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Table of Contents
Preface by the Series Editor; Foreword; Acknowledgments; Abstract; Contents; Chapter 1 Introduction; 1.1 Motivation; 1.1.1 Segmentation of Medical Image Data; 1.1.2 Automation of the Segmentation Task; 1.1.3 Segmentation Accuracy; 1.2 Scope of this Thesis; 1.2.1 Automated Segmentation with Deformable Models; 1.2.2 Selection of Anatomical Structures and Imaging Modalities; 1.2.3 Contribution; 1.2.4 Topics Not Discussed; 1.3 Structure of this Thesis; Part I The Segmentation Framework; Chapter 2 Basic Terms and Notation; 2.1 Images, Segmentations, and Surface Meshes.
2.1.1 Three-dimensional Medical Images2.1.2 Segmentations of Three-dimensional Medical Images; 2.1.3 Triangle Surface Meshes; 2.1.4 From Segmentations to Surface Meshes and Back; 2.2 Deformable Surface Meshes; 2.2.1 Displacement Fields and Sets of Candidate Displacements; 2.2.2 Appearance Cost; Chapter 3 Deformable Meshes for Automatic Segmentation; 3.1 Statistical Shape Models (SSMs) for Segmentation; 3.1.1 Generation of SSMs; 3.1.2 Prerequisites: Shape Correspondences and Alignment; 3.1.3 Image Segmentation via SSM Deformation; 3.1.4 Initial Shape Detection.
3.1.5 Lack of Image Features: SSMs for Extrapolation3.2 A Simple Heuristic Appearance Model; 3.2.1 Appearance Cost Function; 3.2.2 Intensity Parameter Estimation; 3.3 Local Search for Appearance Match; 3.3.1 Unidirectional Displacements; 3.3.2 Optimal Displacement Fields; 3.3.3 Intensity Profiles; 3.4 Shape-constrained Free Mesh Deformations; 3.4.1 Free Deformation within a Narrow Band; 3.4.2 Free Deformation with Bounded Displacement Differences; 3.5 Simultaneous Free Deformations of Multiple Meshes; 3.5.1 Multi-object Graph-based Deformation of Coupled Meshes.
3.5.2 Coupling Adjacent Surface Meshes3.6 Conclusion; Chapter 4 Omnidirectional Displacements for Deformable Surfaces (ODDS); 4.1 The Visibility Problem; 4.2 ODDS: Free Mesh Deformations with All-around Visibility; 4.2.1 Omnidirectional Displacements; 4.2.2 The Mesh Deformation Problem; 4.2.3 Optimal Mesh Deformation via MRF Energy Minimization; 4.2.4 Refined Regularization; 4.2.5 Proof of Concept Synthetic Experiments; 4.3 FastODDS; 4.3.1 Where to use Omnidirectional Displacements; 4.3.2 The Hybrid Mesh Deformation Problem; 4.3.3 Optimal Hybrid Mesh Deformation; 4.3.4 Multi-object FastODDS.
4.3.5 Appendix: Automatic Ridge Detection4.4 Conclusion; Chapter 5 From Surface Mesh Deformations to Volume Deformations; 5.1 Mesh-based Extrapolation; 5.1.1 Introduction; 5.1.2 Affine Transformations; 5.1.3 Polyaffine Transformations; 5.1.4 Mean Value Coordinates; 5.2 Atlas-based Segmentation; 5.2.1 Image-to-image Registration; 5.2.2 Application of Volume Deformations to Atlases; 5.3 Conclusion; Part IIApplications to Medical Image Data; Chapter 6 Fundamentals of Quantitative Evaluation; 6.1 Measures of Segmentation Accuracy; 6.2 Presentation of Results; 6.3 Comparison of Methods.
2.1.1 Three-dimensional Medical Images2.1.2 Segmentations of Three-dimensional Medical Images; 2.1.3 Triangle Surface Meshes; 2.1.4 From Segmentations to Surface Meshes and Back; 2.2 Deformable Surface Meshes; 2.2.1 Displacement Fields and Sets of Candidate Displacements; 2.2.2 Appearance Cost; Chapter 3 Deformable Meshes for Automatic Segmentation; 3.1 Statistical Shape Models (SSMs) for Segmentation; 3.1.1 Generation of SSMs; 3.1.2 Prerequisites: Shape Correspondences and Alignment; 3.1.3 Image Segmentation via SSM Deformation; 3.1.4 Initial Shape Detection.
3.1.5 Lack of Image Features: SSMs for Extrapolation3.2 A Simple Heuristic Appearance Model; 3.2.1 Appearance Cost Function; 3.2.2 Intensity Parameter Estimation; 3.3 Local Search for Appearance Match; 3.3.1 Unidirectional Displacements; 3.3.2 Optimal Displacement Fields; 3.3.3 Intensity Profiles; 3.4 Shape-constrained Free Mesh Deformations; 3.4.1 Free Deformation within a Narrow Band; 3.4.2 Free Deformation with Bounded Displacement Differences; 3.5 Simultaneous Free Deformations of Multiple Meshes; 3.5.1 Multi-object Graph-based Deformation of Coupled Meshes.
3.5.2 Coupling Adjacent Surface Meshes3.6 Conclusion; Chapter 4 Omnidirectional Displacements for Deformable Surfaces (ODDS); 4.1 The Visibility Problem; 4.2 ODDS: Free Mesh Deformations with All-around Visibility; 4.2.1 Omnidirectional Displacements; 4.2.2 The Mesh Deformation Problem; 4.2.3 Optimal Mesh Deformation via MRF Energy Minimization; 4.2.4 Refined Regularization; 4.2.5 Proof of Concept Synthetic Experiments; 4.3 FastODDS; 4.3.1 Where to use Omnidirectional Displacements; 4.3.2 The Hybrid Mesh Deformation Problem; 4.3.3 Optimal Hybrid Mesh Deformation; 4.3.4 Multi-object FastODDS.
4.3.5 Appendix: Automatic Ridge Detection4.4 Conclusion; Chapter 5 From Surface Mesh Deformations to Volume Deformations; 5.1 Mesh-based Extrapolation; 5.1.1 Introduction; 5.1.2 Affine Transformations; 5.1.3 Polyaffine Transformations; 5.1.4 Mean Value Coordinates; 5.2 Atlas-based Segmentation; 5.2.1 Image-to-image Registration; 5.2.2 Application of Volume Deformations to Atlases; 5.3 Conclusion; Part IIApplications to Medical Image Data; Chapter 6 Fundamentals of Quantitative Evaluation; 6.1 Measures of Segmentation Accuracy; 6.2 Presentation of Results; 6.3 Comparison of Methods.