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Modeling and Inverse Problems in Imaging Analysis

  • Textbook
  • © 2003

Overview

Authors:
  1. Bernard Chalmond

    1. Department of Physics, University of Cergy-Pontoise, Cergy-Pontoise Cedex, France

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Part of the book series: Applied Mathematical Sciences (AMS, volume 155)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xxii
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  2. Introduction

    1. Introduction

      • Bernard Chalmond
      Pages 1-19

  3. Spline Models

    1. Front Matter

      Pages 21-21
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    2. Nonparametric Spline Models

      • Bernard Chalmond
      Pages 23-50

    3. Parametric Spline Models

      • Bernard Chalmond
      Pages 51-73

    4. Auto-Associative Models

      • Bernard Chalmond
      Pages 75-95

  4. Markov Models

    1. Front Matter

      Pages 97-97
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    2. Fundamental Aspects

      • Bernard Chalmond
      Pages 99-112

    3. Bayesian Estimation and Inverse Problems

      • Bernard Chalmond
      Pages 113-122

    4. High-Dimensionality Simulation and Optimization

      • Bernard Chalmond
      Pages 123-145

    5. Parameter Estimation

      • Bernard Chalmond
      Pages 147-174

  5. Modeling in Action

    1. Front Matter

      Pages 175-175
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    2. Model-Building

      • Bernard Chalmond
      Pages 177-188

    3. Degradation in Imaging

      • Bernard Chalmond
      Pages 189-226

    4. Detection of Filamentary Entities

      • Bernard Chalmond
      Pages 227-241

    5. Reconstruction from Projections

      • Bernard Chalmond
      Pages 243-268

    6. Matching

      • Bernard Chalmond
      Pages 269-288

  6. Erratum

    1. Erratum

      • Bernard Chalmond
      Pages 313-313

  7. Back Matter

    Pages 289-312
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Keywords

About this book

More mathematicians 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 materials necessary to the models expressed in the third part. These materials include splines (variational approach, regression spline, spline in high dimension), and random fields (Markovian field, parametric estimation, stochastic and deterministic optimization, continuous Gaussian field). Most of these models come from industrial projects in which the author was involved in robot vision and radiography: tracking 3D lines, radiographic image processing, 3D reconstruction and tomography, matching, 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 applied mathematics, computer vision, and physics.

Reviews

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)

Authors and Affiliations

  • Department of Physics, University of Cergy-Pontoise, Cergy-Pontoise Cedex, France

    Bernard Chalmond

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