Image processing by topological asymptotic analysis

This chapter summarizes the work presented in [26,24,18,27,28,25,2].

• Introduction
• Topological asymptotic analysis
  • Presentation of the method
  • Main result
  
  
• Inpainting
  • Crack localization problem
  • Dirichlet and Neumann formulations for the inpainting problem
  • Asymptotic expansion
  • Algorithm
  • Remarks
  
  
• Restoration
  • Variational formulation
  • Topological gradient
  • Algorithm
  • Remarks
  • Extension to color images
  
  
• Classification
  • Introduction to the classification problem
  • Restoration and classification coupling
  • Extension to unsupervised classification
  
  
• Segmentation
  • From restoration to segmentation
  • Power series expansion
  • Algorithm
  
  
• Complexity and speeding up
  • Discrete cosine transform
  • Preconditioned conjugate gradient
  
  
• Coupling between the topological gradient and the minimal path technique
  • Minimal paths
  • Fast marching
  • Coupled algorithm
  
  
• Conclusions and perspectives