Non-rigid registration algorithms

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Table of contents

1 Introduction
1.1 The human brain and its shape
1.1.1 Brain anatomy
1.1.2 Brain imaging techniques
1.1.3 Computational neuroanatomy
1.1.4 Publicly available brain templates
1.1.5 Some application of digital brain templates
1.2 Segmentation and registration
1.2.1 Registration
1.2.1.1 Non-rigid registration methods
1.2.1.2 Application of brain image registration
1.2.1.3 Non-rigid registration algorithms
1.2.2 Segmentation
1.2.2.1 Methods of segmentation
1.3 Template estimation
1.4 Algorithms used in this work
1.4.1 Gradient descent
1.4.2 Stochastic algorithms
1.5 Contributions of this work
1.5.1 Generative Statistical Model
1.5.2 Statistical Learning Procedure
1.5.3 Segmentation of new individuals
2 Probabilistic Atlas and Geometric Variability Estimation
2.1 Introduction
2.2 The Observation Model
2.2.1 Statistical Model
2.2.2 Parameters and likelihood
2.2.3 Bayesian Model
2.3 Estimation
2.3.1 Existence of the MAP estimation
2.3.2 Consistency of the estimator on our model
2.4 Estimation Algorithm using Stochastic Approximation Expectation-Maximization
2.4.1 Model factorization
2.4.2 Estimation Algorithm
Step 1: Simulation step
Step 2: Stochastic approximation step
Step 3: Maximization step
2.4.3 Convergence analysis
2.5 Experiments and Results
2.5.1 Simulated data
2.5.2 Real data
2.6 Conclusion and discussion
2.7 Proof of Theorem 2.1
2.8 Proof of Theorem 2.3
2.8.1 Proof of assumption (A1’)
2.8.2 Proof of assumption (A2)
2.8.3 Proof of assumption (A3’)
3 Bayesian Estimation of Probabilistic Atlas for Tissue Segmentation 
3.1 Introduction
3.2 Material
3.3 Methods
3.3.1 Statistical Model
3.3.2 Estimation Algorithm
3.3.3 Segmentation of new individuals
3.4 Experiments and Results
3.5 Conclusion and Discussion
4 Bayesian Estimation of Probabilistic Atlas for Anatomically-Informed Functional MRI Group Analyses
4.1 Introduction
4.2 Methods
4.2.1 Statistical Model
4.2.2 Estimation Algorithm
4.3 Experiments and Results
4.3.1 Simulated data
4.3.2 In-vivo data
4.4 Conclusion
5 Including Shared Peptides for Estimating Protein Abundances: A Significant Improvement for Quantitative Proteomics
5.1 Introduction
5.2 Method
5.3 Material
5.4 Results
5.5 Conclusion
6 Conclusion and Discussion
6.1 Summary
6.2 Large deformations for deformable template estimation
6.3 Multicomponent generalization of the models
6.4 Other remarks
6.4.1 Extension of the multi-modal atlas
6.4.2 Kernel choice
6.4.3 Algorithm implementation optimization
6.4.4 Bias field correction
A Definition of the most used similarity measures
Bibliography