Page 205 - Digital Analysis of Remotely Sensed Imagery

170 Cha pte r F i v e

• Second, the order of transformation is raised if there is a
sufficient number of GCPs available. Caution must be
exercised in adopting a higher order in that this order of
transformation must have a physical meaning. Furthermore,
the increase in the transformation order has its limits.
Beyond the second order the accuracy of transformation
improves only marginally despite an exponential increase
in the amount of work involved. Besides, higher-order
polynomials produce unreliable results for satellite images
with simple geometric conditions (e.g., near-vertical or
relatively flat areas), while a low-order polynomial is
able to produce submeter rectifications (Rosenholm and
Akerman, 1998).

Thus, the second option is not as effective as the first one. In either
case, the transformation coefficients have to be recalculated with the
revised georeferencing setting, and the RMSE updated before they
are used to create the output image.
Shown in Table 5.3 is an example of image rectification results
using 17 GCPs. The first column represents GCP sequential numbers.
GCP image coordinates expressed in row and column are provided
in the second and third columns, respectively. They can be entered
into the computer by clicking on the points in the image directly.
Their coordinates in the ground coordinate system to be projected
are listed in the next two columns. They have to be entered into the
computer manually. The nature (type) of GCP is identified in the
next column. It can have two possibilities, control or check. In this
particular case, all GCPs were used as control points. Calculated
using Eqs. (5.18) and (5.19), respectively, the residuals in easting and
northing for each GCP are provided in columns seven and eight,
expressed in the image unit (e.g., pixel size). The last column shows
the RMSE at each point, calculated using Eq. (5.20) with n being 1.
Those with the largest residual or largest contribution represent the
worst GCPs. For instance, the unusually large residual at GCP 15 in
easting (4.699) is indicative of the presence of a mistake that could
have stemmed from incorrect entry of the coordinates into the com-
puter or erroneous identification of the GCP on the image or on the
ground. This GCP may be discarded by turning it into a check point.
Of particular note is the connectivity among all residuals. After the
largest residual associated with GCP 15 is removed from the calcu-
lation, residuals at other GCPs will become smaller accordingly. Y
residuals will become larger for some GCPs because its Y residual
(0.157) is smaller than the mean. Also presented in the table are the
overall residuals in both easting (RMSE = 1.4957) and northing
X
(RMSE = 0.4936), with the overall RMSE being 1.575. This out-
Y XY
come, larger than the expected 1, can be reduced to within one pixel
after GCP 15 is turned into a check point.