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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

  • Conference proceedings
  • © 2007

Overview

Editors:
  1. Xue-Cheng Tai

    1. Department of Mathematics, University of Bergen, Bergen, Norway

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  2. Knut-Andreas Lie

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

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  3. Tony F. Chan

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

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  4. Stanley Osher

    1. Department of Mathematics, University of California at Los Angeles, Los Angeles, USA

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  • 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.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Mathematics and Visualization (MATHVISUAL)

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Table of contents (22 papers)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
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    2. Image Inpainting Using a TV-Stokes Equation

      • Xue-Cheng Tai, Stanley Osher, Randi Holm
      Pages 3-22

    3. Error Analysis for H1 Based Wavelet Interpolations

      • Tony F. Chan, Hao-Min Zhou, Tie Zhou
      Pages 23-34

    4. Image Dejittering Based on Slicing Moments

      • Sung Ha Kang, Jackie Shen
      Pages 35-55

    5. CLG Method for Optical Flow Estimation Based on Gradient Constancy Assumption

      • Adam Rabcewicz
      Pages 57-66

  3. Denoising and Total Variation Methods

    1. Front Matter

      Pages 68-68
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    2. On Multigrids for Solving a Class of Improved Total Variation Based Staircasing Reduction Models

      • Joseph Savage, Ke Chen
      Pages 69-94

    3. A Method for Total Variation-based Reconstruction of Noisy and Blurred Images

      • Qianshun Chang, Jing Xu, Weicheng Wang
      Pages 95-108

    4. Minimization of an Edge-Preserving Regularization Functional by Conjugate Gradient Type Methods

      • Jian-Feng Cai, Raymond Chan, Benedetta Morini
      Pages 109-122

    5. A Newton-type Total Variation Diminishing Flow

      • Wolfgang Ring
      Pages 123-148

    6. Chromaticity Denoising using Solution to the Skorokhod Problem

      • Dariusz Borkowski
      Pages 149-161

    7. Improved 3D Reconstruction of Interphase Chromosomes Based on Nonlinear Diffusion Filtering

      • Jan Hubený, Pavel Matula, Petr Matula, Michal Kozubek
      Pages 163-172

  4. Image Segmentation

    1. Front Matter

      Pages 174-174
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    2. Some Recent Developments in Variational Image Segmentation

      • Tony F. Chan, Mark Moelich, Berta Sandberg
      Pages 175-210

    3. Application of Non-Convex BV Regularization for Image Segmentation

      • Klaus Frick, Otmar Scherzer
      Pages 211-228

    4. Region-Based Variational Problems and Normal Alignment – Geometric Interpretation of Descent PDEs

      • Jan Erik Solem, Niels Chr. Overgaard
      Pages 229-248

    5. Fast PCLSM with Newton Updating Algorithm

      • Xue-Cheng Tai, Chang-Hui Yao
      Pages 249-262

  5. Fast Numerical Methods

    1. Front Matter

      Pages 264-264
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    2. Nonlinear Multilevel Schemes for Solving the Total Variation Image Minimization Problem

      • Tony F. Chan, Ke Chen, Xue-Cheng Tai
      Pages 265-288
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Keywords

About this book

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.

Editors and Affiliations

  • 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

Bibliographic Information

  • Book Title: Image Processing Based on Partial Differential Equations

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

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

  • Series Title: Mathematics and Visualization

  • DOI: https://doi.org/10.1007/978-3-540-33267-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2007

  • Hardcover ISBN: 978-3-540-33266-4Published: 01 December 2006

  • Softcover ISBN: 978-3-642-06990-1Published: 30 November 2010

  • eBook ISBN: 978-3-540-33267-1Published: 22 November 2006

  • Series ISSN: 1612-3786

  • Series E-ISSN: 2197-666X

  • Edition Number: 1

  • Number of Pages: X, 440

  • Number of Illustrations: 152 b/w illustrations, 22 illustrations in colour

  • Topics: Image Processing and Computer Vision, Artificial Intelligence, Computer Imaging, Vision, Pattern Recognition and Graphics, Visualization

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