Pattern Theory

The Stochastic Analysis of Real-World Signals

David Mumford, Agnès Desolneux (Autoren)

Buch | Softcover

428 Seiten

2024
Taylor & Francis Ltd (Verlag)
978-1-032-92005-4 (ISBN)

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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

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.

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). Agnès Desolneux is a researcher at CNRS/Université 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.

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

Erscheint lt. Verlag	14.10.2024
Verlagsort	London
Sprache	englisch
Maße	152 x 229 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Technik ► Elektrotechnik / Energietechnik
	Technik ► Nachrichtentechnik
	Technik ► Umwelttechnik / Biotechnologie
ISBN-10	1-032-92005-X / 103292005X
ISBN-13	978-1-032-92005-4 / 9781032920054
Zustand	Neuware