Chapter 2
Projective Geometry

“Let no one ignorant of geometry enter.”


Plato, Greek philosopher.

This chapter starts with an introduction to projective geometry which is of significant importance for the acquisition of 3D images. Using the projective geometry framework, we describe the pinhole camera model that establishes the geometric relationship between a point in the 3D world and its corresponding position in the 2D image. In particular, internal and external camera parameters that indicate the position and settings of the camera are introduced. To estimate these parameters, i.e., calibrate the camera, a practical camera calibration method is then reviewed. We proceed by reviewing the extension of the geometric framework from the single-view to the two-view camera case and finally provide a summary of the parameters and notations employed throughout in this thesis.

 2.1 Projective geometry
 2.2 Pinhole camera model
  2.2.1 Intrinsic camera parameters
  2.2.2 Extrinsic parameters
  2.2.3 Coordinate system conversion
 2.3 Camera calibration
  2.3.1 Camera parameters estimation
 2.4 Two-view geometry
  2.4.1 Epipolar geometry
  2.4.2 Image rectification
 2.5 Summary and conclusions