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 :
- 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.
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.