Contents

• Contents
• Introduction
  • Basic concepts
  • A typical application
  • Implementation issues
  • Aims of this thesis
• A review of distance transformations
  • Definitions.
  • Approximate distance transformations.
    • Chamfering.
    • Vector propagation.
  • Exact Euclidean distance transformations.
    • Parallel processing.
    • Sequential processing by propagation.
    • Sequential processing by raster scanning.
    • Independent scanning
    • Voronoi transformation
  • Extended concepts
    • Geodesic distances
    • k-distance transformations
    • Distance transformations on gray-scale images
  • Applications
  • Discussion.
• Euclidean distance transformation by propagation
  • Propagation with a single neighborhood
  • Errors in approximate EDT
    • Errors with a $3 \times 3$ neighborhood
    • Influence of the neighborhood size
    • Influence of the propagation process
  • Propagation with multiple neighborhoods
    • The PMN algorithm
    • Oriented neighborhoods
  • Computational Complexity
  • Using the Euclidean DT to implement mathematical morphology
    • Mathematical morphology operators
    • Fast implementations
    • Morphological dilation using PMN
    • Discussion
• Application: morphometry of nerve cross-sections
  • Introduction
    • Anatomy of the nervous system
    • Nerve morphometry
    • Image acquisition
  • Segmentation procedure
    • Pixel classification
    • Connected operators filtering
    • Myelin sheath thickness evaluation
    • False positive detection
    • Correction of obliquity
  • Experimental results
    • Detection ratios
    • Comparison with the manual procedure
    • Comparison with an arbitrary sampling
  • Discussion
• Signed Euclidean DT with error detection and correction.
  • Signed EDT and Voronoi diagrams
  • Error correction
  • CSED Algorithm
  • Computational Complexity
• Euclidean DT in 3 dimensions
  • Extending the approximate EDT to 3D
  • Possible error detection and correction methods in 3D
  • Limitations to the 3D error detection and correction methods
  • Hybrid algorithm, combining 4SSED+ and Saito's methods
• Application: registration of MR images
  • Introduction
    • Applications
    • State of the Art
    • Discussion
  • Localization of transcranial magnetic stimulation
    • Registration method
    • Results
  • Registration of MR images with a Computerized Brain Atlas
    • Registration method
    • Results
• Geodesic Distance Transformation
  • Geodesic metrics
  • Geodesic DT algorithms
    • Bucket sorting algorithm
    • Circular propagation algorithm
  • Accuracy
  • Computational complexity.
• Application: Camera path-planning in virtual endoscopy
  • Virtual Endoscopy
  • Computing the shortest path from the B_d-geodesic DT
  • Path centering
  • Experimental results
• k-NN classification and k-distance transformation
  • Introduction
  • The k-DT algorithm.
  • Computational complexity.
• Application: tissue classification in T1, T2 MR images.
  • The physics of T1- and T2-weighted MRI
  • T1,T2 classification
  • Results
• List of Figures
• Bibliography