Contents

• Title page
  • Contents
  • Introduction
    • Volume visualization
    • Volume reconstruction
    • Thesis outline
  • State of the Art
    • The early years: 1D signal processing
    • The eighties: an image processing view
    • Eventually going to 3D
      • How to reconstruct a 3D function from a set of samples
      • 3D derivative reconstruction
    • Miscellaneous reconstruction methods
  • Sampling
    • Important functions in signal processing
      • The ramp and step signals
      • The impulse signal
      • The impulse train
    • The Fourier transform
    • Fourier transforms of base functions
    • Convolution
    • The convolution theorem
    • The process of sampling
    • Summary and conclusions
  • Reconstruction
    • The sampling theorem
    • Ideal reconstruction
    • Reconstruction in practice
      • Nearest neighbor interpolation
      • Linear interpolation
      • Symmetric cubic filters
      • Windowed sinc function
      • Interpolation using zero insertion
    • Evaluation of filters in spatial domain
    • Summary and conclusions
  • Derivative reconstruction
    • Gradient reconstruction
      • Central and intermediate differences
      • Cubic spline derivatives
      • Windowed cosc function
      • An empirical experiment (actually two)
    • Curvature reconstruction
      • Ideal reconstruction and windows
      • Cubic spline derivatives of order two
    • Summary and conclusions
  • Discrete filters
    • Implementation scheme
    • Discrete Filters in Frequency Domain
    • Discrete Filters in Spatial Domain
    • Results
    • Summary and conclusions
  • Implementation
  • Summary
    • Introduction
    • Previous work
    • Sampling
    • Reconstruction
      • Reconstruction in practice
      • Interpolation using zero insertion
      • Evaluation of filters in spatial domain
    • Derivative reconstruction
    • Discrete filters
    • Conclusions
  • Conclusions in general
  • Future work
  • Glossary
  • Windows and frequency responses
  • First derivative reconstruction results
  • Bibliography