© 2007

Image Processing Based on Partial Differential Equations

Proceedings of the International Conference on PDE-Based Image Processing and Related Inverse Problems, CMA, Oslo, August 8–12, 2005

  • Xue-Cheng Tai
  • Knut-Andreas Lie
  • Tony F. Chan
  • Stanley Osher


  • This book is publishing the newest research results and pointing to the contemporary literature in this research field.

  • It is a valuable volume for people working in this area or starting to work in this area.

Conference proceedings

Part of the Mathematics and Visualization book series (MATHVISUAL)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Digital Image Inpainting, Image Dejittering, and Optical Flow Estimation

    1. Front Matter
      Pages 1-1
    2. Xue-Cheng Tai, Stanley Osher, Randi Holm
      Pages 3-22
    3. Tony F. Chan, Hao-Min Zhou, Tie Zhou
      Pages 23-34
    4. Sung Ha Kang, Jackie Shen
      Pages 35-55
  3. Denoising and Total Variation Methods

  4. Image Segmentation

    1. Front Matter
      Pages 174-174
    2. Tony F. Chan, Mark Moelich, Berta Sandberg
      Pages 175-210
    3. Klaus Frick, Otmar Scherzer
      Pages 211-228
    4. Xue-Cheng Tai, Chang-Hui Yao
      Pages 249-262
  5. Fast Numerical Methods

    1. Front Matter
      Pages 264-264

About these proceedings


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

Editors and affiliations

  • Xue-Cheng Tai
    • 1
  • Knut-Andreas Lie
    • 2
  • Tony F. Chan
    • 3
  • Stanley Osher
    • 4
  1. 1.Department of MathematicsUniversity of BergenBergenNorway
  2. 2.Dept. Applied Math.SINTEF ICTOsloNorway
  3. 3.Assistant Director for Math & Physical Sciences DirectorateThe National Science FoundationArlingtonUSA
  4. 4.Department of MathematicsUniversity of California at Los AngelesLos AngelesUSA

Bibliographic information

Industry Sectors
Chemical Manufacturing
Health & Hospitals
IT & Software
Consumer Packaged Goods
Materials & Steel
Energy, Utilities & Environment
Oil, Gas & Geosciences