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Mathematical Models for Registration and Applications to Medical Imaging

  • Otmar Scherzer

Part of the Mathematics in industry book series (MATHINDUSTRY, volume 10)

Table of contents

  1. Front Matter
    Pages i-x
  2. Numerical Methods

    1. Front Matter
      Pages 1-1
    2. Jan Modersitzki, Oliver Schmitt, Stefan Wirtz
      Pages 63-80
    3. Ulrich Clarenz, Marc Droske, Stefan Henn, Martin Rumpf, Kristian Witsch
      Pages 81-101
    4. Joachim Weickert, Andrés Bruhn, Thomas Brox, Nils Papenberg
      Pages 103-136
  3. Applications

    1. Front Matter
      Pages 137-137
    2. Harald Grossauer
      Pages 151-162
  4. Medical Applications

    1. Front Matter
      Pages 163-163
    2. Ulrich Clarenz, Stefan Henn, Joachim Weickert, Reto Bale
      Pages 185-191

About this book

Introduction

Image registration is an emerging topic in image processing with many applications in medical imaging, picture and movie processing. The classical problem of image registration is concerned with ?nding an appropriate transformation between two data sets. This fuzzy de?nition of registration requires a mathematical modeling and in particular a mathematical speci?cation of the terms appropriate transformations and correlation between data sets. Depending on the type of application, typically Euler, rigid, plastic, elastic deformations are considered. The variety of similarity p measures ranges from a simpleL distance between the pixel values of the data to mutual information or entropy distances. This goal of this book is to highlight by some experts in industry and medicine relevant and emerging image registration applications and to show new emerging mathematical technologies in these areas. Currently, many registration application are solved based on variational prin- ple requiring sophisticated analysis, such as calculus of variations and the theory of partial differential equations, to name but a few. Due to the numerical compl- ity of registration problems ef?cient numerical realization are required. Concepts like multi-level solver for partial differential equations, non-convex optimization, and so on play an important role. Mathematical and numerical issues in the area of registration are discussed by some of the experts in this volume. Moreover, the importance of registration for industry and medical imaging is discussed from a medical doctor and from a manufacturer point of view.

Keywords

Interpolation Mathematical Modelling Numerical and Computational Methods Optical Flow Registration Variational and PDE methods image registration ultrasound

Editors and affiliations

  • Otmar Scherzer
    • 1
  1. 1.Institut für InformatikUniversitat InnsbruckInnsbruckAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-34767-5
  • Copyright Information Springer Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-25029-6
  • Online ISBN 978-3-540-34767-5
  • Series Print ISSN 1612-3956
  • Buy this book on publisher's site