Statistical Computing on Non-Linear Spaces for Computational Anatomy ぱらぱらめくる『Handbook of Biomedical Imaging Methodologies and Clinical Research』

• Computational Anatomy: Aims and Methods
• Mathematical bases of computing on manifolds
  • The basic structure: the Riemannian metric
  • Exponential chart
  • Practical implementation
  • Example of Metrics on Covariance matrices
• Statistical Computing on Manifolds
  • First statistical moment: the mean
  • Covariance matrix and Principal Geodesic Analysis
  • Interpolation and filtering as weighted means
  • Harminig diffusion and anisotropic regularization
  • Diffusion-based interpolation and extrapolation
• Modeling the Anatomy
  • A statistical shape model of the scoliotic spine
  • Learning Brain Variabiliy from Sulcal Lines
• Challenges