This book introduces a new theory in Computer Vision yielding elementary techniques to analyze digital images. These techniques are a mathematical formalization of the Gestalt theory. From the mathematical viewpoint the closest field to it is stochastic geometry, involving basic probability and statistics, in the context of image analysis. The book is mathematically self-contained, needing only basic understanding of probability and calculus. The text includes more than 130 illustrations, and numerous examples based on specific images on which the theory is tested. Detailed exercises at the end of each chapter help the reader develop a firm understanding of the concepts imparted.

From Gestalt Theory to Image Analysis: A Probabilistic Approach (Interdisciplinary Applied Mathematics, 34)

Computers & Technology

Desolneux, Agnès

Morel, Jean-Michel

Moisan, Lionel

Computer Science

Springer

Like its widely praised, best-selling predecessor, Pattern Theory: The Stochastic Analysis of Real-World Signals, Second Edition 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.  New to theSecond Edition:  • A new chapter discussing Convolutional Neural Networks (CNN’s) including the hierarchical structure of, and learning, with CNN’s  •Additional topics, including flexible templates in medical applications, Gaussian models for texture synthesis, exponential models and their use.

Pattern Theory: The Stochastic Analysis of Real-World Signals, Second Edition

Mumford, David Bryant

Gousseau, Yann

Chapman and Hall/CRC

This book introduces a new theory in Computer Vision yielding elementary techniques to analyze digital images. These techniques are a mathematical formalization of the Gestalt theory. The text includes numerous illustrations, and chapter-end exercises, to reinforce understanding.

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.

Pattern Theory (Applying Mathematics)

Mumford, David

A K Peters/CRC Press

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