Pattern Theory From representation to inference

Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer
science, and electrical engineering with a good background in mathematics and probability, the text include numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website.
The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric
transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum.
Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at
inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

Pattern Theory: From Representation to Inference provides a comprehensive and accessible overview of the modern challenges in signal, data and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via conditioning structure and Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn, and Chapters 10, 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy, and finally Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

1 - Introduction
2 - The Bayes paradigm, estimation and information measures
3 - Probabilistic directed acyclic graphs and their entropies
4 - Markov random fields on undirected graphs
5 - Gaussian random fields on undirected graphs
6 - The canonical representations of general pattern theory
7 - Matrix group actions transforming patterns
8 - Manifolds, active modes, and deformable templates
9 - Second order and Gaussian fields
10 - Metrics spaces for the matrix groups
11 - Metrics spaces for the infinite dimensional diffeomorphisms
12 - Metrics on photometric and geometric deformable templates
13 - Estimation bounds for automated object recognition
14 - Estimation on metric spaces with photometric variation
15 - Information bounds for automated object recognition
16 - Computational anatomy: shape, growth and atrophy comparison via diffeomorphisms
17 - Computational anatomy: hypothesis testing on disease
18 - Markov processes and random sampling
19 - Jump diffusion inference in complex scenes

Ulf Grenander is the L. Herbert Ballou University Professor at Brown University. He is a member of the Royal Swedish Academy of Science and an honorary fellow of the Royal Statistical Society in London Michael Miller is the Professor of Electrical and Computer Engineering, Director of the Center for Imaging Science, and Professor of Biomedical Engineering at Johns Hopkins University, Baltimore. He completed his Ph.D. in Biomedical Engineering at The Johns Hopkins University in 1983.