Image Processing Based on Partial Differential Equations

1. Fast Numerical Methods

   1. Fast Implementation of Piecewise Constant Level Set Methods

      • Oddvar Christiansen, Xue-Cheng Tai

      Pages 289-308

   2. The Multigrid Image Transform

      • Paul M. de Zeeuw

      Pages 309-324

   3. Minimally Stochastic Schemes for Singular Diffusion Equations

      • Bernhard Burgeth, Joachim Weickert, Sibel Tari

      Pages 325-339

2. Image Registration

   1. Front Matter

      Pages 342-342

      PDF

   2. Total Variation Based Image Registration

      • Lars Hömke, Claudia Frohn-Schauf, Stefan Henn, Kristian Witsch

      Pages 343-361

   3. Variational Image Registration Allowing for Discontinuities in the Displacement Field

      • Sven Kabus, Bernd Fischer, Astrid Franz

      Pages 363-377

3. Inverse Problems

   1. Front Matter

      Pages 380-380

      PDF

   2. Shape Reconstruction from Two-Phase Incompressible Flow Data using Level Sets

      • Rossmary Villegas, Oliver Dorn, Miguel Moscoso, Manuel Kindelan

      Pages 381-401

   3. Reservoir Description Using a Binary Level Set Approach with Additional Prior Information About the Reservoir Model

      • Lars Kristian Nielsen, Xue-Cheng Tai, Sigurd Ivar Aanonsen, Magne Espedal

      Pages 403-426

4. Back Matter

   Pages 427-440

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The book contains twenty-two original scienti?c research articles that address the state-of-the-art in using partial di?erential equations for image and signal processing. The articles arose from presentations given at the inter- tional conference on PDE-Based Image Processing and Related Inverse Pr- lems, held at the Centre of Mathematics for Applications, University of Oslo, Norway, August 8-12, 2005. The purpose of the conference was to bring together international - searchers to present various aspects of new developments in using numerical techniques for partial di?erential equations to analyse and process digital - ages. Various aspects of new trends and techniques in this ?eld were discussed in the conference, covering the following topics: • Level set methods and applications • Total variation regularization and other nonlinear ?lters • Noise analysis and removal • Image inpainting • Image dejittering • Optical ?ow estimation • Image segmentation • Image registration • Analysis and processing of MR images and brain mapping • Image construction techniques • Level set methods for inverse problems Inverse problems for partial di?erential equations have large areas of app- cations. Although image analysis and PDE inverse problems seem to be - related at a ?rst glance, there are many techniques used in one of these two areas that are useful for the other. One goal of the conference was to highlight some of the recent e?orts in merging some of the techniques for these two research areas.

• 3D
• Alignment
• Analysis
• Diffusion
• Interpolation
• Moment
• image processing
• image registration
• signal processing
• simulation
• visualization

• Department of Mathematics, University of Bergen, Bergen, Norway

  Xue-Cheng Tai

• Dept. Applied Math., SINTEF ICT, Oslo, Norway

  Knut-Andreas Lie

• Assistant Director for Math & Physical Sciences Directorate, The National Science Foundation, Arlington, USA

  Tony F. Chan

• Department of Mathematics, University of California at Los Angeles, Los Angeles, USA

  Stanley Osher

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