Fernerkundung I (Digitale Bildverarbeitung) - Friedrich-Schiller ...

Determining the Accuracy of the Polynomial Fit GCP Works 9 be determined by selecting
Model Coefficients from the Reports menu on the GCP Selection and Editing panel.
Determining the Accuracy of the Polynomial Fit:
In order to determine the accuracy of the derived coefficients of the GCPs, examine the
results of the least squares regression of the initial GCPs:
• The GCP scatter plot report, which can be activated by selecting GCP Scatter Plot from
the Reports menu on the GCP Selection and Editing panel, shows the X and Y residual
errors for each GCP point on a crosshair graph.
• The RMS error for each GCP is reported in the lists of Accepted and Check GCPs on the
GCP Selection and Editing panel. A total RMS error is also reported on this panel.
The RMS error is calculated in pixel units by these equations:
RMS error = ( ( x1 - xorg ) 2 + ( y1 - yorg ) 2 ) 1/2
x1 = computed row coordinate in the uncorrected image.
y1 = computed column coordinate in the uncorrected image.
xorg = original row coordinate of the GCP in the image.
yorg = original column coordinate of the GCP in the image.
By computing the RMS errors for all of the GCPs, it is possible to see which GCPs exhibit
the greatest error and to sum the RMS errors. If a given set of control points produce a
total RMS error that exceeds your acceptable limit, you should consider deleting the
GCPs that have the greatest errors. An error of less than the dimension of one pixel is
suggested as an acceptable limit.
The Image Fit Report is also available to help you assess the fit of the regression model.
This report can be activated by selecting Image Fit from the Reports menu on the GCP
Selection and Editing panel. It shows a graphical representation of the outline of the
georeferenced image area, uncorrected image area, mosaic cut line, and GCP points. The
uncorrected image outline is transformed according to the current GCP model. This
preview of how the uncorrected image would map onto the georeferenced data set with
the current set of GCPs allows the registration to be visually assessed before it is
performed.
Thin Plate Spline:
Thin Plate Splines (TPSs) provide an attractive alternative to the traditional polynomials.
Thin Plate Splines are also global (i.e., all GCPs are used simultaneously to derive the
transformation), but the derived functions have minimum curvature between control
points and become almost linear at great distances from the GCPs. The influence of an
individual GCP is localized and diminishes rapidly the further away from the points. The
TPS functions interpolate the values at all ground control points, within the numerical
round-off error limits, and therefore a GCP can always be added in an area where the
transformation is not satisfactory. The main disadvantage of TPSs is that, to represent a
warping transformation accurately, they should be constrained at all extreme points of
the warping function. This is not a problem in smoothly varying transformations, such as
the change of coordinate systems (if the exact transformation functions are
not known). However, when using TPSs to georegister a photograph in rough terrain, it
may be necessary to acquire hundreds of GCPs, since there should be a point at every
extreme of terrain (peak or valley bottom), and along breaklines. The derivation of TPS
transformation parameters involves solving an equation system with a square (N+3) by
(N+3) matrix, where N is the number of GCPs. For a very large N it is a time consuming
task. Moreover, the evaluation of TPS functions at every image pixel requires calculation
of N values of natural logarithms, and for large N this calculation may be prohibitively