Modeling and Inverse Problems in Imaging Analysis / Edition 1

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Overview

More mathematics have been taking part in the development of digital image processing as a science, and the contributions are reflected in the increasingly important role modeling has played solving complex problems. This book is mostly concerned with energy-based models. Through concrete image analysis problems, the author develops consistent modeling, a know-how generally hidden in the proposed solutions.

The book is divided into three main parts. The first two parts describe the theory behind the applications that are presented in the third part. These materials include splines (variational approach, regression spline, spline in high dimension) and random fields (Markovian field, parametric estimation, shastic and deterministic optimization, continuous Gaussian field). Most of these applications come from industrial projects in which the author was involved in robot vision and radiography: tracking 3-D lines, radiographic image processing, 3-D reconstruction and tomography, matching and deformation learning. Numerous graphical illustrations accompany the text showing the performance of the proposed models.

This book will be useful to researchers and graduate students in mathematics, physics, computer science, and engineering.

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Editorial Reviews

From the Publisher

From the reviews:

"...This book is an excellent introduction to Bayesian imaging and spline models in image analysis. It can be used for courses aimed at both mathematical statisticians who want to learn more about applications to imaging and engineers who aim to incorporate adequate mathematical formalism into their research."— MATHEMATICAL REVIEWS

"The introduction of this book clearly explains – at a level any undergraduate student in mathematics can understand – the basic concepts of image analysis. The examples throughout the book are well-explained and rich. The different types of modeling are also explained … . this book can be advised to students or beginning researchers who want to have a good overview with an easy, self-contained introduction to the field of Image Analysis." (Peter Leoni, Physicalia, Vol. 28 (4-6), 2006)

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Product Details

  • ISBN-13: 9780387955476
  • Publisher: Springer New York
  • Publication date: 6/4/2008
  • Series: Applied Mathematical Sciences Series , #155
  • Edition description: 2003
  • Edition number: 1
  • Pages: 314
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.81 (d)

Table of Contents

Foreword
Acknowledgments
List of Figures
Notation and Symbols
1 Introduction 1
I Spline Models 21
2 Nonparametric Spline Models 23
3 Parametric Spline Models 51
4 Auto-Associative Models 75
II Markov Models 97
5 Fundamental Aspects 99
6 Bayesian Estimation 113
7 Simulation and Optimization 123
8 Parameter Estimation 147
III Modeling in Action 175
9 Model-Building 177
10 Degradation in Imaging 189
11 Detection of Filamentary Entities 227
12 Reconstruction and Projections 243
13 Matching 269
References 289
Author Index 301
Subject Index 305
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