3D Coordinate Systems


  • Euclidean transformations
  • 3D coordinates
  • 3D rotations and translations
  • Homogeneous coordinates
  • Planar algebraic equations, the Hessian normal form, and signed distance.
  • Measuring the distance between a 3D point and a plane. 


Different representations for rotation :

  • quaternion
  • axis-angle
  • Euler angles 

Given 2 views of a 3D object, we compute the intrinsic parameters for each camera and their extrinsic parameters which relate their location to the world coordinate system.

  • The projection matrix
  • Factoring the projection matrix into a 2-matrix product where matrix 1 includes the camera intrinsic parameters and matrix 2 includes the camera extrinsic parameters.


Multi-Camera Calibration

We seek to know the intrinsic and extrinsic parameters of 2 cameras relative to a world coordinate system. We can estimate these parameters by having the camera pair take images of a known 3D object in the world coordinate system. Solving for these parameters is the process of camera calibration.

Linear techniques for camera calibration : 

  • Camera calibration via the projection equations (explicit camera calibration).
  • Camera calibration using the  6-point algorithm.