From Gestalt Theory to Image Analysis: A Probabilistic Approach

✍ Scribed by Agnés Desolneux, Lionel Moisan, Jean-Michel Morel (auth.)

• Publisher: Springer-Verlag New York
• Year: 2008
• Tongue: English
• Leaves: 277
• Series: Interdisciplinary Applied Mathematics 34
• Edition: 1
• Category: Library

✦ Synopsis

This book introduces the reader to a recent theory in Computer Vision yielding elementary techniques to analyse digital images. These techniques are inspired from and are a mathematical formalization of the Gestalt theory. Gestalt theory, which had never been formalized is a rigorous realm of vision psychology developped between 1923 and 1975.

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 intended for a multidisciplinary audience of researchers and engineers. It is self contained in three aspects: mathematics, vision and algorithms, and requires only a background of elementary calculus and probability. A large number of illustrations, exercises and examples are included. The authors maintain a public software, MegaWave, containing implementations of most of the image analysis techniques developed in the book.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction....Pages 1-9
Gestalt Theory....Pages 11-30
The Helmholtz Principle....Pages 31-45
Estimating the Binomial Tail....Pages 47-63
Alignments in Digital Images....Pages 65-93
Maximal Meaningfulness and the Exclusion Principle....Pages 95-114
Modes of a Histogram....Pages 115-131
Vanishing Points....Pages 133-151
Contrasted Boundaries....Pages 153-176
Variational or Meaningful Boundaries?....Pages 177-190
Clusters....Pages 191-202
Binocular Grouping....Pages 203-226
A Psychophysical Study of the Helmholtz Principle....Pages 227-235
Back to the Gestalt Programme....Pages 237-248
Other Theories, Discussion....Pages 249-259
Back Matter....Pages 261-269

✦ Subjects

Partial Differential Equations; Signal, Image and Speech Processing; Image Processing and Computer Vision; Visualization; Applications of Mathematics; Algorithms