. However, inferences based on these statistics are, in fact, limited. The reason for this is the motivation of Part 3, which presents nonlinear features. While it is true that the statistical components are independent in the theoretical model, computational vision calculates estimates from the real image data, so that numerically they become dependent. Thus, while linear features would suffice for the theoretical model, such transformations have too few parameters for the practical model. Hence, nonlinear features that can handle an array of parameters need to be considered. The authors honestly point out that the models proposed in the book are still a distance away from constructing a complete description of the natural image statistics, but each feature computed provides new information about the visual data. Some of the features considered are energy correlations and energy detectors. Normalization issues and complex datasets are also considered. The first three parts of the book comprise the major framework presented. The last three parts are included to finalize prior discussions and to draw conclusions (Part 5); as such, they are shorter. The independent component analysis model proposed by the authors deals with extracting features from grayscale images. Part 4 considers the effects of color on statistical correlations and energy computations. Another extension to this model considers stereopsis, which obtains depth information from binocular disparity-the horizontal difference in image location of an object seen from the left and right lens, respectively. The natural images analyzed to this point were static, and scenes from natural environments change over time. Just as temporal sequences of the natural images are now considered, the properties of the visual system need to incorporate temporal parameters. Part 6 provides additional mathematics tutorials on more advanced topics. The authors did a wonderful job of introducing the field of natural image statistics, comprehensively. The book provides the underlying fundamental mathematics-in the introduction and in the appendix-in order to make the material presented accessible to a wide audience. The book provides exercises and computer assignments at the end of the chapters. The authors provide MATLAB code on their Web site [1] for reproducing most of the experiments in the book. This, coupled with the fact that the advanced topics are treated in a similar manner to basic theory, makes the book suitable to be used as a textbook for advanced students and by researchers in any discipline related to computer vision. Online Computing Reviews Service