Description
This book is about pattern theory, which is a branch of mathematics that deals with the analysis of signals in the real world. The book starts by introducing the reader to some examples of signals in the real world and how mathematics can be used to analyze them. It then goes on to discuss various aspects of pattern theory, including how to generate mathematical models of signals, how to analyze data based on these models, and how to use these tools to solve problems in various fields.
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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