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

Preface

Contents

Part I Digital Image Inpainting, Image Dejittering, and Optical Flow Estimation

Image Inpainting Using a TV-Stokes Equation

1 Introduction

2 The Mathematical Principles

3 Numerical Experiments

4 Conclusion

References

Error Analysis for H1 Based Wavelet Interpolations

1 Introduction

2 Variational Wavelet Interpolation Models

3 Recovery Bound for the H1 Model

4 A Numerical Example

References

Image Dejittering Based on Slicing Moments

1 Introduction

2 Slicing Moments of BV Functions

3 Moments Regularization for Image Dejittering

4 Application to Image Dejittering and Examples

5 Conclusion

References

CLG Method for Optical Flow Estimation Based on Gradient Constancy Assumption

1 Introduction

2 Review of the CLG Method

3 Formulation of the CLG(H) Method

4 Algorithmic Realization

5 Comparison Between Methods

6 Summary

References

Part II Denoising and Total Variation Methods

On Multigrids for Solving a Class of Improved Total Variation Based Staircasing Reduction Models

1 Introduction

2 An Overview of Staircasing Reduction Models

3 Algorithms for the Combined TV and H1 Models

4 A Modifed Staircasing Reduction Model

5 Conclusion

References

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

1 Introduction

2 Idea and New Method

3 Algorithms for Solving the Nonlinear System of Equations

4 Models and Blur Operators

5 Numerical Experiments and Discussions

References

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

1 Introduction

2 Review of Two Phase Methods

3 Our Method

4 Convergence of the Method

5 Simulation

6 Conclusion

References

A Newton-type Total Variation Diminishing Flow

1 Introduction

2 A Newton-type Flow for the Minimization of the Area of Level- Sets

3 Geometric Properties

4 Numerical Examples

5 Conclusion

References

Chromaticity Denoising using Solution to the Skorokhod Problem

1 Introduction

2 Mathematical Preliminaries

3 Stochastic Representation of Solution to the Heat Equation

4 Image Denoising

5 A Numerical Scheme

References

Improved 3D Reconstruction of Interphase Chromosomes Based on Nonlinear Di . usion Filtering

1 Introduction

2 Improved Reconstruction of Interphase Chromosomes

3 Conclusion

Acknowledgment

References

Part III Image Segmentation

Some Recent Developments in Variational Image Segmentation

1 Introduction

2 Active Contours Methods

3 Multi-Channel Extensions in Chan–Vese Model

4 Multi-Phase Extensions

5 Fast Algorithms

6 Acknowledgment

References

Application of Non-Convex BV Regularization for Image Segmentation

1 Introduction

2 Review on the Mathematical Analysis of Evolution Processes

3 Variational Level Set Model for Image Segmentation

4 Relaxation

5 Numerical Simulations

6 Conclusion

References

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

1 Introduction

2 Background

3 Descent Directions

4 Region-Based Functionals

5 Quadratic Normal Alignment

6 Computing Gˆ ateaux Derivatives using Shape Gradients

7 Conclusions

References

Fast PCLSM with Newton Updating Algorithm

1 Introduction

2 PCLSM for Image Segmentation

3 Newton Updating

4 Numerical Examples

5 Conclusion

References

Part IV Fast Numerical Methods

Nonlinear Multilevel Schemes for Solving the Total Variation Image Minimization Problem

1 Introduction

2 Review of Unilevel Methods for the TV Formulation

3 Review of a Class of Multigrid Methods

4 NSSC Method for Equation (1)

5 Numerical Experiments

6 Conclusions

Acknowledgements

References

Fast Implementation of Piecewise Constant Level Set Methods

1 Introduction

2 Piecewise Constant Level Set Formulation

3 Operator Splitting Scheme

4 Operator Splitting and Newton Methods for Image Segmentation

5 The Algorithm

6 Numerical Experiments

7 Conclusion

References

The Multigrid Image Transform

1 Introduction

2 Recapitulation on Multigrid

3 The Multigrid Image Transform

4 Comparative Results

5 Concluding Remarks

References

Minimally Stochastic Schemes for Singular Di . usion Equations

1 Introduction

2 Schemes Based on Two Pixel Interaction

3 Numerical Experiments

4 Conclusion

References

Part V Image Registration

Total Variation Based Image Registration

1 Introduction.

2 Continuous Total Variation Minimization.

3 Numerical Minimization

4 Results

5 Summary and Conclusion

References

Variational Image Registration Allowing for Discontinuities in the Displacement Field

1 Introduction

2 Variational Approach

3 Variable Regularizer

4 Numerical Results

5 Conclusion and Outlook

References

Part VI Inverse Problems

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

Summary

1 Introduction

2 The Reservoir Model

3 The Forward Problem

4 The Shape Reconstruction Problem

5 Formal Derivation of the Shape Evolution Algorithm

6 The Adjoint Technique for Calculating Sensitivities

7 The Algorithm

8 Numerical Examples

9 Conclusions and Future Work

Acknowledgments

References

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

1 Introduction

2 The Inverse Problem

3 The Binary Level Set Approach

4 The Binary Level Set Method for the Inverse Problem

5 Numerical Optimisation

6 Numerical Results

7 Summary and Conclusions

8 Acknowledgements

9 Nomenclature

References

A Color Figures

From Image Inpainting Using a TV-Stokes Equation,” by Tai, Osher, and Holm

From Image Dejittering Based on Slicing Moments,” by Kang and Shen

From Chromaticity Denoising using Solution to the Skorokhod Problem,” by Borkowski

From Some Recent Developments in Variational Image Segmentation,” by Chan, Moelich, and Sandberg