Pattern Theory: The Stochastic Analysis of Real-World Signals

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 self-similarity.

David Mumford is a professor at Brown University in the Division of Applied Mathematics. He has been the recipient of many prestigious awards including most recently the American Mathematical Society's Steele Prize for Mathematical Exposition in 2007. He was awarded the Fields Medal in 1974.AgnFs Desolneux is a former student of David Mumford's and received her Ph.D in applied mathematics from CMLA, ENS Cachan, France. Since 2001 she has been working as a researcher at CNRS (Centre National de la Recherche Scientifique). Desolneux has been published widely, most notably she contributed to From Gestalt Theory to Image Analysis: A Probabilistic Approach, ôInterdisciplinary Applied Mathematicsö, vol. 34, 2008.