Mathematical Models for Registration and Applications to Medical Imaging

1. Front Matter

   Pages i-x

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2. Numerical Methods

   1. Front Matter

      Pages 1-1

      PDF

   2. A Generalized Image Registration Framework using Incomplete Image Information – with Applications to Lesion Mapping

      • Stefan Henn, Lars Hömke, Kristian Witsch

      Pages 3-25

   3. Medical Image Registration and Interpolation by Optical Flow with Maximal Rigidity

      • Stephen L. Keeling

      Pages 27-61

   4. Registration of Histological Serial Sectionings

      • Jan Modersitzki, Oliver Schmitt, Stefan Wirtz

      Pages 63-80

   5. Computational Methods for Nonlinear Image Registration

      • Ulrich Clarenz, Marc Droske, Stefan Henn, Martin Rumpf, Kristian Witsch

      Pages 81-101

   6. A Survey on Variational Optic Flow Methods for Small Displacements

      • Joachim Weickert, Andrés Bruhn, Thomas Brox, Nils Papenberg

      Pages 103-136

3. Applications

   1. Front Matter

      Pages 137-137

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   2. Fast Image Matching for Generation of Panorama Ultrasound

      • Armin Schoisswohl

      Pages 139-150

   3. Inpainting of Movies Using Optical Flow

      • Harald Grossauer

      Pages 151-162

4. Medical Applications

   1. Front Matter

      Pages 163-163

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   2. Multimodality Registration in Daily Clinical Practice

      • Reto Bale

      Pages 165-183

   3. Colour Images

      • Ulrich Clarenz, Stefan Henn, Joachim Weickert, Reto Bale

      Pages 185-191

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.

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

• Institut für Informatik, Universitat Innsbruck, Innsbruck, Austria

  Otmar Scherzer

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