Non rigid Surface Registration Using Spherical Thin Plate Splines 1st Edition by Guangyu Zou, Jing Hua, Otto Muzik ISBN 9783540757573

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ISBN 10: 
ISBN 13: 9783540757573
Author: Guangyu Zou, Jing Hua, Otto Muzik

Accurate registration of cortical structures plays a fundamental role in statistical analysis of brain images across population. This paper presents a novel framework for the non-rigid intersubject brain surface registration, using conformal structure and spherical thin-plate splines. By resorting to the conformal structure, complete characteristics regarding the intrinsic cortical geometry can be retained as a mean curvature function and a conformal factor function defined on a canonical, spherical domain. In this transformed space, spherical thin-plate splines are firstly used to explicitly match a few prominent homologous landmarks, and in the meanwhile, interpolate a global deformation field. A post-optimization procedure is then employed to further refine the alignment of minor cortical features based on the geometric parameters preserved on the domain. Our experiments demonstrate that the proposed framework is highly competitive with others for brain surface registration and population-based statistical analysis. We have applied our method in the identification of cortical abnormalities in PET imaging of patients with neurological disorders and accurate results are obtained.

Non-rigid Surface Registration Using Spherical Thin-Plate Splines 1st Table of contents:

• Introduction
  1.1 Motivation and Background
  1.2 Importance of Non-Rigid Surface Registration
  1.3 Challenges in Surface Registration: Deformation, Variability, and Accuracy
  1.4 Overview of Spherical Thin-Plate Splines (STPS)
  1.5 Key Contributions and Objectives of the Paper
  1.6 Structure of the Paper

• Preliminaries
  2.1 Surface Registration: Definitions and Methods
  2.2 Non-Rigid Transformations in Surface Matching
  2.3 The Concept of Thin-Plate Splines in Image and Surface Registration
  2.4 Mathematical Formulation of Thin-Plate Splines (TPS)
  2.5 Spherical Coordinate Systems and Their Role in STPS

• Spherical Thin-Plate Splines (STPS)
  3.1 The Theory Behind Spherical Thin-Plate Splines
  3.2 Mathematical Formulation of STPS for Surface Deformations
  3.3 Properties of Spherical Thin-Plate Splines
  3.4 STPS for Handling Non-Rigid Deformations in Spherical Domains
  3.5 Comparison with Other Non-Rigid Registration Techniques

• Methodology
  4.1 Data Acquisition and Surface Representation
  4.2 Preprocessing of Surfaces for Registration
  4.3 Formulating Non-Rigid Surface Registration Using STPS
  4.4 Algorithm for Computing STPS-Based Surface Registration
  4.5 Optimization and Regularization in Non-Rigid Surface Matching

• Experimental Results
  5.1 Dataset Description and Experimental Setup
  5.2 Quantitative Evaluation Metrics for Surface Registration (e.g., Mean Square Error, Hausdorff Distance)
  5.3 Visual Comparison of STPS with Other Registration Methods
  5.4 Case Studies: Applications in Medical Imaging, Face Recognition, and 3D Object Matching
  5.5 Robustness of STPS to Noise and Surface Variability

• Applications
  6.1 Applications in Medical Imaging (e.g., Brain Surface Matching, Organ Registration)
  6.2 Use in 3D Object Recognition and Computer Vision
  6.3 Applications in Shape Analysis and Statistical Shape Modeling
  6.4 Role in Animation and Computer Graphics for Shape Deformation
  6.5 Integration with Other Image and Surface Processing Techniques

• Discussion
  7.1 Insights from STPS in Non-Rigid Surface Registration
  7.2 Strengths and Limitations of the STPS Approach
  7.3 Computational Complexity and Efficiency Considerations
  7.4 Challenges in Scaling STPS to Large Datasets or Complex Geometries
  7.5 Future Directions for Improvement and Generalization

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