PATTERN THEORY: THE STOCHASTIC ANALYSIS OF REAL-WORLD SIGNALS

Subject ISBN Author Publisher Number of Pages Title Year Price
MATHEMATICS 9781138626928 David Mumford, Agnès Desolneux CRC India 375 PATTERN THEORY: THE STOCHASTIC ANALYSIS OF REAL-WORLD SIGNALS 2016 Rs. 1250/-
Author: David Mumford, Agnès Desolneux
Description: 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 text includes online access to the materials (data, code, etc.) needed for the exercises.
Table of Content: * Preface * Notation * What Is Pattern Theory? * The Manifesto of Pattern Theory * The Basic Types of Patterns * Bayesian Probability Theory: Pattern Analysis and Pattern Synthesis * English Text and Markov Chains * Basics I: Entropy and Information * Measuring the n-gram Approximation with Entropy * Markov Chains and the n-gram Models * Words * Word Boundaries via Dynamic Programming and Maximum Likelihood * Machine Translation via Bayes Theorem * Exercises * Music and Piece wise Gaussian Models * Basics III: Gaussian Distributions * Basics IV: Fourier Analysis * Gaussian Models for Single Musical Notes * Discontinuities in One-Dimensional Signals * The Geometric Model for Notes via Poisson Processes * Related Models * Exercises * Character Recognition and Syntactic Grouping * Finding Salient Contours in Images * Stochastic Models of Contours * The Medial Axis for Planar Shapes * Gestalt Laws and Grouping Principles * Grammatical Formalisms * Exercises * Contents * Image * Texture, Segmentation and Gibbs Models * Basics IX: Gibbs Fields * (u + v)-Models for Image Segmentation * Sampling Gibbs Fields * Deterministic * Algorithms to Approximate the Mode of a Gibbs Field * Texture Models * Synthesizing Texture via Exponential Models * Texture Segmentation Exercises * Faces and Flexible Templates * Modeling Lighting Variations * Modeling Geometric Variations by Elasticity * Basics XI: Manifolds, Lie Groups, and Lie Algebras * Modeling Geometric Variations by Metrics on Diff * Comparing Elastic and Riemannian Energies * Empirical Data on * Deformations of Faces * The Full Face Model * Appendix: Geodesics in Diff and Landmark Space * Exercises * Natural Scenes and their Multiscale Analysis * High Kurtosis in the Image Domain * Scale Invariance in the Discrete and Continuous Setting * The Continuous and Discrete Gaussian Pyramids * Wavelets and the

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