Pattern theory is a distinctive approach to the analysis of all forms of real-world signals. At its core is the design of a large variety of probabilistic models whose samples reproduce the look and feel of the real signals, their patterns, and their variability. Bayesian statistical inference then allows you to apply these models in the analysis of new signals.

This book treats the mathematical tools, the models themselves, and the computational algorithms for applying statistics to analyze six representative classes of signals of increasing complexity. The book covers patterns in text, sound, and images. Discussions of images include recognizing characters, textures, nature scenes, and human faces. The text includes online access to the materials (data, code, etc.) needed for the exercises.

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This book is an introduction to pattern theory, the theory behind the task of analyzing types of signals that the real world presents to us. It deals with generating mathematical models of the patterns in those signals and algorithms for analyzing the data based on these models. It exemplifies the view of applied mathematics as starting with a collection of problems from some area of science and then seeking the appropriate mathematics for clarifying the experimental data and the underlying processes of producing these data. An emphasis is placed on finding the mathematical and, where needed, computational tools needed to reach those goals, actively involving the reader in this process. Among other examples and problems, the following areas are treated: music as a realvalued function of continuous time, character recognition, the decomposition of an image into regions with distinct colors and textures, facial recognition, and scaling effects present in natural images caused by their statistical selfsimilarity.

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