Pattern Theory: The Stochastic Analysis of Real-World Signals [Hardcover]

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.

Preface
Notation
What Is Pattern Theory?
English Text and Markov Chains
Music and Piece wise Gaussian Models
Character Recognition and Syntactic Grouping
Image Texture, Segmentation and Gibbs Models
Faces and Flexible Templates
Natural Scenes and their Multiscale Analysis
Bibliography
Index

Pattern theory is a field in applied mathematics that analyzes all types of signals that the world presents to us. For each chapter, the authors present a real-world problem - a class of signals that we want to model. Then they present the basic mathematical tools needed before moving into the model. Then the model is compared with the original data. Each chapter ends with a set of exercises. Discussions of images include recognizing characters, textures, nature scenes, and human faces.

David Mumford is a professor emeritus of applied mathematics at Brown University. His contributions to mathematics fundamentally changed algebraic geometry, including his development of geomelÍ