Contents

• Contents
• Foreword and Motivation
  • Intuitive Considerations About Perspective Projection
    • An Infinitely Strange Perspective
    • Homogeneous Coordinates
  • The Perspective Camera
    • Perspective Projection
    • Real Cameras
• Basic Properties of Projective Space
  • Projective Space
    • Canonical Injection of $I\!\!R^{n}$ into ${I\!\!P}^{n}$
    • Projective Mappings
    • Projective Bases
    • Hyperplanes and Duality
  • Linear Algebra and Homogeneous Coordinates
    • Lines in the Plane and Incidence
    • The Fixed Points of a Collineation
• Projective Invariants & the Cross Ratio
  • Some Standard Cross Ratios
    • Cross-Ratios on the Projective Line
    • Cross Ratios of Pencils of Lines
    • Cross Ratios of Planes
  • Harmonic Ratios and Involutions
    • Definition
    • The Complete Quadrangle
    • Involutions
  • Recognition with Invariants
    • Generalities
    • Five Coplanar Points
• A Hierarchy of Geometries
  • From Projective to Affine Space
    • The Need for Affine Space
    • Defining an Affine Restriction
  • From Affine to Euclidean Space
  • Summary
• Projective Stereo vision
  • Epipolar Geometry
    • Basic Considerations
    • The Fundamental Matrix
    • Estimating the Fundamental Matrix
  • 3D Reconstruction from Multiple Images
    • Projective Reconstruction
    • Affine Reconstruction
    • Euclidean Reconstruction
  • Self Calibration
    • The Absolute Conic and the Camera Parameters
    • Derivation of Kruppa's Equations
    • Explicit Computation
• Bibliography