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 geometric invariant theory and his study of the moduli space of curves. In addition, Dr. Mumford's work in computer vision and pattern theory introduced new mathematical tools and models from analysis and differential geometry. He has been the recipient of many prestigious awards, including U.S. National Medal of Science (2010), the Wolf Foundation Prize in Mathematics (2008), the Steele Prize for Mathematical Exposition (2007), the Shaw Prize in Mathematical Sciences (2006), a MacArthur Foundation Fellowship (1987-1992), and the Fields Medal (1974).

Agnes Desolneux is a researcher at CNRS/Universite Paris Descartes. A former student of David Mumford's, she earned her Ph.D. in applied mathematics from CMLA, ENS Cachan. Dr. Desolneux's research interests include statistical image analysis, Gestalt theory, mathematical modeling of visual perception, and medical imaging.

PrefaceNotationWhat Is Pattern Theory?English Text and Markov ChainsMusic and Piece wise Gaussian ModelsCharacter Recognition and Syntactic GroupingImage Texture, Segmentation and Gibbs ModelsFaces and Flexible TemplatesNatural Scenes and their Multiscale AnalysisBibliographyIndex