1-4 Coordinate Transformation

Coordinate transformation is to transform a coordinate system (x, y) to another coordinate system (u, v). The transformation is needed in the following cases;

- to transform different map projections of many GIS data sources to an unified map projection in a GIS database,
- to adjust errors which occur at map digitization due to shrinkage or distortion of the map measured, and
- to produce geo-coded image by so called geometric correction of remote sensing imagery with geometric errors and   distortions.

Coordinate transformation is executed by a selected transformation model (or mathematical equation), with a set of reference points (or control points), that are selected as tic masks at the corner points, reseau or ground control points as shown in Figure 1.13.

The following transformations are commonly used in GIS as well as photogrammetry and remote sensing

Figure 1.14 shows major transformations.

Helmert Transformation (scale, rotation and shift) Quadratic Transformation (parabolic distortion)
Affine Transformation (skew, scale of x and y,and shift) Perspective Projection (rectification of aerial photo)
Pseudo Affine Transformation(bi-linear distortion) Cubic Transformation(cubic and distortion)