Tuesday, July 26, 2016

Map transformations


Map transformation involves transformation of points from one map to points on another map while minimizing the differences between the two sets of points.

  • The 'Helmert transformation' is the best choice for the vast majority of applications.
  • The 'Helmert transformation' translates the points of one map horizontally and vertically and also rotates and scales the points (it uses 4 parameters).
  • The 'affine transformation' is useful in cases where the paper has pronounced directional shrinking due to orientation of the fibers.
  • The 'affine transformation' is also useful to compensate for some shearing in the map or for computing the shearing angle.
  • The 'affine transformation' with five parameters translates points in the x direction and y direction, a rotation and two scale factors (one in the x direction and one in the y direction)
  • The 'affine transformation' with six parameters consists of:
    • translation in x direction
    • translation in y direction
    • two rotation and two scale factors (both axes are rotated and scaled separately)
Other map transformations used are:

  1. Robust Helmert
  2. Huber estimator
  3. Vestimator and
  4. Hampel estimator