9.4 Geometric Correction

9.4 Geometric Correction

Geometric correction is undertaken to avoid geometric distortions from a distorted image, and is achieved by establishing the relationship between the image coordinate system and the geographic coordinate system using calibration data of the sensor, measured data of position and attitude, ground control points, atmospheric condition etc.

The steps to follow for geometric correction are as follows (see Figure 9.4.1)

(1) Selection of method
After consideration of the characteristics of the geometric distortion as well as the available reference data, a proper method should be selected.

(2) Determination of parameters
Unknown parameters which define the mathematical equation between the image coordinate system and the geographic coordinate system should be determined with calibration data and/or ground control points.

(3) Accuracy check
Accuracy of the geometric correction should be checked and verified. If the accuracy does not meet the criteria, the method or the data used should be checked and corrected in order to avoid the errors.

(4) Interpolation and resampling
Geo-coded image should be produced by the technique of resampling and interpolation. There are three methods of geometric correction as mentioned below.

a. Systematic correction
When the geometric reference data or the geometry of sensor are given or measured, the geometric distortion can be theoretically or systematically avoided. For example, the geometry of a lens camera is given by the collinearity equation with calibrated focal length, parameters of lens distortions, coordinates of fiducial marks etc. The tangent correction for an optical mechanical scanner is a type of system correction. Generally systematic correction is sufficient to remove all errors.
b. Non-systematic correction
Polynomials to transform from a geographic coordinate system to an image coordinate system, or vice versa, will be determined with given coordinates of ground control points using the least square method. The accuracy depends on the order of the polynomials, and the number and distribution of ground control points(see Figure 9.4.2).
c. Combined method
Firstly the systematic correction is applied, then the residual errors will be reduced using lower order polynomials. Usually the goal of geometric correction is to obtain an error within plus or minus one pixel of its true position(see Figure 9.4.3).