Contents

• List of Figures
• List of Tables
• Introduction
• General Tools
  • Notation, First Definitions
    • Basic Notations
    • Functions
    • Sets and Collections
    • Matrices and Vectors
    • Other Common Notation
  • Basics on Continuous Optimization
    • Generalities on Optimization
    • Optimization Algorithms
  • Parametric Models of Function
    • Splines
    • The B-spline Representation
    • Non Uniform Rational B-Splines (NURBS)
    • Radial Basis Functions
  
  
• General Points on Parameter and Hyperparameter Estimation
  • Parameter Estimation
    • General Points on Parameter Estimation
    • Specific Techniques in Parameter Estimation
  • Hyperparameters
    • Generalities
    • Automatic Computation of the Hyperparameters
  
  
• Range Surface Fitting
  • First Definitions and Concepts
    • First Definitions
    • Acquisition of Range Data
    • An Introductory Example
  • The L-Tangent Norm
    • Supplementary Details on Range Surface Fitting
    • The L-Curve Criterion
    • The L-Tangent Norm Criterion
    • Experimental Results
  • Range Surface Fitting with Heteroskedastic Noise
    • Fitting a B-spline on Mesh Data
    • Our Approach to Handle Heteroskedastic Noise and Discontinuities
    • Experiments
  
  
• Image Registration
  • General Points on Image Registration
    • Background
    • Problem Statement
  • Direct Image Registration without Region of Interest
    • Introduction
    • Region of Interest: State of the Art
    • Direct Image Registration without Region of Interest
    • Experimental Results
    • Conclusion
  • Pixel-Based Hyperparameter Selection for Feature-Based Image Registration
    • Introduction
    • Reminder and Complementary Elements on Automatic Hyperparameter Selection
    • Our Contribution: the Photometric Error Criterion
    • Experimental Results
    • Conclusion
  
  
• NURBS Warps
  • Introduction
  • Affine Interpretation of the BS-Warps
  • NURBS-Warps
  • Parameter Estimation
    • The BS-Warp
    • The NURBS-Warp
  • Experiments
    • Simulated Data
    • Real Images
  • Conclusion
  
  
• Monocular Template-based Reconstruction of Smooth and Inextensible Surfaces
  • Introduction
  • Related Work on Inextensible Surface Reconstruction
  • Convex Formulation of the Upper Bound Approach with Noise in all Images
    • Noise in the Template Only
    • Noise in Both the Template and the Input Images
  • Smooth and Inextensible Surface Reconstruction
    • Parametric Surface Model
    • Surface Reconstruction as a Least-Squares Problem
  • Experimental Results
    • Experiments on Synthetic Data
    • Experiments on Real Data
  • Conclusion
  
  
• Conclusion
• Feature-Driven Direct Non-Rigid Image Registration
  • Introduction
  • Problem Statement and Previous Work
    • Forward Additive Algorithms
    • Inverse Compositional Algorithms
  • Feature-Driven Registration
    • Feature-Driven Warp Parameterization
    • Threading Warps
    • Reverting Warps
    • Compositional Feature-Driven Registration
  • Local Registration Algorithms
    • Local Registration with Gauss-Newton
    • Learning-Based Local Registration
  • Feature-Driven Warps
    • The Feature-Driven Thin-Plate Spline Warp
    • The Feature-Driven Free-Form Deformation
  • Experimental Results
    • Representational Similarity of the TPS and FFD Warps
    • Comparison of Registration Algorithms
  • Conclusions
    • Framework
    • Experimental Results
  
  
• Bibliography